The idea of law 
1. Individuality in physics (1968)
2. Criteria for a law sphere (1988)
3. The cosmochronological idea in natural science (1994)
4. The idea of natural law (1999)
5. Components of a critical realistic scientific worldview, with special attention to the status of natural law (2002)
6. Laws, subjects and objects (1980, 2019)



The idea of law is one of the most important themes in Dooyeweerdian philosophy, which indeed was initially called the ‘philosophy of the law idea’ (wijsbegeerte der wetsidee). The present collection of papers covers half a century of my career as a philosopher.  ‘Individuality in physics’ (1968) was my second publication, ‘The law as boundary between time and eternity’ (2020) is much more recent. 'Laws, subjects and objects' discussing the distinction of subjects and objects as related to laws, including the important concept of 'objectivity', is copied from Time and again (1980, revised 2019). 

The idea of law implies that the temporal creation is lawful, subjected to natural laws and normative principles, but this does not mean that everything would be determined by laws. The first paper argues that even in physics lawfulness has individual variety as its counterpart.   

Vollenhoven’s and Dooyeweerd’s philosophy is well known because of the grouping of laws into ‘lawspheres’, ‘modal aspects’, or ‘relation frames’ as I prefer to call these. The second paper formulates some criteria for a lawsphere. It was written as a critical reflection on some preceding papers by several adherents of this philosophy.

The third paper is my contribution to a conference at Zeist in 1994. I used the expression ‘cosmochronologica idea’ only on this occasion, in order to stress that reality is both lawful and temporal.

‘The idea of natural law’ and ‘Components of a critical realistic scientific worldview’ both dicuss the idea of natural law in the context of any scientific world view.



The idea of law    



1. Individuality in physics (1968)


‘Individualiteit in de fysica’ [1]


Philosophical discussions about quantum physics usually pay much attention to the deterministic character of classical physics in contrast to the indeterminism of modern physics. In general one does not consider whether individuality can be attributed to a physically qualified thing. The answer to this question is, however, very important for the problem of (in)determinism.

In fact, in a theory that aspires to describe its object entirely in a determinist way there is no place for individuality. Conversely, if one ascribes individuality to the investigated ‘things’ or ‘events’, one does not need to be surprised about the occurrence of laws of probability, like those of quantum physics.

Indeed, the philosophy of the cosmonomic idea poses that the type law (the ‘structure of individuality’) for physically qualified things and events makes possible and limits their individuality. We shall find in how far this vision sheds light on the problem of (in)determinism.

By its formal simplicity and its success in explaining in particular the motion of celestial bodies, classical mechanics, founded by Galileo and Newton, served as the prototype of natural science until the start of our century. For our subject matter it is important that mechanics is a functional theory, i.e., treating a modality: it almost exclusively deals with motion as a mode of being of physically qualified things. This means that at the subject side of concrete things one abstracted from all properties that does not concern the kinematic aspect. Every concrete thing is abstracted into a modal kinetic subject. Because it is nevertheless physically qualified, it has to achieve mass: the simplest object of mechanics is the ‘mass point’.

In a deterministic interpretation this aspect, this abstraction, is absolutized: one loses sight of everything else, constituting concrete reality together with the kinetic mode. This applies in particular to individuality, which did not disappear entirely, but led a rudimentary existence as ‘motion subjectivity’: when at a certain moment mass, position, velocity, and external circumstances (conceived as forces, eventually as a field of force) are given, than motion is fixed, both to the past and to the future.

A correction to the rigorous, functionalistic determinism was soon given by classical chemistry, founded by Dalton and Berzelius at the start of the nineteenth century. This became distinguished from mechanics because it ascribed specific properties to its objects: each chemical element consists of mutually equal atoms, and each chemical compound of molecules, all built op from atoms in the same way; but for different elements and compounds, the atoms respectively molecules are different, distinguishable because of specific properties.

In this way, until the end of the nineteenth century a division of tasks was maintained between physics and chemistry: the first investigated general, modal properties, the second specific ones, the individuality structure of physically qualified ‘things’. Only in our century this division came to an end, because it became untenable:  one cannot be considered apart from the other.

Already in the past age physics came into trouble with its deterministic program – at first concerning gas theory. Initially there was only thermodynamics, having nothing to do with motion, hence designed independent of ‘official’ physics by engineers on behalf of machine technology. It only became ‘real physics’ when one attacked the problem to explain the thermodynamic laws from the motion of the many, very many molecules (conceived of as mass points) present in an amount of gas of, e.g., one litre. From the start it turned out impossible to do that directly. Indeed, even determinism knows its law side and subject side: not only the modal-kinetic law determines the course of any process, but also the ‘initial state’ (the position and velocity of each mass point at one moment). For a gas the description of this initial state is an impossible task.

A way out appeared to be not to consider one, but a large number (an ‘ensemble’ of) equivalent systems (in this case, amounts of gas) with any possible initial state. For this ensemble it is possible to formulate statistical laws similar to those of thermodynamics. At first sight the problem seems to be solved; for, in a theoretical way one has found rules that can be verified empirically. A problem remains, however: the laws of statistical mechanics are valid for an average (the ‘ensemble average’) of a large number of similar systems with different initial states, the (formally equal) laws of thermodynamics are supposed to concern a temporal average for a single system.

On mathematical grounds, one presumed initially that these two averages would be the same: in the course of time, each system would pass through all possible states. It was soon established that this ‘ergoden hypothesis’ was not correct, and had to be replaced by the ‘quasi-ergoden hypothesis’: in the course of time each system approaches every possible state arbitrarily close. This supposition, first formulated in 1907 by P. and T. Ehrenfest, is up till now neither proved nor disproved. 

For the development of statistical mechanics it was always assumed that the motion of molecules is completely determined. Only in 1919 Exner observed that this assumption is superfluous: starting from indeterminism the same result would be achieved.

Ever when it is impossible to exhaustively investigate, describe, determine, or predict the behaviour of any subject – whether it concerns an amount of gas or a housewife – science can take recourse to probability statements. By considering a large number of subjects together in a sensible way – depending on the nature of the problem – the individual differences can be ‘averaged out’; what rests in the average gives an impression (in fact: a quantitative approximation) of the specific law, the individuality structure of the investigated subjects. In this way one may speak of the buying habits of the Dutch housewife, or of the behaviour of a lithe hydrogen gas.

The second phenomenon with which the deterministic view of nature collided was radioactivity. After extensive research one had to recognize that no external force influences the radioactive decay process: independent of temperature, pressure, etc. after a certain period of time (the ‘half-life’) half of the initially present radioactive atoms ‘decay’. The half-life is different for each radioactive element.

Here the concept of ‘accident’ entered physics. For the law of decay could be derived by assuming that it is completely accidental which atoms decay, as long as the number of atoms that decays is proportional to the number initially present.

It makes no sense to speak of the half-life of an individual atom, unless one conceives this as a probability, such that the chance that the atom decays in this period is 50%. If the atom does not decay within this period, the probability that it will do so in the next equal time span is again 50%. One could now say that the atom determines ‘in freedom’ when it will disintegrate, although this freedom is limited by the individuality structure of the atom.

Meanwhile this does not prove that radioactive atoms should be attributed individuality; it is still possible that the process is determined by ‘hidden parameters’, for the time being not manifest to us in an observable way. We meet the same situation as in the case of the gas theory: the assumption of an allowed individuality is not contrary to the empirically established state of affairs, but is also not proved by it.

At the end of the previous century one could still believe in determinism. Radioactivity was considered one of a few unsolved problems, and the deterministic basis of the gas theory was only doubted later on.

This changed by the development of quantum physics, starting in 1900 with the discovery of Planck’s constant, and reaching its tentative endpoint about 1925.

Sharper than before, in quantum physics a physically qualified subject – like an atom – was distinguished from the ‘state’ in which the ‘system’ finds itself. In a sense, the state has a latent character, because it manifests itself only when the system exerts or experiences an action – for instance when it is subjected to a physical measurement process.

The measurement instrument forces so to say the system to choose between a limited number of possible states (besides by the measurement instrument these are determined by the system’s individuality structure). Here the individual behaviour of the atoms becomes manifest. For, given the measurement instrument, and given the initial state of the system, the outcome of the measurement is still not fixed. One can do probability statements, and verify these experimentally by measuring a large number of similar systems in the same initial state, and quantum physics calculates this average result with a large accuracy; but at the measurement nothing can be predicted with certainty about the individual behaviour of one atom. Also now there is still some ‘latitude’ for the atom, within the possibilities allowed by the internal structural law of the system, and the external circumstances (the measuring instrument).

Yet this discovery has not led to a general recognition that atoms etc. are individual ‘things’. In principle three interpretations can be pointed out, although their distinction is neither sharp nor exhaustive.

A small number of physicists (among them Einstein, Schrödinger, Bohm, and the school of De Broglie) sticks to determinism, supposing the existence of ‘hidden parameters’, unknown for the time being. In his mathematical analysis of quantum physics, Von Neumann has shown that ‘hidden parameters’ cannot affect the indeterministic structure of quantum physics. Physicists who keep to determinism have to assume that the quantum physical formalism describes the phenomena correctly, yet is wrong or incomplete. In principle this assumption is difficult to refute, but the said physicists have (not yet) succeeded in designing an ‘improved’ theory.

The large majority of physicists emphasize the measurement procedure. In fact we know nothing about a closed system: only what comes to the fore as a measurement result can be verified, and during a measurement the system is not closed. But the measurement result is not only determined by the nature and state of the measured system, but just as well by the action which it suffers from the measuring system: one speaks of the measurement disturbance. As such this phenomenon is not unfamiliar; classical physics too knew it, but it was assumed that it could be arbitrarily small, at least in principle. In quantum physics this is impossible: the existence of Planck’s constant, featuring in all ‘indeterminacy relations’, makes that the measurement disturbance cannot be made arbitrarily small as a matter of principle.

According to this ‘Copenhagen interpretation’ it is very well possible that a closed system is completely determined, but this would be a meaningless statement, because experimentally not verifiable.

The question arises, however, what is here cause or effect, as Niels Bohr observes:

‘The question was whether, as to the occurrence of individual effects, we should adopt a terminology proposed by Dirac, that we were concerned with a choice on the part of “nature” or, as suggested by Heisenberg, we should say that we have to do with a choice on the part of “the observer” constructing the measuring instruments and reading their recording. Any such terminology would however, appear dubious since, on the one hand, it is hardly reasonable to endow nature with volition in the ordinary sense, while on the other hand, it is certainly not possible for the observer to influence the events which may appear under the conditions he has arranged. To my mind, there is no other alternative than to admit that, in this field of experience, we are dealing with individual phenomena, and that our possibilities of handling the measuring instruments allow us only to make a choice between the different complementary types of phenomena we want to study.’[2]

According to a third interpretation the state function does not concern a single system, but a large number, an ensemble of similar systems. From the result of a large number of measurements on the ensemble it can be reconstructed what the state function before the measurement was, and this procedure has no meaning for a single system. Now the state function is an expression of our knowledge which we have about the ensemble.

At first sight this course of thought has much in common with what we said about the gas theory. However, in that case the ensemble concerned systems being in all possible initial states. In quantum physics one should restrict the ensemble to a number of systems, in initial conditions, described by the same state function. It would be possible to maintain to a certain extent, that this function does not describe the state completely; for instance, if the state function corresponds to a sharply determined momentum, the system’s position is completely undetermined. In so far there is some agreement with the ensemble from statistical mechanics. But one can hardly propose that this state function (the sharply determined momentum) would not be attributable to any member of the ensemble, and thereby the starting assumption of this interpretation fails.[3]

These three interpretations have two things in common. First they refer, willing or not, all to the deterministic interpretation of classical mechanics. In the first case the determining factors are initially assumed to be unknown, in the second case it is principally stated that they are not measurable, in the third case it is stated that quantum physics does not say anything about determining factors for individual systems, but the ‘ensemble’ is conceived to be completely determined. In fact there is no principal break with determinism; Heisenberg, for instance, states that only the premise (‘if at a certain moment position and velocity of all mass points is known’) is invalid, meaning that determinism is not judged to be wrong, but useless.

Because one clearly did not leave determinism definitely, one necessarily fell back into a fundamental dualism, indicated as ‘complementarity’, considered characteristic for quantum physics. It means that it is not possible to consider elementary physical entities entirely as ‘particle’ or entirely as ‘wave’.[4] The two descriptions are both required (as a consequence of the so-called principle of correspondence) to make a connection between the non-graphic, mathematical formalism of quantum physics, and classical mechanics, which is considered ‘graphic’ [aanschouwelijk]. (We leave alone that here classical mechanics is identified with daily experience.) The two ways of description are both restricted in their applicability by the so-called indeterminacy relations of Heisenberg. Because one remains stuck to a functionalist description of reality one is unable to reconcile two at first sight contrary views, and one is forced to accept a dualistic interpretation. As we saw already, within this interpretation the question cannot be solved whether it would be possible to attribute a certain kind of individuality to separate electrons, atoms, etc., so to say, because this question arrives at the end, after the dualism is already accepted.

If one wants to get out of this impasse, one has in his interpretation first to pose this individuality – which in no way can be proved, but is given in natural experience.[5] The several mutually irreducible modalities of temporal reality are grouped together in each structure of individuality in a typical way, such that this structure makes their individuality possible and limits it. Now it is clear from the start, that an atom is neither merely a set of particles, nor merely a system of waves, because in both cases one could not talk of individuality.

Secondly, the mathematical formulation of physics is not properly judged. It is generally agreed that this has a statistical character. The above mentioned first interpretation recognizes that the formalism accurately describes the phenomena, but refuses to accept the conclusion that the natural phenomena themselves have a statistical character, that they allow of a certain ‘margin of play’. The second interpretation overlooks that the measurement disturbance does not influence the calculation of the probable measurement result. And the third interpretation ignores the fact, that the mathematical formalism ascribes to each system apart a state function.

The undervaluation of the mathematical formalism is not so strange, because it is usually considered a useful frame in which the empirically found natural law conformities can be summarized; for, is not mathematics a free creation of the human mind?

The philosophy of the cosmonomic idea recognizes the latter, as far as mathematics is a theoretical disclosure of some modalities of temporal reality. But these modalities have reality: they are real aspects of concrete, individual things, events, etc., making possible both their existence and understanding. The mathematical formalism of quantum physics is more than a businesslike representation of our knowledge of the anorganic nature; it is a theory about its mathematical aspects.

The state function, being a theoretical-mathematical approximation of the subject, teaches us that the state is not completely determined, leaving space for the individuality of the ‘thing’ and the processes in which it plays a part.

In discussions about the indeterministic character of modern physics sooner or later the word ‘accident’ appears. Of course, in a deterministic theory accidents have no place. When applying laws of chance in classical physics, one soon arrives at difficulties.

The starting point is always the ‘a priori equal chance’ for the occurrence of different cases: when a priori with a die the chance of throwing a two equals that of throwing a six, the calculation of chances is not difficult. However, it has proved to be a big problem how to arrive at a priori equal chances in a deterministic theory. A way out was the assumption that de circumstances (at throwing a die) are such complicated and variable, that they cannot be known in sufficient detail to predict the result of the throw. In this way the laws of chance (and in particular their starting point, the a priori equal chance) were supposed to be an expression of our knowledge, or rather our lack of knowledge. It has, however, many times been proved that on this basis the concept of ‘probability’ cannot be defined, i.e., any attempted definition turned out to be based on a circular reasoning.

In contrast, if one recognizes an individuality limited by law, there is no objection against the principle of a priori equal chance. Now the ‘a priori’ refers to the typical law, the system’s structure of individuality, and does not rest on our insight into this law. We now arrive at the significance of symmetry relations for physics. In the case of the die it is clear that it is symmetrical: it belongs to its structure that it has equal sides, otherwise it is not a good die. And this structure determines the individual possibilities of the outcome of the game: there are six, which are the same thanks to the structure.

In the deterministic classical physics symmetry considerations do not play a decisive part. In contrast, quantum physics pays much more attention to it. It turns out to be possible to solve quite a few problems in close approximation by merely paying attention to symmetries, and of many systems no more than their symmetry is known.

In fact, in this way by leaving determinism (contre coeur), physics is enriched with a powerful tool for its investigation.

Up till now we have not yet paid attention to the question of the identity of elementary material parts. This is a question apt to give rise to misunderstandings, because in physics terms have been common which are at the least unfortunately chosen. It is said, e.g., that all electrons are ‘identical’, meaning that they are all equal. Next, that they are ‘indistinguishable’ and that is certainly wrong without further elaboration.

It concerns here systems in which several equal particles appear simultaneously – for instance, an atom consisting of a nucleus and a number of electrons. Physics attributes one state function to the atom, which can be closely approximated as the product of a number of state functions (one for each electron), determined by the atom’s character, and each describing the state of one electron.

For us it is relevant that the electrons satisfy the so-called Pauli exclusion principle, saying that no two electrons can occupy the same state; for instance, in a measurement one will always find the electrons in different states. Hence, each electron manifests itself different from any other electron, and not only during a measurement: the whole atomic theory is based on the assumption that each possible electron state can only be ‘occupied’ by a single electron.[6]

Now one observes that the electrons, apart from their state, are not distinguishable, and therefore one calls them indistinguishable. The use of this term betrays a bond to the nineteenth-century concept of a moving mass point, which orbit could in principle be followed from point to point, such that it was continuously distinguishable from other mass points. It is remarkable that this ‘absolute identity’ could only be achieved by stripping the mass point from every individuality: for the supposed possibility to identify the mass point at any time rests on the complete determinateness of its motion.

In this sense modern physics cannot establish the identity of an electron. It manifests itself always as an individual ‘thing’, when it is ‘asked after its identity’ [by establishing the state it exclusively occupies]. But when one shortly later repeats the measurement, in general one cannot establish whether the electron that manifests itself in a certain state is the same as the one that turned out to occupy that state at the former measurement. In such a measurement electrons are distinguished by some functional magnitudes: position, velocity, energy, etc. If it would be possible to determine their identity completely in this way, it would be functionalised and determined as was the case in classical physics, and one could not speak of ‘individuality’.

In fact, quantum physics does not state that the two electrons in e.g. a helium atom cannot be distinguished, but that the states which do not differ otherwise than that the two electrons are exchanged are identical. Not the two electrons, but the said states are identical (and therefore, in fact, one state). To conclude from this that the electrons are indistinguishable is only possible] from a certain point of view on the relation of a whole and its parts, namely when one considers the whole as nothing but the sum of its parts. According to the philosophy of the cosmonomic idea’s theory of ‘enkaptic structural interlacement’ nothing from what we discussed can be concluded about the individuality of the two electrons; as a condition of the said identity of the two states only counts that the two electrons are of an equal kind, i.e., have the same structure of individuality.

Finally we observe that Pauli’s principle is not valid for all so-called ‘elementary particles’ – e.g., not for light quanta. However, there are more reasons – not to be discussed at present – to deny these ‘particles’ a ‘thing’-structure. Next, quantum physics describes some processes, in which an electron changes its state, such that an electron is ‘annihilated’ in one state, and ‘created’ in a different one. With respect to this formulation we can only observe that in the framework of the philosophy of the cosmonomic idea ‘things’ endowed with individuality does not need to be ‘eternal and unchangeable’. If we distinguish at the one hand ‘systems’, being in a more or less stationary state, from ‘events’ at the other hand, happening ‘on’ these systems, then the Pauli exclusion principle is only applicable to the former.

From this survey it should not be concluded that quantum physics proves that physically qualified ‘things’ have individuality, but that it leaves room for it. Science cannot solve this philosophical question definitively. A scientific theory – seeking of course contact with empirical, concrete reality – can display a deterministic, all individuality excluding structure, as well leaving open the possibility of individuality. The first was done by classical physics, the second modern physics does.

As such it is correct that science takes distance from individuality: by its nature, science is abstracting, and the first abstraction is from individuality. Although a solid-state physicist, for example, performs his measurements on a single crystal of white tin, he is not really interested in this one crystal, but either in modal-physical laws, to which the crystal is subjected, or to its structure of individuality. In the analysis of his measurement results he always abstracts from the subjective individuality of his measurement object. In other words, it is inherent to scientific activity to forgo each individuality. Quantum physics does so no less than classical physics.  However, it has become clear that the natural phenomena cannot be described restless conform laws. The necessary application of probability laws points out that the law side is correlated to an individual-factual side of reality.

Each separate science being concerned with one or more aspects of reality and the individuality structures qualified thereby must in its exposing activity necessarily abstract from individuality. It is philosophy’s task to supply a synthesis between the modalities, accounting for the individuality of concrete created things, as it presents itself to daily experience.

Therefore it is not wise to hypostasize science such that all individuality is denied. Knowing that the theoretical is merely an aspect of human activity and of all actual existence, science ought to leave room for that from which it abstracts as a matter of course.

No doubt, this is one of the most important themes of the philosophy of the cosmonomic idea.



[1] This paper is a translation of Stafleu, M.D. 1968, ‘Individualiteit in de fysica’, in: D.M. Bakker e.a. 1968, Reflexies, opstellen aangeboden aan Prof. Dr. J.P.A. Mek­kes, ter gelegen­heid van zijn zeventigste verjaardag, Amsterdam: Buijten en Schipperheijn, 287-305. .

[2] Bohr, N. 1949, ‘Discussion with Einstein on epis­temologi­cal problems in atomic physics’, in: Schilpp (ed.), Albert Einstein, Philosopher-Scientist, New York: Harper, 201-241, p. 223.

[3] Also the quantum physical gas theory works with an ensemble, which is completely analogous to that of classical statistical mechanics, but that clearly differs from the ensemble, about which said interpretation speaks.

[4] In fact, the contrarity is not sharply indicated with the terms ‘particle’ and ‘wave’. It concerns the two retrocipating moments in the kinetic modality (motion quantity and motion extension), whereas one had better speak of the pre-physical aspects of physically qualified subjects, discrete quantity, spatial extension and extensive motion opened up toward the physical aspect, see Stafleu, M.D. 1966, ‘Quantumfysica en wijsbegeerte der wetsidee’, Philosophia Reformata 31: 126-156..

[5] Because atoms, electrons etc. do not appear in daily experience, their individuality is not given there, but must be extrapolated from daily experience. As soon as one has concluded (on the basis of any kind of phenomena) to the existence of separate atoms, one may consider these as ‘things’ which simply are smaller than the smallest things observable with a microscope. Meanwhile, with the help of a ‘field ion microscope’ it has recently become possible to make a photo of a metal crystal in which the separate atoms in their regular order are visible. In other words: the fact that the atoms do not belong to our daily experience does not mean that they have a theoretical origin, but is only an effect of their small extension.

[6] Strictly speaking, the Pauli principle does not concern a measurement. The principle follows from the possibility to describe the state of a system of electrons with the help of a so-called Slater determinant. This possibility rests on the logical-analytical distinguishability of the separate electron states, not on the psychic observability.




The idea of law



 2. Criteria for a law sphere (1988)


(with special emphasis on the ‘psychic’ modal aspect)


Philosophia Reformata 53 (1988) 171-186



Ever since Herman Dooyeweerd during a walk in the dunes of Holland conceived of the idea of mutually irreducible ‘law spheres’, people have objected to his designation of these ‘modal aspects’. Recently, J.D.Denge­rink proposed to consider ‘time’ as a modal aspect preceding all others,[1] and W.J.Ouweneel put forward arguments to replace the so-called psychic modal aspect by a ‘perceptive’ and a ‘sensi­tive’ one.[2]

In this paper I intend to investigate these claims from a methodolo­gical point of view, summing up various methods for distinguishing a modal aspect. This means I shall only engage in a discussion of Dengerink's view of time and Ouweneel's psycholo­gy as far as these are relevant to the investigation of the philosophi­cal criteria for the distinction of the various modal aspects. By way of example my investigation will be focussed on the psychic modal aspect, the law sphere that according to Dooyeweerd appears between the biotic and the logical aspects.

My approach will be heuristic and practical. Because the modal aspects are found by abstraction I shall start with a discussion of struc­tures qualified by the supposed aspect, and proceed with a discussion of the psychic aspect itself. This means that the order of the various criteria to be discussed is not necessarily the most satisfactory from a systematic point of view.

I shall not explicitly discuss the so-called ‘meaning-nucleus’ of the modal aspect concerned. Dooyeweerd calls it ‘feeling’, but Ouweneel's extensive discussion shows how confusing such an epithet can be. My own perceptive feeling is that nobody has ever succeeded in finding an adequate name for any modal aspect. Hence I prefer a conventional but rather empty label like ‘physical’, ‘biotic’, or ‘logical’, without further questioning its possible meaning.

I realize that what I am about to write is not generally accepted. Therefore I have adopted a more personal style than is usual in a philosop­hical article. I want to add that I shall discuss only a small part of Dengerink's and Ouweneel's works, and this paper should not be considered a book review.


1. A modal aspect determining a ‘kingdom’


In Dooyeweerd's theory of structural types, the structures having a common qualifying modal aspect form a ‘kingdom’ of structures. He recogni­zes three natural kingdoms or ‘radical types’, ‘... viz. 1) that of the inorganic kinds of matter, things and events, all of which have a typical qualification in the energy-aspect; 2) that of plants and their bio-milieu, which kingdom has a typical biotic qualification; 3) that of animals, inclusive of their typical symbiotic relationships, their form-products and animal milieu, a kingdom which is typically qualified in the psychical aspect.’[3]

This distinction is based on tradition as well as on common sense or natural experience.[4] Both can be and have been challenged. One modern taxonomy of organic structures distin­guishes five kingdoms: Monera (proka­ryotes); Protoctista (mostly unicellular plants and animals); Fungi; Animalia; and Plantae.[5] I shall not be concerned with biotically qualified structures,[6] and only observe that merely one kingdom of animals is mentioned in this taxonomy. However, it may be worthwhile to discuss the distinction of animals and ‘plants’ (in the wider sense of all biotically qualified subjects).

A biologist questioned about the difference between plants and animals may answer that plants are autotrophic, animals heterotrophic. Plants derive their food and energy directly from their physical environ­ment, whereas animals depend at least partly on plants for their food.[7] This distinction is not universally applicable. There are (parasitic) plants that depend on other plants or their debris, and some higher plants depend on bacteria for the assimilation of nitrogen. Apart from that it seems an unsatisfactory criterion, for it does not regard the qualifying functions  of  plants  and  animals, respectively.

The criterion seems to be inspired by a philosophy that reduces everything biological to physical and chemical processes. In that view metabolism is unduly stressed.[8]

It is also precarious to rely too heavily on our natural experience of plants and animals. Lever observes that in our habitat the differences between plants and animals are obvious enough, such that nobody can avoid to see them. But, he con­tinues, in a maritime environment the difference is not that large, and he suggests that if human beings were living in the sea, they would perhaps never have made a fundamental distinction between plants and animals.[9] Lever says there is only one kingdom of organisms, albeit with two specialization trends: on the one hand the vegetative trend in the direction of food in a general sense, on the other hand the anima­listic trend towards manipulation in the environment, hence to behaviour.

From a Dooyeweerdian point of view it must be granted that animals have a vegetative substructure, which is enkaptically interlaced with and disclosed by the leading animal structure. It can also be granted that in some plants anticipations can be found towards the behavioural structure of animals. One may think of flowering and fruit bearing plants, which have an obvious symbiosis with insects distributing pollen, or with birds and mammals eating fruits and scattering the indigestible seeds. (In the evolutionary order, ‘plantae’ come after ‘animalia’). Therefore, Lever's arguments do not necessarily lead to the conclusion that separate kingdoms of plants and animals do not exist, even if it is not always easy to determine for a certain species to which kingdom it belongs.

The methodologically sound way of distinguishing two kingdoms is to investigate their respective qualifying functions. Let us first have a look at the biotic aspect. The genetic relation between organic systems is the most typical feature for all living beings, both with respect to their individuality and their structure.[10] As an explanatory model for the functioning of plants and animals we might think of a computer with a built-in program. For plants this program is fixed in the DNA of the cell nucleus (and partly in other cell bodies). It is rigid and unchangeable, it is a so-called ‘closed’ program. Only by sexual reproduction (and eventual­ly mutations etc.) the program changes, but then a new individual comes into existence.

In animals the program is partly fixed in a similar genetic code, partly in the nervous system. The first is just as closed as is the case in a plant. The program located in the nervous system, however, appears to be partly open and adjustable. An animal is able to learn, and by learning it changes its program, such that it can react upon its environment in a new way. This learning ability is small for primitive animals, but it increases with increasing differentiation.

The acquired experience of an animal is probably not hereditary, at least not directly. Sometimes an animal can communicate its experience to others, and an animal can establish a lead in natural selection because of its experience. In this indirect way acquired experience can influence the evolution of the species.

For the lower (more primitive) animals, learning is based on trial and error. An animal has a certain freedom of choice. At first decisions will be made at random, but the animal remembers its choices, and evaluates their results. This influences its choice on a later occasion, whose circumstances are not neces­sarily the same as on the preceding occasion but must have some similarities. If the result of the new choice receives the same response, the change of program will be reinforced. Besides trial and error, one finds other kinds of association in animals, such as habituati­on, classical and operant conditioning, Gestalt perception, environment recognition, and AH-Erlebnis. [11]

For higher animals learning occurs far less through trial and error. They have an ‘expectation pattern’, allowing them to calculate the conse­quences of a certain choice. Several methods of learning can be observed: exploration, initiation, games, imprinting (the first impression of an animal after its birth, in particular the identification of its parents), etc.

Learning ability itself is inborn, is genetically deter­mined, and therefore differs structurally for different species, and individually for different individuals. It even changes during the life time of a single animal. Usually a young has more learning capability than an older one. The content of what an animal learns belongs to its individual experience. It gives an animal  qualitatively  more   individuality  than  a  plant  has.

The identity of an animal is not exclusively determined by its genetic identity, but is further determined by its individual experience, by what it has learned. By changing its experience an animal changes, it develops its identity.

If a plant reproduces in a non-sexual way, the daughter plant is genetically identical to the parent plant. If two animals have the same genetic identity, they will still develop a different psychic identity (a different ‘character’) because of their different experience.

It will be clear that the criterion based on an investiga­tion of ‘kingdoms’ cannot be applied to all modal aspects. In particular it cannot be applied to the first modal aspect, whether one considers this to be the numerical one, or, with Dengerink, the temporal one. The first law sphere does not qualify a kingdom or radical type. [12]

Hence we should not absolutize this criterion. Ouweneel says he only accepts those modal aspects that determine a kingdom. [13] In his Psycholo­gie he ignores the modal aspects preceding the physical one,[14] and he attributes human beings a ‘spiritive aspect’. Those law spheres which according to Dooyeweerd come after the psychic one Ouweneel calls ‘sub-aspects’ of the spiritive aspect, characteristic of mankind.[15]

Even apart from the question, that we shall presently discuss, of how many kingdoms there are, I don't consider it recommendable to reduce the idea of mutually irreducible modal aspects to their qualifying function of a kingdom.

Ouweneel states there are two psychic aspects, which he calls the ‘perceptive’ and the ‘sensitive’, respectively. Hence, he distinguishes two kingdoms of animals, the ‘higher’, i.e., the mammals, and the ‘lower’.[16] The lower animals have a perceptive structure as a leading structural principle. This includes reflexes, instincts, and tendencies or needs. Mammals have a sensitive structure, including affections, impulses (by sensitive unrest accompanied desires, lusts, inclinations, impulses, and passions) and emotions (positive and negative, and often violent).

I shall raise several objections to Ouweneel's proposal, but in the present section I restrict myself to its consequence - the recognition of two separate kingdoms of animals. For a ‘hard fact’, Ouweneel points to the so-called limbic system in the mammalian brain. It controls their feelings, affections, impulses, and emotions. He also points to the distinction of a sympathetic and a parasympathetic system in the nervous system.

However, both are also present in birds (at least the so-called hypothalamus, an organ that plays a significant part in this).[17] Hence we should at least ask whether birds belong to the kingdom of higher animals or to that of the lower animals ? Do not birds show emotional behaviour no less than mammals ? Ouweneel says very little about birds.[18]

Also octopuses have a lobe in their brain with functions comparable to that of the limbic system in mammals.[19] It is no accident to mention mammals, birds and octopuses in one context. All three form end stations in an evolutionary line, and have a highly developed and complex nervous system. One cannot maintain that mammals are ‘higher’ than birds or octopuses, as far as taxonomic or evolutionary arguments are concerned. It is for instance striking that the animals in all three categories have senses (in particular eyes) which are completely comparable as to complexi­ty and appropriateness.

If Ouweneel wants to restrict the ‘higher’ animals to the mammals, his argument with respect to the limbic system etc. fails. It would be difficult to maintain that birds lack emotions and affections, which mammals like elephants and mice would share. So let us assume that Ouweneel includes birds, and perhaps also octopuses, among the kingdom characterized by the ‘sensitive’ aspect. It is, however, clear that birds, mammals and octopuses have so little in common with each other that this kingdom would immediately fall apart into three sub-kingdoms. The birds and the mammals have more in common with the reptiles than with each other. I think that most biologists would consider it a dubious proposal to have reptiles in a kingdom separate from that of mammals and birds, which in turn includes the octopuses. Still, it is a possibility to be considered, for the distinction of psychic types should be based on psychic argu­ments, not on morphological or physiological ones.

However this may be, from a methodological point of view it is unsatisfactory that Ouweneel does not include birds and octopuses in his discussion, if not in his sensitive kingdom.


2. A modal aspect founding a structural type


In Dooyeweerd's theory of structural types, a modal aspect cannot only serve to qualify a certain type, it is also able to found one (except, of course, for the final modal aspect). Besides the primary distinction of ‘radical types’ or ‘kingdoms’, we meet here a secondary distinction of types having the same qualifying function but different foundation functi­ons. In principle, in each kingdom one can expect as many secondary types as there are law spheres preceding the modal aspect qualifying that kingdom. Hence, in the kingdom of physical things and events, one may expect three secondary types, founded in the numerical, spatial and kinematic aspects, respectively.[20] And in the kingdom of living beings (except animals) four secondary types may be expected.[21]

One reason why I am not happy with Dengerink's proposal to consider a ‘temporal’ modal aspect preceding the numerical one is that it would upset my analysis of structural types. This is a very personal remark, and as such of little value. But I regret that Dengerink does not pay much attention to the consequences of his proposal for Dooyeweerd's theory of types. If one takes the existence of structural types founded in a modal aspect as a criterion for the existence of that aspect, then - at least for the time being - it does not provide us with an argument to consider ‘time’ to be an irreducible law sphere.

But again, one should not absolutize any criterion for the distincti­on of modal aspects, and perhaps the ‘temporal’ forms an exception. One should not observe that all individual things and events are ‘temporal’, and are as such founded in the temporal aspect, for this is not a structu­ral feature. It only points to the universality of being temporal, and the univer­sality of time is not disputed.

With respect to the animal kingdom, I think it needs a very thorough investigation to arrive at even a tentative designation of the five secondary structural types to be expected. Before entering into this problem (in section 4) I want to observe that the distinctions made by Ouweneel between mammals and the ‘lower’ animals appear to be secondary rather than primary, meaning that mammals (and perhaps birds and octopuses) belong to a different secondary type than other animals. For instance, Ouweneel does not say that mammals have a limbic system exclusively. Rather, they have a ‘developed’ limbic system, contrary to reptiles, for instance, whose limbic system is ‘rudimentary’.[22]

Hence, by rejecting Ouweneel's proposal to distinguish more than one kingdom of animals, I am not stating that his arguments concern­ing the differences between mammals and other animals are irrelevant to an investi­gation of structural types. It is regrettable, however, that Ouweneel only takes into account the primary distinction of radical types, and omits from his discussion the secondary distinction as defined above.


3. Interlude: Subjects and objects


According to the standard representation of the Philosophy of the Cosmonomic Idea, animals cannot function subjectively in the modal aspects following the psychic one.[23] This is in line with the traditional view that man is different from animals in particular because of his rationali­ty. Therefore, it distracts from another view proposed by this philosophy, namely that a human person is first of all a religious being.

I should like to endorse Dengerink's suggestion that animals can be subject in the aspects following the psychic one, albeit, of course, different from human beings.[24] It can hardly be denied that animals have limited capabilities of logical distinction. Some animals produce structu­red things like nests or holes. These should be distinguished from organic products like wood or manure, which are by-products, however important. Initially these are enkaptically interlaced in the structure of a plant or an animal, and only achieve a relatively independent existence after having broken this connection.

In this respect, wood and manure differ strikingly from an individual object like a bird's nest. It has an evident struc­ture, which is biotically and psychically determined. It is produced with a clear purpose. Its structure is recognizable as belonging to a certain species - the nest of a blackbird differs from the nest of a heron. But the nest itself does not live, and shows no behaviour, it is not a subject in the biotic and psychic aspects, but an object. It is a subject in the physical aspect, but that does not determine its typical structure. It is an individual structured object with respect to the animals which make it or use it. We find this figure not only with birds and mammals, but also with insects (bees, ants), with spiders and with fish.

This formative activity has invariantly an instinctive character. The animals concerned can only act in one way, which is usually genetically determined, it is species-specific. Often it is coercive.

In a similar way it can be observed that some animals have a primiti­ve supply of lingual signs. The bees' dance is an example. Birds are able to warn each other against danger. In groups of apes a recognizable lingual communication system has been established. Many animals show social behaviour: bees, ants, birds during migration, mammals living in herds, etc. Sometimes a division of labour and leadership is unmistakably present. Also economic, aesthetic, and even primitive ethic behaviour is recogniza­ble.

In all these examples it is striking that the behaviour concerned is retrocipatory. All post-psychic functions of an animal serve its biotic and psychic needs, in particular the acquisi­tion of food, reproduction, and survival of the species. Therefore, animals remain qualified by the psychic aspect. (As a consequence, the modal aspect qualifying a kingdom is not necessarily the highest subject-function of the individuals belonging to that kingdom).

In this respect mankind differs from the animal kingdom. Man is subject in all modal aspects, and, during his evolution, has been able to develop all of them into the anticipatory direction, guided by his faith, and by his calling as a responsible person.

The behaviour of a person is not merely directed to food, reproduc­tion, and survival. It is no longer genetically restric­ted, but culturally determi­ned. The laws, to which animals are subjected by necessi­ty, receive a normative character for mankind. Normativity is correlated to responsibili­ty. I would not apply normati­vity to the post-psychic law spheres, but to human responsibili­ty, i.e., the manner by which human beings respond to laws. For humanity, laws have a normative character. This could just as well pertain to pre-logical laws.

Now returning to the psychic modal aspect, I think it is sound philosophy to state that (apart from human beings) only animals can be subject in this aspect. I was struck by Ouweneel's treatment of instincts, emotions, etc. as being ‘subject’ in the ‘percep­tive’ and ‘sensitive’ aspects. [25] I consider this a mistake of categories. There is no doubt that these states or drives are psychically qualified. Nevertheless they have an objective function in this (or, for Ouweneel: these) modal as­pect(s). Feelings do not feel, percep­tions do not perceive. It is like the magnitude of a spatial subject, the volume of a cube for instance. ‘Volume’ is an objective spatial magnitude, but unlike a cube it is not a subject in the spatial aspect. [26]

The objective ‘states’ of psychic subjects have an objec­tive, psychically qualified structure. In the preceding section I said that we should expect five secondary structural types in the animal kingdom. This refers to differently struc­tured psychic subjects. In a similar way, it may be expected that five differently founded objective structures can be distinguished. It is deplorable that Ouweneel did not use this lead for his analysis of reflexes, instincts and tendencies, which he calls ‘percepti­ve’; and affections, impulses and emotions, which he calls ‘sensitive’. It is regrettable, because he overlooks one of the most promising possiblities in Dooyeweerd's theory of structures.


4. A law sphere as an aspect of explanation


In the preceding sections we were mainly concerned with the modal aspects as aspects of being. Now we shall consider them as aspects of explanation, in particular regarding animal behaviour and its organic basis, the nervous system.

The study of typical structures qualified by the psychic modal aspect is extremely difficult, because these structures are always interlaced with sub-structures which are qualified by the biotic, physical, and probably the kinematic and the spatial aspects. These sub-structures are opened up by the leading psychic structure. The investigation of this intricate ‘enkapsis’ provides another means to distinguish the various modal aspects -although it will usually be the other way around: the distinction of the modal aspects allows us to investigate the structure of reality. Anyhow, for the psychic aspect, this means a study of the nervous system (as well as the study of the endocrine glands, which I shall ignore, for convenien­ce).

The Philosophy of the Cosmonomic Idea sometimes considers ‘sensorial experience’ to be characteristic for the modal aspect qualifying the animal kingdom. Now the senses are merely highly specialized external organs of the nervous system and only appear in higher developed animals. The existence of a nervous system would be more characteristic.

The nervous system as such has first of all an organic charac­ter, its structure and functioning are genetically determined. The nervous system has a biotically qualified structure, albeit opened up by the psychic aspect. It is comparable to DNA-molecules, enzymes, the spatial structure of a cell, etc., which are physically qualified, but opened up by the biotic aspect. The nervous system is the organic basis for the psychic functioning of an animal, its behaviour. When discussing the structure of a plant, we can use the term ‘organism’ to summarize its physical sub-structure as opened up by the biotic function of the plant. Similarly, we can use the term ‘body’ to summarize the biotic (and physical, kinematic and spatial) sub-structure of an animal, opened up by its psychic structu­re, which shows itself in the animal's behaviour. Compared with the organism of a plant, the body of an animal is morphologically and physiolo­gically more differentiated, specialized, and integrated.

Moving from primitive to higher developed animals, we do not only see an increasing complexity, integration and differentia­tion, but also an increasing ‘internalization’. This begins with the appearing of a stomach in very primitive multicellular animals, making necessary the formation of a mouth and eventually an anus or a vent.[27] The vertebrates have an internal skeleton, internal organs like blood vessels, kidneys, liver, lungs, etc. As far as a plant has differentiated organs (leaves, flowers, roots, the bark), these are typically peripheral, directed outwards. In animals these organs are gradually more directed inwards. This development is compensated by the formation of new organs directed outwards: propelling organs like feet or fins, clutching organs like a mouth or hands, food-intake organs like mouth and nose, and in particular sense organs.

The taxonomy of the animal kingdom is largely based on similarities and differences with respect to morphology and physiology, and is therefore not basically different from the taxonomy of plants. But there are examples of species which can only be distinguished because of their difference in behaviour. In the formation of a new species a change in behaviour (in particular with respect to breeding) precedes a change of morphology or physiology.[28] This means that behaviour plays a leading part in the formation of a new species. Because of the multiformity of species-specific behaviour there are far more species of animals than species of plants.

The function of the nervous system in an animal body is not first of all to observe, to perceive. Perception is rather means than aim of the animal's psychic functioning. The nervous system has a cybernetic function, it controls the animal body, and is in need of observation, registration and processing of external and internal data.

Also in plants one meets regulating processes. The DNA-based cell nucleus controls the biochemical processes in the cell. Hormones stimulate or check the growth. The manner by which a plant reacts to the change of day and night or the seasons is determined by internal factors, even if influenced by external physical circumstances like temperature, sunshine, and humidity. Really regulating organs (like nerve cells) are lacking in plants, however. They occur only in the animal kingdom as the organic basis of a new ordering principle, psychic control.

By the presence of a nervous system the animal body disposes of an organization of mutually tuned co-operating organs and processes. After the conception, in an animal embryo first the nervous system is developed. In turn, this controls the develop­ment of the other organs. The highly specialized and differen­tiated functioning of the animal organs is only possible because of the integrating function of the nervous system.

Accepting, for the sake of argument, Ouweneel's distinction of two psychic aspects, I would still hesitate to consider ‘perception’ to be characteristic of the first of them. In my view, perception is merely a phase in the kind of control that distinguishes animals from plants. Perception is a necessary condition for animal behaviour rather than its characteristic. An animal that would only be able to perceive would not survive -it also has to act on its perceptions. A similar remark could be made with respect to ‘sensitive’ as characteristic for Ouweneel's second psychic aspect.

The nervous system reacts on stimuli, which come partly from the animal's own body, partly from outside. It amplifies and processes the stimuli, and controls the body, e.g., the motion of the muscles. The processing of the stimuli occurs according to a certain program, which is partly closed, partly open (see section 1 above). An important difference is that for animals the program is no longer localized in the cell nucleus, as it is in plants. During and after the development of the embryo its function is taken over by the nervous system, except with respect to the typical biotic and biochemical functioning of the cells themsel­ves. As a consequence animals are able to react faster and more flexibly than plants can do.

If we consider the nervous system as most characteristic for the animal body, we can gain some insight in the secondary structural types defined in section 2 above - but I like to emphasize the tentative and perhaps premature character of the following suggestions.

The numerical unit of the nervous system is the nerve cell, which is fed by stimuli. These are amplified, communicated, and transformed into an instruction, for instance for a muscle or a gland. A unicellular animal does not ‘have’ a nervous system, but I suggest it ‘is’ a nerve cell. A nerve cell occurring in the body of a higher developed animal can be considered to be a psychic subject with its own idionomic structure, qualified by the psychic aspect. Its structure is enkaptically interlaced in the structure of the nervous system and of the animal as a whole.

The nerve cells are spatially integrated (enkaptically bound) into the nervous system, that (with some exceptions) shows a typical left-right symmetry, having consequences for the spatial structure of the animal body. In the nervous system simultaneously received stimuli are co-ordinated, and various instructions given at different positions in the body are integra­ted.

The next (and I suggest: kinematic) level of integration is the memory. It needs a certain amount of differentiation of nerve cells and groups of them, and probably the integration of nerve cells into a central nervous system: the brain. The short-term memory allows the animal to perceive and process stimuli which arrive successively rather than simulta­ne­ously, hence to perceive changes in its environ­ment.

Usually one distinguishes this short-term memory from the long-term memory, which needs even more specialized parts of the nervous system, in particular sense organs. These can dis­criminate between stimuli of diffe­rent kinds, and integrate them into a ‘picture’ (not only visual, but also tactile, auditive, olfactory, etc.). This allows the animal to form an image of its environment relative to the state of its own body, and to store it for some time, such that it can be compared with a new image formed at a later time. Succeeding images can be used (in a feed-back process) to invoke corrections during a course of action. This suggests a physically founded structure, because these images ‘interact’ with each other or with inborn programs. (This ‘interaction’ is not physical, of course, but psychic). Hence, on this level one can expect emotions, like conflicting desires. Perhaps the distinction of a separate autonomic nervous system (only in vertebrates) is relevant at this level.

As the highest, i.e., biotic level of integration the phantasy or imagination would count, meaning the generation of information, allowing higher animals to anticipate on expected situations, and to solve problems. On this level feelings like pleasure and fear can be expected, and the limbic system (see section 1) may play an important part.

Whatever these suggestions are worth, they serve to illustrate the potential power of Dooyeweerd's theory of types for an analysis of both typical subjects (like nerve cells and the animals themselves) and typical objects (like instincts and feelings of various kinds).


5. A law sphere in relation to other law spheres


From the assumption that the law spheres are both mutually irreduci­ble and universal, one derives two other methods of distinguishing modal aspects: the method of antinomy, and the method of analogy. Both are highly valued in the Philoso­phy of the Cosmonomic Idea.[29] However, as a heuris­tic tool both are weak if considered apart from other methods.

The method of antinomies states that if one fails to make a distinc­tion between two mutually irreducible aspects, one runs into antinomies. I have the impression that antinomies are only recognized ‘after the fact’, that is, after one has become convinced that two aspects are mutually irreducible. Therefore it is not surprising that Ouweneel finds antinomies after his discovery that the ‘perceptive’ and the ‘sensitive’ are different modal aspects.[30] But if one is not convinced by his arguments, one sees his ‘antinomies’ in a different light. I make two remarks.

First, referring to what I said in section 2 about the secondary distinction of types, an anomaly can also arise if one does not realize that two types (though having the same qualific­ation function) have different foundation functions.

Second, Ouweneel states that something cannot be both subject and non-subject in the same law sphere.[31] This is a common misunderstanding. In the physical aspect, for instance, unlike nucleons (protons, neutrons, etc.), electrons are not subject to the laws for strong nuclear interacti­on, whereas they are subject to the laws for weak nuclear interaction, electromag­netic interaction, and gravity. In the spatial aspect, a twodi­mensional subject like a triangle can only be an object with respect to a threedimensional subject like a pyramid. In many cases, the relation between an animal and its prey must be considered a subject-object relati­on, even if the prey is a living animal (see section 6, below). Hence, if Ouweneel (inaccurately) says that percep­tions are not subject to the laws for impulsivi­ty, affectivity and emotivity, this does not necessarily lead to the conclusion that an anomaly is at stake. It is a bit inaccura­te to say that something is a subject or object with respect to a lawsphere (as I did myself in section 3 above), and occasionally it leads to mistakes. We call something a ‘subject’ with respect to a certain law (rather than a law sphere) if it is directly subjected to this law; and we call it an ‘object’ if it is only intermediate­ly, via a certain ‘subject’ subjected to this law.

The other method, the study of retrocipations and anticipa­tions, is more fruitful, at least if one takes distance from a merely verbal appro­ach, that is very tempting in the Dutch and German langua­ges, but hardly translatable into English. Ouweneel's discussion of the anticipations and retrocipations of the ‘perceptive’ and the ‘sensitive’ aspects abounds with metaphorical terms like ‘gevoelsleven’ (sense life) and ‘levens­gevoel’ (sense or feeling of life). [32]

The Dutch are fond of these contractions, whose philosophi­cal relevance is minimal. It is true that these verbal excercises constituted a necessary stage in the early development of the Philosophy of the Cosmono­mic Idea. However, quod licet Iovi non licet bovi: after fifty years we should proceed beyond the first steps towards a fully scientific research into the structure of the modal aspects. Analogies can best be studied in the context of the criteria discussed in sections 1 and 2, and in the context of the theory of time.


6. A law sphere as an aspect of time


As observed, Dengerink recently proposed to consider ‘time’ to be the first modal aspect. His main argument seems to be that time is universal (which would be endorsed by Dooyeweerd) but is not characteristic of the whole creation in the way Dooyeweerd takes it. It is difficult to argue with Dengerink. Where Dooyeweerd states that a modal aspect is (inter alia) an aspect of time, Dengerink merely recognizes an analogy of time, and where Dooyeweerd states that every structure and individual is temporary, Dengerink agrees, pointing to the universality of each modal aspect. They also agree that time has a subject side and a law side. The difference will only become clear after Dengerink has elaborated his view into a more comprehensive theory of time. Dengerink's critique of Dooyeweerd's concep­tion of time is probably right in several respects[33] but does not compel to such a radical revision. I prefer to work in Dooyeweerd's program, which I find more promising (even if more complicated) and more challen­ging than Dengerink's proposal.

Each modal aspect, then, is an expression of time, having a law side, i.e., the order of time, and a subject side, which comes to the fore both in subject-subject relations and in subject-object relations. Time is relative, and the modal aspects together form inter alia a universal and abstract frame of reference for all kinds of relations, assuring that nothing exists in isolation. For the psychic modal aspect I suggest that the order of time is teleological; that the subject-subject relation is most adequate­ly expressed by ‘communication’, and the subject-object relation by ‘recognition’. Both communication and recognition are nothing if not purposive.

Under the influence of a mechanist world view, together with the deserved­ly bad reputation of eighteenth and nineteenth century natural theology, and reinforced by reductionalist philosophies, teleological arguments have been banned from the philosophy of nature for a long time. Nevertheless, zoologists have always been aware that the behaviour of animals cannot be understood if it is not considered to have some purpose, even if it is instinctive or coercive. Botanists do not need such argu­ments, for plants do not show purposive behaviour. (One could make an exception with respect to flowering and seed bearing plants, whose structu­re is opened up by the interaction with animals, see section 1 above. This functioning anticipates the purposive behaviour of animals). The age-old discussion whether the creation is purposive is put into a new perspective by pointing out that the psychic aspect is a universal aspect of the creation, and that teleology is the psychic aspect of ‘cosmic time’ in Dooyeweerd's sense. This means that the physical universe and the biotic cosmos are purposive as well, even if this can only be recog­nized if we study them in their relation to animal and human behaviour.[34]

If anything, teleology is an order of time. As such it presupposes the numerical order of before and after, the spatial order of simultaneity, the kinematic order of continuous succession, the physical order of irreversibility, and the biotic order of genetic descendence.

As a law, the teleological order is correlated to the psychic subject-subject relation determining the temporal relations  of  a  certain  individual  with  other   individuals.

This relation could be called ‘perceptive’, but this is usually understood to be one-sided. ‘Communication’ of information and feelings between animals, and between various parts of the body of a single animal, comes closer. In turn, communication depends on ‘recognition’, which also plays a part in the psychic subject-object relation. This pertains both to the inborn, genetically determined ‘instinctive’ functioning of an animal, and to what it has learned.

A nerve cell recognizes a stimulus, transmits it in a recognizable way, and transforms it in a recognizable stimulus for a gland or a muscle. Even the most primitive animal is able to orientate itself in its environ­ment. By co-ordinating various stimuli a pattern can be recognized, and by co-ordinating various instructions a differentiated unity of behaviour arises, which again has a certain pattern. An animal is able to recognize changes in its environment, sometimes directly, sometimes by comparing the observed pattern with what is registered in its memory. The animal is able to recognize its food, sometimes a prey, or reversely, an enemy.

In particular, animals are able to recognize individuals of the same species - as partners, as offspring, as parents, or as belonging to the same or a different herd, flock or nest. Recognition can be the basis of territorial behaviour and for the order in groups of animals: the pecking order of chickens, the hierarchy in herds of elephants or troups of apes.

Recognition consists of remembrance, observation and foresight, which refers to the numerical time order. In the recognition of a pattern simultaneously registered signals are related, and it is also a continuous process. The processing of a signal or a pattern, or a succession of images is irreversible, and there is a genetic relation between the stimulus and its response. Recognition lies at the foundation of feelings of various kinds, such as fear or pleasure.

For animals, communication outside the body is an in­dividualized form of recognition, often restricted to members of a species or a population. In many cases, relations between animals of different species are of a subject-object character, for instance, if an animal serves as food for another one. Communication occurs between the members of a group or herd, between a male and a female, between parents and their offspring. Many patterns of communication are inborn, but sometimes they are achieved by learning, in particular during the first phase of life of a young animal. Characteristic for communication is that an animal produces signals with the purpose of being recognized (and sometimes with the purpose of preven­ting recognition).

A typical example of communication is the courting behaviour of a male that recognizes the presence of a female, and acts accordingly. Also in the migration behaviour of birds and other animals, of which the details are largely unknown, communication and recognition probably plays a significant part.

These few remarks should be sufficient to show that the study of a law sphere as a mode of cosmic time is a fruitful method for the designati­on of the various modal aspects. However, time is more than modal time. The temporality of the creation also means that it is dynamic, it evolves continuously.

A study of the physical, biotic and psychic aspects of reality is wanting if it ignores the evolution of the cosmos. It is true that Dooye­weerd seems to restrict the so-called opening process to the cultural sphere of mankind. But he was certainly not afraid of evolutionary theo­ries, even if he was critical with respect to some of them, and in particu­lar with the philosophical hypostatization embodied in ‘evolutionism’.

It is hardly avoidable to arrive at a rather static view of reality if one rejects all kinds of evolution, and even if one restricts evolution to development within the limits of a certain species. The assumption that species are unchangeable is called ‘essentialism’ and is reminiscent of Platonic idealism.[35] The theory of types initiated by Dooyeweerd should be developed into a theory that would account for the evolution (or perhaps the gradual actualization) of types. We shall have to go a long way before we reach this goal. It is simply impossible to ignore both evolutionary theories and evolution itself. If the theory of the modal aspects and structural types would fail to account for evolution (astrophysical as well as biological), it would fail entirely. But this is by no means the case. In particular, this theory has a great potential in giving an account of the order of evolution, if not of its actual course. And reversely, the empirically established order of evolution may help us in the investigation of structural types.




With respect to the modal aspects discussed in this paper, my conclusion is that neither Dengerink nor Ouweneel has provided sufficient arguments for his proposal, respectively, to consider ‘time’ as a modal aspect, or to consider two separate psychic aspects, the ‘perceptive’ and the ‘sensitive’. My chief aim, however, was to discuss criteria for suchlike decisions. In particular, I did not enter into a discussion of Ouweneel's psychological arguments, which should be left to psychologists. As a philosopher I am interested in methodology, and from this viewpoint I arrive at the above mentioned conclusion.

There is no royal road to science. There is no infallible unique way to decide which modal aspects should be recognized, and therefore one cannot afford to neglect one. I have discussed various methods to investi­gate a modal aspect, and I identified three fruitful ways: the study of the ‘primary’ distinction of kingdoms or radical types; the study of the ‘secondary’ distinc­tion of types having the same qualifying aspect but different founding aspects; and the study of the temporal order and the corresponding intersubjective relations. Implicit in all three methods is the study of retrocipations and sometimes anticipati­ons of one modal aspect to another.

In my view, a far less fruitful method is a mainly verbal discus­sion of the ‘meaning nucleus’ of a modal aspect, based on a search in the literature or based on intuition or natural experience. A scientific investigation of the modal aspects and the typical structures of reality should critically transcend both tradition and natural experience. I do not say that tradition and intuition do not play a part, in particular at an early stage of investigation. Such was the case when Dooyeweerd and Vollenhoven started to work on the idea of mutually irreduci­ble law spheres. There is no deprecia­tion in the observation that the fathers of the Philosophy of the Cosmonomic Idea made mistakes. On the contrary, not only animals and human beings, but also philosophers should be ready to learn from their mistakes, in order to survive.

The modal and typical structures of reality are not immediately available, neither for human thought or intuition (a fallacy of rationa­lism) nor for human perception (a fallacy of empirism). These structures are hidden, and can only partly, tentatively and successively be laid bare by a careful, respect­ful and laborious exploration of God's creation.


[1]. J.D.Dengerink, De zin van de werkelijkheid, Amsterdam 1986, 240-245. Already in 1953, Dooyeweerd observed that ‘... some adherents of my philosophy are unable to follow me in this integral conception of cosmic time’, cf. H.Dooyeweerd, A New Critique of Theoretical Thought, Amsterdam 1953-1957, vol. I, 31.

[2]. W.J.Ouweneel (a), Psychologie, Amsterdam 1984, 24-25,  39, 43, and beyond. W.J.Ouweneel (b), De leer van de mens, Amsterdam 1986, hoofdstuk 2. (As a thesis defended at the Free University at Amsterdam it is titled Christelijke transcendentaal-antropolo­gie). Ouweneel is by no means the first to challenge the ‘psychic’ aspect, see Ouweneel op.cit. (b) 75-91.

[3]. Dooyeweerd, op.cit. III, 83.

[4]. M.D.Stafleu (a), ‘Spatial Things and Kinematic Events’, Philosophia Reformata 50 (1985) 9-20.

[5]. L.Margulis, K.V.Schwartz, Five Kingdoms, San Francisco 1982. Although these authors distinguish only one kingdom of  animals, it should be observed that they define animals as being multicel­lular. Hence the monocellular protozoa find a place in their kingdom of Protoctista.

[6]. M.D.Stafleu (b), ‘Some Problems of Time - Some Facts of Life’, Phil.Ref. 51 (1986) 67-82 discusses biotically qualified structures. The present paper is more or less a sequel to my (b).

[7]. e.g., P.G.Smelik, ‘Het sympathisch-psychische functioneren van dier en mens’, Phil.Ref. 34 (1969) 134-141.

[8]. Ouweneel op.cit. (a) 44 characterizes the biotic aspect by metabolism. I consider this a mistake. ‘Food’ with respect to living beings can only have an objective meaning, and therefore metabolism cannot serve to characterize the aspect of organic life.

[9]. J.Lever, Geïntegreerde biologie, Utrecht 1973, hoofdstuk 2.

[10]. Stafleu, op.cit. (b). In this context, 'structure' points to the law side, 'individuality' to the subject side of reality.

[11]. R.A.Wallace, Animal Behaviour, Santa Monica, Cal. 1979, 151-174. I.Eibl-Eibesfeldt, Ethology, New York 1975 (1970) 251-302. K.Lorentz, De weerzijde van de spiegel, Amsterdam 1975, hoofdstukken 4-7 (translation of: Die Rückseite des Spiegels, München 1973).

[12]. cf. Stafleu op.cit. (a): a radical type has both a qualifying and a founding aspect.

[13]. Ouweneel op.cit. (a) 43: ‘Wij geven er de voorkeur aan - ... - slechts die aspecten teaanvaarden die elk een bepaald rijk van stoffelijke (sic) entiteiten kwalificeren’ (italics by WJO).

[14]. Ouweneel op.cit. (a) mentions them, but they do not play a part in Ouwe­neel's analysis. In Ouweneel op.cit. (b) these aspects are discussed with respect to Dooyeweerd's views.

[15]. Ouweneel is not quite consistent in his terminology. In his op.cit. (a) he speaks of one ‘spiritual’ (‘geestelijk’) aspect, with the logical, historical, etc. as ‘sub-aspects’. In his op.cit. (b) he summarizes the post-psychical aspects under the name ‘spiritive aspects’ (plural).

[16]. see footnote 2.

[17]. Wallace op.cit. 85

[18]. Ouweneel op.cit. (b) 100 is the only place I could find, and it says about nothing.

[19]. Wallace op.cit. 142-143.

[20]. M.D.Stafleu (c), Time and Again, Toronto 1980, Chapter 10.

[21]. Stafleu op.cit. (b).

[22]. Ouweneel op.cit. (b) 100. Similarly, when Ouweneel discusses the distinction between human beings and mammals, he points to the ‘neo-cortex’ which is ‘developed’ in humans, and underdevelo­ped but not absent in mammals. Again, this can hardly serve to make a distinction between two ‘radical’ types, which needs more ‘radical’ differences.

[23]. Dooyeweerd op.cit.  I, 39; II, 81, 114; III, 58, 85.

[24]. Dengerink op.cit., 222-223, 249. See also Lever op.cit., 187-193; Smelik op.cit.; Ouweneel op.cit. (b) 216-217.

[25]. e.g., Ouweneel op.cit. (b) 112, 115.

[26]. I shall briefly return to the distinction of subjects and objects in section 5, below.

[27]. Margulis, Schwartz, op.cit., 161. After conception, every animal starts its development by forming a ‘blastula’, a hollow ball of cells.

[28]. Wallace op.cit. 23; G.Thines, Dierpsychologie, Arnhem 1966, 254-264.

[29]. Dooyeweerd op.cit. II, 3-54.

[30]. Ouweneel op.cit. (b) 113-118.

[31]. ibid., 115; see also Dooyeweerd op.cit. II, 370.

[32]. Ouweneel op.cit. (b) 118-126. Also Dengerink does not always escape verbalism in this respect. It should be observed, however, that these metaphors can be very helpful in a didactic context, and also that Ouweneel has several really interesting examples of analogies.

[33]. cf. Stafleu op.cit. (b); in his op.cit. (b), Chapter 5, Ouweneel discusses Dooyeweerd's theory of time, but he does not apply it in his analysis of the psychic modal aspect(s) in Chapter 2.

[34]. Even in modern physical cosmologies, the ‘teleological dimension’ is recognized, see e.g. J.D.Barrow, F.J.Tipler, The Anthropic Cosmological Principle, Oxford 1986.

[35]. E.Mayr, The Growth of Biological Thought, Cambridge, Mass. 1982, 38, 87, 304-305: ‘Without questioning the importance of Plato for the history of philosophy, I must say that for biology he was a disaster.’ (p. 87).



 The idea of law


3. The cosmochronological idea

in natural science (1994)



Fifth International symposium, Association for Calvinist Philosophy,

August 24, 1994

S. Griffioen, B.M. Balk (eds.), Christian philosophy at the close

of the twentieth century, Kampen 1995, 93-111.



In 1948, George Orwell coined the phrase ‘Big brother is watching you’ (Orwell 1949, 5), and in 1970, Ira Levin predicted in the near future everybody to wear a bracelet which on a scanner would identify the bearer’s ‘nameber’ (Levin 1970, 17). It does not require much fantasy to recognize our wrist-watch and bar-code. Ten years after 1984, we realize it is not big brother watching us, but us watching our watch. Tempus vitam regit (Landes 1983, 360): ‘Time rules life’ could have been Dooyeweerd’s motto, too.

Never to become finished, the fourth volume of his great work, De wijsbegeerte der wetsidee, was to deal with the philosophy of time (WdW I, 37; III, v). Instead Dooyeweerd published his views in a number of papers, later to be incor­porated into the first volume of A new critique of theoretical thought (Dooyeweerd 1936-39, 1940; NC I, 22-34; Popma 1965; Brüggemann-Kruyff 1981-82). In 1935 (WdW I, 505), Dooyeweerd included the study of time into his five ‘fundamen­tal, but mutually insepara­bly cohering themata (themes)’, but in 1953 he wrote:

‘The problem of time cannot be a particular theme, since it has a universal transcenden­tal character, and as such embraces every particular philosophical question. It is the transcen­dental back­ground of all our further inqui­ries.’ (NC I, 542)

Dooyeweerd’s concepti­on of ‘cosmic time’, as he called it, turned out to be both original and controver­sial. As a tribute to his centennial, this paper reviews cosmochrono­logy to be an integrating idea in a Christian philosophy of modern natural science.

Dooyeweerd’s systematic philosophy is dominated by the idea of time. Like meaning makes religious sense of our life, cosmic time makes philos­ophical sense of the cosmos. Everything that is created is also temporal and vice versa, yet being created is entirely different from being temporal. Both terms are referential.

On the one hand, being created refers to the origin of the cosmos. It says that everything has a meaning which it does not derive from itself but from its maker.

‘Meaning is the [mode of] being of all that has been created and the nature even of our selfhood. It has a religious root and a divine origin.’ (NC I, 4)

The Christian idea of creation implies that nothing has autonomy, that all exist in Christ, in whom everything in heaven and on earth has been created, in whom the cosmos finds its religious unity. Moreover, for human people being created implies to bear responsibility. Dooyeweerd calls this dimension of human existence ‘supratemporal’ (NC I, 31, 101).

On the other hand, being temporal means that anything is related to eve­rything else, in past, present and future.

‘The intent of philosophy is to give us a theoreti­cal insight into the coheren­ce of our temporal world as an inter-modal coherence of meaning ... It is a temporal coherence .­.. Man is bound to time together with all creatures that are fitted with him in the same temporal order.’ (NC I, 24)

The cosmochronological idea expresses the diversity, the coherence and the dynamics of the cosmos. It is a philos­op­hical idea, by no means to be confused with our daily experience of time, which we shall call `common time’, the time of our natural ex­perience, the time of common sense (NC I, 33-34). Cosmic time is a philosophi­cal generalization of common time.

Ours is the century of science and technology. Western society has been changing at an unprece­dented rate. The status of science and technology evolved accordingly from a position at the fringe of civilization to its most dominant factor. Simultaneously, natural science became more and more aware of the temporal and transient charac­ter of the cosmos, of the biosphere and of the society we live in.

The first thing to observe is that science has become aware of the importance of many kinds of relations. Relations form the frame­work of cos­mochrono­logy.


1. Coherence: time makes reference


The use of calendars, diaries and clocks, agendas and time-tables, in short, public time, serves to organize our mutual relations. In a more general sense, cosmochro­nol­ogy means mapping the cosmos. The first thing one needs in a map is a grid, a system of reference, by which everything can be located and identified. Nothing exists in itself, and the existence of whatever can only be established by its relations to other things or events. Reversely, the reference systems have no meaning apart from the things they do relate, even cosmic time does not exist apart from concrete reality.

Such a grid is provided by each of the modal aspects. The order expressed by the first modal aspect applies to the numerical relations between any pair of things or events. The spatial order refers to relative spatial positions, the kinematic order to relative motions, etc. (NC II, 79-106). Because each modal aspect is univer­sal, each provides us with a cosmic map. We don’t have a single map of the cosmos, but as many as there are modal aspects. And although these maps are all universal, we cannot do without any of them. Each modal aspect corresponds to a specific intersubjective relationship (Stafleu 1970, 1980).

The numerical aspect orders everything in a sequence, not only by numbers, but also by magnitudes like length, speed or energy. Common time contains this linear order, the order of earlier to later, the quantitative order of hours, days and years. But the numerical order does not imply an idea of the present, nor of simultaneity. It only displays an order of relative past and future, of earlier and later.

The spatial aspect provides us with the order of simul­taneity. At any time, as measured on the numerical scale, there are lots of spatially different things and events related to each other by their relative spatial positions. Together, the numerical and spatial aspects give a sense of diachro­nism and synchronism. Until the beginning of our century it was taken for granted that motion does not influence the numerical and spatial measures of time. But in 1905 Albert Einstein shocked the world by demonstrating the kinematic order to imply a relativiza­tion of the numerical and spatial orders. This relativiza­tion is unheard of in the common concepti­on of time and surprised physicists and philosophers alike. If two events are synchronous as determi­ned by one observer, they may be perceived diachronous by another one. The static order of relativity, the so-called `block universe’ or Minkow­ski’s space-time continuum, is often assumed to exhaust the idea of time (Minkowski 1908). However, the block universe does not provide a distinc­tion between past and future, and the present (the ‘now’) is absent.

Even common time contains more than diachronism and synchro­nism alone. These would not suffice to explain a common watch, for there is no transient flow of time in the combination of dia- and synchro­nism. In the block universe a temporal interval is nothing but the differen­ce between two tempo­ral moments, like a spatial interval is nothing but the dis­tance between two points in space. We need the kinema­tic aspect to give us a referen­ce system for any kind of motion. Motion is only conceivable if whatever is moving remains identi­cal to itself. This is the first instalment of present­ness. Relativity theory has shown that the present is not universal, its determination depends on the speed of the reference system. The present is invariably connected to some kind of in­dividuality, it is a particu­lar point of reference of something or somebody remaining itself. The present is determi­ned by the choice of one’s individu­al point of view, and is only the same for systems that do not move very fast with respect to each other. Hence the `now’ is based in the kinematic aspect, although it presup­poses the simultaneity of all events which also occur ‘now’. By the choice of an individual point of reference the past and the future are separated but still sym­metric, there is no distinction in prin­ciple.

The discrimination between past and future arises from the physical aspect, by order of the irreversibility of physical and chemical proces­ses. As a reference system the physical aspect implies everything in the cosmos to interact with anything else. If something would not be able to interact with other things (if it would be completely `inert’ or isolated from the rest of the world) it would not exist in a physical sense, it would have no physical meaning, it would not belong to the physical cosmos. Everything that exists in a physical or any other sense is embedded in cosmic time. Distinguishing past and future, the order of irrever­sibility allows of causal connections, a cause always preceding its effect. Irrever­sibility is highly relevant to the idea of individual­ity, things and events being subject to laws of probability. The actuali­zation of possibilities constituting the present is irre­ver­sible. Whereas the past is determined, leaves traces, and can be remembered, the future is open and can be influen­ced. Hence the asymmetry of past and future is based in the physical aspect.

There are as many temporal orders and relationships as there are modal aspects (Staf­leu 1985, 1986, 1988, 1991). These include the biotic order of the generations, the order of descendence concerning the living beings, allo­wing of a taxonomy relating all species to each other. Biologists assume correctly that all living beings are geneti­cally related to each other. The psychic order concerns teleolo­gy, intentionality and purposive behaviour. These two orders cannot simply be reduced to the orders of dia- or synchronism, or to the kinematic and physical orders of time flow and irreversi­bility.

The temporal orders and the corresponding intersubjec­tive relations have given rise to much scientific thought and discus­sion during the present century. The revision of the ideas of time and space in the theory of relativity, the so-called measurement problem in quantum physics, and the discussion of the so-called arrow of time have greatly in­fluenced the development of physics and its philosop­hy (Stafleu 1970, 1980). The irrever­sibility of time is still hotly debated, because it does not fit into reductio­nist mechanist views, and this has its impact on the everlas­ting discussion of the interpre­tati­on of quantum mechanics (Coveney, Highfield 1990).


2. Interdependence: the metric of time


The modal aspects constituting the various maps are not indepen­dent of each other, on the contrary, they are strongly related. They display a numerical order, they are simultaneously operative, they refer dynamically to each other, one is irreversibly founded on the other, and they deepen each other’s meaning. For instance, the relativity of time and space mentio­ned above means the development of the numerical and spatial orders anticipating the kinematic one. The origin­ally static orders of dia- and synchron­ism become depen­dent on motion when an­ticipating the kinematic order of time. Also, the order of irrever­sibility which in physical systems would lead to a disconso­late uniformity is opened up in living systems that grow and flourish, apparently defeating physical laws.

With respect to the usual order of the modal aspects, retrocipati­ons and anticipa­tions concern references back­ward and forward (NC II, part I). They refer the various maps to each other and enrich their meaning. In fact, the maps would be quite useless if they were not related. [By an unfortunate term, the anticipations and retrocipations are called ‘analogies’. This is unfortunate (if not wrong), because analogy’ is a logical rather than a cosmological category, like ‘metaphor’ is a lingual one. The modal aspects are analogous to each other because of having retro- and anticipations. However, calling these intermodal relati­ons ‘analogies’ both obscures their meaning and impedes the analysis of real analogies with their help (cf. Stafleu 1994b).]

The natural sciences heavily depend on the possibility of making measurements. Retrocipations make numerical relati­onships to show themselves not only in mathematical states of affairs, but also in spatial, kinematic and physical magnitudes. The law for a magnitude, called its metric, allows of expres­sing spatial, kinematic, physical or technologi­cal relati­onships in numerical terms. By projecting the spatial, kinematic and physical maps on the numerical one, they become measurable. This is the basis of the mathema­ti­zation of modern science, the possibility to apply statis­tics and to design mathema­tical models of natural and technological systems, and to measure them. In turn, the avail­ability of measuring instru­ments is a fruit of the tech­nological opening up of physical systems, the explora­tion of the anticipations in the mathema­tical and physical aspects. Hence, the fact that physical relations can be measured depends in principle on numerical retrocipa­tions, in practice on technological anticipati­ons.

Now common time as measured by your watch turns out to be kinematic time, retrocipating to spatial and numerical time and anticipating later aspects. The standard of common time is determined by the kinematic law concerning motion uninfluenced by physical forces. This law for iner­tial motion covering equal distan­ces in equal time inter­vals delivers the norm for an accurate clock, whether mechanical or electronic. Common time as measured by a calendar is purely numerical, but the time measured by a clock, both in science and in common sense, is the metric of kinema­tic time, the objective measure of the flow of time. It is a small but important segment of cosmochrono­logy. Your personal watch shows you the present, here and now, in the flow of time. Because you want to partake in public time, you take care to have your watch synchronized with other clocks.

This is the moment to observe a remarkable shift in the natural sciences and technology. It is well known that during the 19th century mechanism was the leading world view of the natural sciences. Newton’s mechanics, now called classical, was considered the paradigm of all sciences. This world view broke down by the introduc­tion of relativity theory and quantum physics. An additional breakdown is generally overlook­ed, however. During the 20th century, mecha­nics as a standard of measurement was replaced by electro­nics, not only in physics but in chemistry, biology and technology as well. In the first half of this century all measure­ments were still ultimately reduced to the measure­ment of mechanical forces, the received standard of physi­cal interac­tion. After the rise of solid state technology and the development of transistors and chips, measuring now means the comparison with electric effects. For an example consider the measurement of ordinary time. You all remember that accurate clocks used to be mechanical ones. But now probably each of you carries an electronic watch, and you are aware that you hardly ever have to adjust it, contrary to your earlier mechanical devices. The paradigm of the natural sciences is no longer mechanics, but elec­tronics.

Mechanism is a kind of reductionism, the view that all states of affairs in one aspect can be reduced to an earlier aspect, in this case the aspect of motion determi­ned by mechanical forces acting between unchangeable elementary particles. Mechanism is no longer fashionable, but the idea that physics can be reduced to mathematics, and biology to physics and chemistry is still very much alive. The existence of retrocipations accounts for the success of reductionist schemes, but the neglect of anti­cipations bars the develop­ment of a fruitful philosophy of science. This is reinforced by the usual neglect of the duality of modal laws and typical structures, to which we now turn.


3. Diversity: temporal being


If we compare each modal aspect with a grid on a map, the structures could be compared with towns. The structures form nodal points in our cosmochronology. In fact, Dooye­weerd’s theory does not concern structures, but structural types (not towns but types of towns), and Dooyeweerd only discussed so-called thing-like structures. (For a review of this typology see Stafleu 1994a.) It is tempting to demon­strate Dooyeweerd’s philosophy to be able to account for the intrica­te structures as discovered by the natural sciences in the past century. However, I shall restrict myself to making some brief remarks on the temporal character of individual things, plants and animals, in order to show the transition from the modal aspects to the nodal points of individu­ality.


Unity and diversity

Dooyeweerd stressed the unity and persistent identity of a thing to be an unalienable part of our natural expe­rience. However, many states of affairs discovered by scientific research are not open to natural experience. Moreover, natural experience cannot provide science with data, because by its nature it is not documented, not open to scienti­fic research. Yet there is a continuity between natural and scientific experience.

Both in daily life and in science, a thing is experienced as a unit with specific properties. Nearly a century ago an atom was established to consist of a nucleus and a number of electrons. Yet an atom is known as a unit with a specific mass and chemical properties. It is a unity, and there are a lot of them, there are many hydrogen atoms with the same characteristic properties. The unity of a thing is based in the aspect of quantity, but its meaning is not confined to quantity.

For instance, the structural likeness of all electrons gives rise to an important structural law for systems containing more than one electron. This is the so-called exclusion princi­ple discovered by Pauli in 1925, saying that two electrons can never occupy the same physical state. This structural law accounts for the enormous diversi­ty of nuclei, atoms, molecules and crystals. Without this law, and without the structural likeness of all electrons, life and this confe­rence would be impossible.


Coherence or wholeness

With the exception of elementary particles like electrons, a thing exhibits a spatial coherence of its parts. The spatial coherence of a physically qualified thing like an atom is of a physical nature, it is determined by an equilibrium of physical forces. Likewise, the unity and coherence of a plant is biotically determined. Yet coherence is a spatial category, subject to the order of simultaneity. It has only sense to speak of coherence if it concerns simul­taneously present parts.


Identity and persistence

The identity and persistence of a thing comes to the fore when it is subject to change. The original kind of change is local motion. It has only sense to speak of local motion if the moving subject remains itself, maintaining its identity, and this is also the case in other kinds of change, like the metamorphosis of a caterpillar. Only when ceasing to exist the thing loses its identity.

A criterion of identity is the law that a moving thing cannot be simultaneously at different positi­ons. According to the theory of relativity the speed of a material thing is always less than the speed of light. Faster moving things, called `tachyons’, could be at two different positions at the same time, such that their identity could not be established. In the event that according to one observer a tachyon is emitted, another observer would see it being absorbed. The order of emer­gence and perishment would be reversible. For these rea­sons it is doubtful whether we would be able to recognize a tachyon. We would have to invent a new definition of `existence’.


Stability and duration

The individual duration of a thing is the time between its coming into existence and its perishment. Dooyeweerd considered duration to be the subject side of cosmic time, but in my opinion this is too narrow, the subjectside of cosmic time also including the modal and structural inter­subjective relations.

During its existence a thing has a certain stability. An atom has  stable and metastable states. If it is in a metastable state, sooner or later it emits light or some other kind of radiation. A radioactive nucleus transforms itself into a different nucleus. Most elementary particles are unstable. The duration of a metastable state is deter­mined by the law of decay, saying that at every moment the probability for the system to be transformed during a specified time to come is 50%. The so-called half-life time is specific for the system or state concerned. I want to draw your attention to the fact that the validity of the law of decay is absolutely independent of the system’s past, and to the fact that the law applies to structural wholes, not to mixtures. The composition of a mixture betrays its past, but a physical­ly qualified structural whole has no past.

The existence of a thing can be terminated by some external cause, for instance a collision. The stability of a thing means that it is able to resist such external influences, to a certain extent. In physics this is ex­pressed by the system’s binding-energy, the minimum energy needed to break it up. A stable molecule remains intact as long as its binding energy is more than the mean energy of the collisions of the molecule with other ones. The mean collision energy is determi­ned by the temperature.

In a solid a criterion for stability is its melting point. The higher its melting point, the stabler the solid. Only chemically pure systems have a definite mel­ting point, solid mixtures have not. Stable things have a measure of periodicity. In atoms, molecules, nuclei and the solar system this is a numerical periodicity, the constant frequency of circular or elliptic motion. In a solid it is the spatial periodicity of the long-distance order of the crystalline structure.

For plants and animals stability has consequences for their mean future life time, which sometimes depend on their age, sometimes not. More than for physical systems, the actual life time of an individual plant or animal is determined by external influences.


Differentiation and integration

Since the 19th century it is known that a new plant or animal develops itself starting from a single fertilized cell, after the fusion of a female with a male cell. This process is strongly controlled by a DNA-molecule. In the fertilized egg cell the DNA-molecule is derived half from the female, half from the male parent. In processes con­trolled by DNA both lawlike and individual elements play a part. The lawlike part implies that fertilization usually only occurs if the parents belong to the same species and have similar DNA-molecules. The individual part means that a DNA-molecule also contains a lot of stochastic informa­tion, determining the individual appearance of the new plant or animal.

The DNA-molecule controls the functioning of each cell of the plant, and also its development, the growth of one single cell to the adult plant or animal during its exis­tence. During this process many new cells emerge which though having the same DNA-structure differ from one to the next. The identity of the cells is limited by but also distinguishable from the identity of the plant of which it is a part. Besides this differentiation we see a process of integra­tion, of cells forming a tissue, tissues forming organs like roots, leaves or flowers, together making the plant an organized whole.

This idionomic development of a plant, by differentia­tion and integration, is typical for biotically qualified structures. It is determi­ned by the internal structural law for the plant.



The internal differentiation and integration gets a new dimension in the form of the experience of every animal during its life, in particular during its youth. The individuality of an animal is to a large extent determined by its experience. This is structurally limited by its specific ability to learn and by its age.

Animal behaviour is partly inborn, partly determined by the animal’s ex­perience, and partly by its perception of the environment. Hence an animal has a sense of past, present and future and of their continui­ty. An animal has a memory, it has knowledge of its environ­ment and it has expectations, together leading to purposive actions. A higher animal feels emotions like fear, anger, uncertainty, when its memory of the past, perception of the present and expecta­ti­ons of the future do not match.

To conclude, although each of these six categories is based in one of the first six modal aspects, they are nevertheless not determi­ned by modal laws but by the idionomic structure of the individuals concer­ned. Together they are knotted into a single structural whole. They show how the modal aspects of tempora­lity are tied up into a typical structure. And I should add, they relate to human persons as well.


4. Dynamics: temporal becoming


During the twentieth century, the standard philosophy of science has become more realistic. At first it was domina­ted by the positivist view that science is only concerned with observations of pheno­mena, but the succes­ses of solid state theory, astro­phy­sics, nuclear physics, and their technological applica­tions have forced philosop­hers to acknowledge the existence of a structured reality behind the phenomena. This development confirms Dooye­weerd’s theory of structu­res.

His typology concerns structures of individual things. Therefore Dooyeweerd’s system gives the impression of being static, and his famous review of Lever’s Creation and evolution (Dooyeweerd 1959) reinforced that impressi­on. But the core of cosmochronology is the dynamic develop­ment of the cosmos, of the earth, and of mankind. In our century, astrophysical and biologi­cal theories of evolution have matured, beco­ming more and more consistent. In order to account for this, I propose to pay attention to the structures of aggregates, events and proces­ses. If structures of things can be compared with towns, events and processes look like traffic in and between towns.


Theories of everything

At the close of a century it seems tempting to assume that physical science is nearing completion. At the close of the 18th century Laplace thought that after Newton only a few minor problems remained to be solved, but in the 19th century chemistry came to fruition, electricity was deve­loped and thermal physics arrived at new in­sights. At the end of the 19th century people like Michelson and Kelvin were of the opinion that virtually all physical problems were solved, and Max Planck as a student was advised to study something more promising. Shortly after came relati­vity and quantum mechanics, followed by nuclear physics, solid state physics and astro­physics.

And now we are made to believe that physics is at the verge of discovering the philos­opher’s stone, the Theory of Everything (Hawking 1988, Barrow 1990). It is supposed to explain the coherence of the so-called fundamen­tal forces of nature, to wit, electro­magnetism, the nuclear forces and gravity. The unified theory should include both quantum physics and general relativity. To call this a Theory of Everything is both preposterous and wrong.

It is preposterous like somebody’s claim to understand everything about chess or football because he knows the rules of the game. Knowledge of the coherence of the fundamental interactions would be very interesting and a great achievement, but it would not help us a bit to understand the structures studied in a field like solid state physics.

It is also utterly wrong as far as it stems from an old-fashioned reductionism, as if everything could be explained from the knowledge of physical laws, presumably modal laws.

This unified theory does not exist yet, quantum theory and general relativity being at cross-purposes. Among other things, it aims to explain the genesis of the physi­cal cosmos. As you know, astrophysics assumes that the universe has started its existence some fifteen billions years ago in a big bang. The now received theory does not claim to explain the very start of this process, it only describes its development after the start. It describes what Dooyeweerd has called the opening process of the creation, the coming into being of natural things accor­ding to laws, given by the Creator. This is a natural process, which does not mean that it could have occurred without the continuous support of the Lord. The theory does neither explain where the natural laws come from nor why they are universally valid.

The astrophysicists tell us that during the process not only things and events came into existence, but even physical space and time themselves. From our point of view, this means that space and time only make sense if providing a framework for the mutual relations between concrete things and events, and do not exist apart from the latter. Space, time and concrete matter were created toge­ther.

It should be clear that the big bang is not to be identified with the creation in a religious sense. At the start of this review I emphasized the distinc­tion between ‘creational’ and ‘temporal’. The temporal is subject to scientific research, the creational is not. Science is only concerned with what happened and happens in cosmic time. It is not concerned with the relation of the temporal universe to the Eternal.



There is another reason why a theory of everything cannot be expected to explain all that happens. I refer to the occurrence of probability as a main factor of the theory, which includes quantum physics. In order to calculate the effects of large numbers of systems like the molecules in a gas, nineteenth century physics made use of probabi­li­ty, but only for practical reasons. It was generally believed that the future motions and interacti­ons of the molecules were fully deter­mined by present positions, velocities and forces. But radioacti­vity first and atomic physics next have taught us that most processes are intrinsi­cally stochastic. This means, first that molecules and similar systems have an individu­ality of their own, secondly that their motions and inter­actions are not completely determined by natural laws. They do not occur independent of laws, but every law leaves room for individuality. It also means that a theory can never give a complete account of what happens, even at the physical level. From a philosophical point of view this is one of the most revolu­tionary changes in our world view.

Probability refers to processes and events, and the fact that each process has its own probability shows that it has a typical structure.



In quite a different way determinism got a blow from the so-called chaos theory. Natural laws were assumed to determi­ne the course of events in any closed system if its state was fully established at some initial time. Recently it has become clear that even a very slight difference in the initial state gives rise to very large differences after a relative­ly short time. It all depends on the precision with which the initial state can be determined. Now this is limited in two ways. First, quantum mechanics has shown that even for a closed system the initial state cannot be defined with infinite accuracy. Second, it has become clear that a closed system is an idealization that cannot be achieved. A well-known example concerns the terrestrial atmosphere, which cannot be treated as a closed system. Therefore our knowledge of its present state, however accurate, does not allow of predicting the weather for more than a couple of days.

More than in the nineteenth century, modern science is interested in events and processes. The natural laws have not lost their charac­ter of causal laws, but to apply them to open systems demands a new approach.


Events and processes

Whereas the structure of a thing, a plant or an animal concerns a more or less well defined individual, events concern relations between individuals. Above I mentioned the modal intersubjective relations, such as the relative position or motion of two things. Besides these general modal relations, many events have a specific character and therefore a structure of their own. Consider, for instan­ce, two kinds of collision between the molecules in a gas. Usually a collision only changes the particles’ position and state of motion, and such an encounter has a purely modal character. But sometimes the colliding molecules form a new molecule, and this is only possible if the colliding molecules match. A typical amount of energy is needed or is released. A chemical process (consisting of a large number of such collisions) conforms to a typical law, it has a typical structure which does not fit into Dooye­weerd’s typology.

Even the existence of the so-called elementary parti­cles appears to be a continuing process. Quantum electro­dynamics shows that no electron can ever be isolated from its surroundings. It continuously interacts with the electromagnetic field, and in the process positive and negative electrons besides photons are created and annihi­lated. This is in striking contrast with the age old idea that the fundamen­tal building stones of matter, whether atoms or elementary particles, are unchangeable and ever­lasting.


Aggregates of life

Typical processes occur on the basis of aggregates or mixtures, under strictly determined circumstances, such as temperature. Life on earth could never have arisen without a rich variety of chemical elements and their compositions. (For a recent review, see Mason 1992.) In the universe hydrogen and helium are abundantly present, all other elements being rare compared to these two. At a very high tempera­tu­re such as occurs in a star, elements are formed from hydrogen and helium, at a lower temperature to be con­centrated into planets.

Typical processes do not occur in all kinds of mixtures, but only in aggregates with a certain kind of compo­sition, often within rather strict limits. The members of the aggregate must have a structural relatedness allowing of typical processes.

On our map of the cosmos we find various kingdoms. In the kingdoms of plants and animals aggregations constitute the basis of evolu­tionary processes. Elsewhere I have pointed out that four typical aggregates of life are operative in biotic evoluti­on: genes, biotopes or ecosys­tems, niches and populations (Stafleu 1986, 1989). They exhibit a certain kind of individuality different from that of a plant or a cell or a flower. Their typicality is not determined by their own struc­tures, but by structural relation­s between the members of the aggrega­te. Each of them is based in one of the modal aspects preceding the biotic one.

The theory of evolution turns out to depend on a number of unchan­geable laws concerning heredity, abundancy, equilibrium and exclusion in biotic aggregates. The kingdoms of plants and animals are in a permanent state of evolution. The present theory of evolution is only able to explain small nearly continuous transitions, in other respects it is far from complete. Nevertheless, apart from a number of gaps or missing links the general picture of the evolution from the big bang to the present state of the plant and animal kingdoms is quite satisfactory (Van Till 1986, Lindberg, Numbers 1986, Bowler 1989).

Any philosophy of nature should be able to account for the natural processes occurring in various types of aggre­gates. Still absent in our philosophy, a typology of aggregations, processes and events would provide a valuable contribution to the continuing debates on evoluti­on.

But before that we should get rid of some dualisms.


5. Complementarity: the temporal position of mankind in and beyond the animal kingdom


The main purpose of any cosmochronology is to determine the position of mankind in the cosmos. I shall discuss a possible entrance to anthropology starting from natural philos­ophy (Stafleu 1991). It should go without saying that this is not the only possible entrance.


Functioning of animals in the post-psychic aspects

In the philosophy of the cosmonomic idea it is common understanding that animals do not function as subjects in the post-psychic aspects (NC I, 39; II, 81, 114; III, 58, 85). The logical aspect being the first aspect after the psychic one, this view confirms the tradi­tional opinion that a human person distin­guishes himself from an animal in particular because of his rational­ity, his ability to think, his intelligence. It therefore detracts from another view of this philosophy, namely that a person is primarily religious.

Recently I have called in question whether it is true that animals, or at least the so-called higher animals, cannot be subjects (rather than objects) in the post-psychic aspects,­ putting forward the following hypothesis. In the post-psychic aspects, if animals act as subjects, they do so always retrocipatory, i.e., referring to their biotic and psychic needs. (Stafleu 1989, 1991. Cf. Lever 1973, 187-193, Dengerink 1986, 214, Hart 1984, 176-182.)

The subjec­tive function­ing of animals in the post-psychic aspects is invariantly primitive and instinctive, often coercive, though animals are able to learn from their mistakes. It is retrocipatory, never anticipatory. It is retrocipatory, because even post-psychic behaviour of animals serves their biotic and psychic functioning, in particular fee­ding, reproduc­tion and survival of the species. Human activity, on the con­trary, is opened-up, anticipating, transcend­ing the temporal order, and therefore religious. Human anticipato­ry acts are cultural, contrary to the natural, retrocipatory behaviour of animals.

This view induces a new understanding of the distinc­tion between ‘normative’ and ‘natural’. In Dooyeweerd’s philosophy, the first six modal aspects are called natu­ral, the others normative. I don’t think this makes sense. I propose to call the activity of human beings ‘normati­ve’, because only men and women have to answer to laws, even natural laws, in a responsible way. For instance, it is a norm that an accurate clock conforms to the natural law of inertial motion. Animals are not responsible for their behavi­our, even if they are subject to the post-psychic modal aspects. Hence normativity is not coupled to aspects but to humanity.

This view makes transparent the fallacy of evolutio­nism, that attempts to explain everything, even human behaviour, in evolutionary terms. By ignoring the distinc­tion between animal retrocipatory natural behaviour and human anticipatory normative acts, reductionist evolutionism foregoes any insight into the uniqueness of humanity, in particular human responsibility.


The structure of the human body

In biological taxonomy a human being is considered a mammal, belonging to the order of the primates. Dooyeweerd’s theory of ‘enkapsis’, the interlace­ment of structures, accounts for this state of affairs. The structure of a human body is inter­laced with an animal substructure, and its nature determines a person’s position in the animal kingdom. Likewise, because of its organic substructure, an animal belongs to the organic kingdom, which it simultaneously transcends. The structure of an animal is not biotically but psychically qualified. Hence to assign mankind a place in the animal kingdom does not imply that its structu­re is psychically qualified.

The structure of the animal body, in which biotic, physical, kinema­tic and spatial substructures are interlaced, is designed for the animal’s behaviour, whereas the human body is designed for responsible activi­ty. In several respects the animal substructure of a human being is much more developed than the structu­re of any animal (Lever 1956, Chapter 5). Human thought is localized in the cerebral cortex, in particu­lar the neo­cortex, which is absent in most animals. In mammals it is present only to a small extent. The cultural aspect of human activity is most pregnantly expressed in the hand, an organ that is far more developed than whatever compara­ble animal organ. The nerve cells related to the hands take a relatively large volume in the human brain. The lingual aspect finds its counter­part in the speech centre, again a substantial part of the brain. The larynx, the tongue and the muscles of the jaws are such as to make speech possible. The structure of the human face is made to show joy, sorrow or anger. In fact, a human being is far more emotional than any animal.

All these and many more differences in the body struc­ture of humans and the most related animals point to the open character of the ‘act struc­ture’ of a human person.

‘The erect gait, the spiritual expression of the human face, the human hand formed to labour after a free project, testify to the fact that the human body is the free plastic instrument of the I-ness, as the spiritual centre of human existence.’ (NC III, 88. See also Dooyeweerd 1959).

It shows how much the human body is directed to spiritual life. The open character can be under­stood from the view that a person knows what it is to be called to bear res­ponsibili­ty, because he or she knows the difference be­tween good and evil.

Scientific knowledge of the functioning of the human body has increased enormously during the twentieth centu­ry, yet much is still not understood. In particular the age-old distinction of body and mind is still haunting us. The main pitfall is to identify the `body’ with the mate­rial, i.e. the physical, organic and psychical substructure of human existence on which the `mind’ is superposed.


Duality versus dualism

The distinction between human persons and animals is often expressed by the supposed lack of a ‘mind’ or ‘spirit’ in animals. This leads to the suggestion to relate the dis­tinction of body and spirit to the complemen­tary directi­ons of retrocipation and anticipa­tion. Complemen­tarity is a concept introduced in quantumphysics by Niels Bohr in order to account for the dual aspects of wavelike and particlelike functioning of electrons and photons (Bohr 1934, chapter 2).

Animal functioning in the post-psychic aspects (if present) is always retrocipatory, instinctive, directed to biotic and psychic needs. The functioning of a person, as far as it is retrocipatory, does not differ very much from that of the higher animals. But the human spiritual func­tioning (the `act-structure’ according to Dooye­weerd) is mostly anticipat­ory, directed towards the opening up of all modal aspects, and even transcending them.

This should not be misunderstood as the resurrection of the age old dualism of body and mind, supposed to be two different substances, whether or not interacting with each other (Popper, Eccles 1977). I reject this dualism as much as I question the dualistic division between the ‘natural’ modal aspects and the ‘spiritual or ‘normati­ve’ aspects. A dualism means a division into parts, like the nineteenth century dualism of electro­magnetic and other waves versus material particles, or the division of a human being into a body and a soul as distinct substances, or the division of natural and normative aspects. A duali­ty means that something has two sides, like the wave-particle duality in quantum physics, or the law-subject duality, or the duali­ty of anticipato­ry and retrocipato­ry directi­ons in the order of the modal aspects.

The structure of a human person is characterized by the simul­taneous occurrence of retrocipato­ry or bodily and an­ticipatory or spiritual functioning of a human person as a whole. This applies to all modal aspects of human functio­ning. Hence, the death of a person does not mean the separation of body and spirit, and his resurrection con­cerns the human body as well as the spirit.

This concept of spirit or mind should not be confused with the idea of the human soul, his heart, the centre of his existence as a religious being. The main incentive for human anticipatory activity is the ex­perience of good and evil, to which we now turn.


The temporal experience of good and evil

It is now generally accepted that the fundamental distinc­tion between human beings and animals cannot be determined on biological grounds only. Of course, there are relevant biotic differences between human persons and their nearest relatives, the apes. Nevertheless, the biotic distinction between a human and an ape is smaller than that between an ape and a horse. Humans and apes constitute different families of the same order of the primates.

When paleontologists want to establish whether certain fossils are derived from ape-like or human-like beings they have to take recourse to non-biological characteris­tics, like the use of fire, clothing, tools and ornaments, the burial of the dead, in short, anticipatory activity. During its history mankind has disclosed the various modal aspects. Unlike animal behaviour, human activity is not merely guided by the fulfillment of biotic and psychic needs, but is directed to answering a calling.

The awareness of good and evil marks the birth date of humanity. The fact that animals can learn shows them having a sense of lawful­ness. But only people consider laws as normative, as providing principles for normative activity. Human beings have discovered the exis­tence of good and evil, in the animal world, in their environ­ment, and last but not least in their own communi­ties. This discovery included the phenomenon of illness of plants and animals. Every biologist can explain that illness as such is a natural condition. Only from a human point of view does it make sense to say that a plant or an animal being ill is anti-normative. The so-called struggle for life, too, is experienced as anti-normative by people only.

All persons experience the calling to combat evil. This not only applies to evil observed in the plant and animal worlds, but also to evil in themselves and in their fellow people. The calling to combat evil implies a sense of respon­sibility for plants and animals and for humanity, for the `environment’ as it is now called. An animal takes the world as it is, as given, whereas a human person attempts to improve the world. The awareness of good and evil con­stitutes the start of cultural development, including science and technology.

The sense of calling and responsibility is at the heart of human existence, it is the driving force of any world view and cannot be traced back in a scientific way. From a philosophical point of view it can only be established to exist as a matter of fact. The question of the origin of this calling cannot be answered scientifically or philos­ophically, because it is a religious question. Hence the development of humanity from the animal kingdom cannot be scientifi­cally explained or even dated. Rhetorical questi­ons like: `Can you imagine that a gorilla mother gives birth to a human child?’ are therefore quite irrelevant. Animals have no self-consciousness, and nobody can tell how self-consciousness in human beings arises.

Increasing insight into the distinction between good and evil enables human beings to understand much better how to commit evil themselves. The belief in a calling degenerates into belief in one’s own pos­sibilities, love for one’s neighbour into love for oneself, justice into arbitrariness, division of labour into slavery, care into neglect. Humanity wants to be allowed to use evil in order to further what is good in one’s own eyes, the goal sanc­tifying the means. Natural science did not escape from this, as testifies the development and use of poison gas, atomic bombs and smart projectiles. This is the fall into sin, from which humanity can only be saved by the complete sacrifice and self-denial of Christ.

The most pregnant expression of evil is death, destruc­tion. In a strictly biological sense death is not wrong, if it concerns the natural end of a plant or animal as a living individual. Human beings fight death, seeking eternal life. In a Christian sense, eternal life does not mean the perpetuation of temporal life, but the true knowled­ge of God. It is like a window, from which a human person can look outside the plant and animal kingdoms, in the anticipatory direction. This window is opened by God himself, who allowed his son to become a man in order to teach us who is the father of humanity and the creator of the cosmos.

By meeting Jesus Christ in our heart and in our fellow men we also meet oursel­ves. True knowledge of oneself is absolutely dependent on the knowledge of God in the person of Jesus Christ, who is the only image of God. Hence our self-knowledge is dependent on temporal relations between human persons, of whom Christ is the first, the alpha and omega of cosmic time.

Our religious experien­ce starts from our heart, our self-conscious­ness, and pro­ceeds through our anticipa­ting activity, pervading all aspects of human experience. Both philosophers and scientists have become aware that the natural sciences themselves are dependent on the point of view taken by the human observer. This has been emphasized in relativity theory and quantum mechanics, and recently in the so-called anthropic principles, which explore the relevance of human existence for astronomy, physics and biology (Barrow, Tipler 1986).


6. Conclusion


I have presented a survey of cosmic time, ending up with anthropology. This is, I think, in line with the words of Dooyeweerd with which he concluded his New critique:

‘So it appears that the theory of the enkaptic struc­tural whole forms the necessary connective link between the theory of the individuality-structures and their temporal interweavings, and what is called a philosophical anthropology.

All our previous investigations have been nothing but a necessa­ry preparation for the latter. They all implicitly tended to the ultimate and doubtless most important problem of philosophical reflection: What is man’s position in the temporal cosmos in relation to his divine Origin ? ... The really philosophical problems concerning man’s position in the temporal cosmos cannot be rightly posited without a due in­sight into the transcendental conditions of philosop­hic thought. And in addition a philosophic anthropo­logy presupposes an inquiry into the different dimen­sions of the temporal horizon with its modal and individuality struc­tures.’ (NC III, 781)

I have taken the liberty of exploring one way to a philos­ophical anthropology, the way through the natural king­doms. I am not suggest­ing this to be the only possible way, I am not an evolutionist. But it is a necessary part of a Christian philosophy of nature and of mankind. The various modes of temporal experience and existence which I have mentioned are concentrated into the human selfness, in our consciousness of being a temporal creation, embed­ded in the whole cosmos, with knowledge of the eternal. The natural sciences are not able to explain the rise of humanity, but if the results of science could not be related to anthropology, our philosophy would be in vain.

By introducing a new term, cosmochronology, I wish to emphasize the importance of the idea of cosmic time both in Dooyeweerd’s philosophy and in science. Relations constitute the framework of cos­mochrono­logy, the structures form its nodal points. The core of cosmochronology is the dynamic develop­ment of the cosmos, and its main purpose is to determine the position of mankind in the cosmos.

Dooyeweerd’s vision of time, now over fifty years old, is able to account for many modern insights. It deserves to be stu­died, to be amplified, and to be developed in continuous confrontation with current views in philosophy and in science, not only at the close of the present century, but also in the century to come. In particular Dooyeweerd’s philosophy should be developed into a theory of change, in order to account for a world that is not static but dyna­mic.




Barrow, J.D., Tipler, F.J. (1986), The anthropic cosmo­logi­cal principle, Oxford: Clarendon Press.

Barrow, J.D. (1990), Theories of everything, The quest for ultimate explanation, Oxford: Oxford University Press.

Bohr, N. (1934), Atomic theory and the description of nature, Cambridge 1961: Cambridge U.P.

Bowler, P.J. ([1983], revised 1989), Evolution, The history of an idea, Berkeley: University of California Press.

Brüggemann-Kruyff, A.T. (1981-82), `Tijd als omslui­ting, tijd als ontsluit­ing’, Philosophia Reformata 46: 119-163, 47: 41-68.

Coveney, P., Highfield, R. (1990), The arrow of time, London: Allen.

Dengerink, J.D. (1986), De zin van de werkelijkheid, Amsterdam: V.U. Uitgeverij.

Dooyeweerd, H. (1935-36), De wijsbegeerte der wetsidee (3 vols.), Amster­dam: Paris (referred to by `WdW’).

   -, (1936, 1939) `Het tijdsprobleem en zijn an­tinomieën op het immanentie-standpunt’, Philosophia Reformata 1: 65-83; 4: 1-28.

   -, (1940) `Het tijdsprobleem in de wijsbegeerte der wetsidee’, Philosophia Reformata 5: 160-182, 193-234.

   -, (1953-57), A new critique of theoretical thought (4 vols.), Amsterdam: Paris (referred to by `NC’).

   -, (1959), `Schepping en evolutie’, Philosophia Refor­mata 24: 113-159.

Hart, H. (1984), Understanding our world, Lanham: University Press of America.

Hawking, S.W. (1988), A brief history of time, New York: Bantam.

Landes, D.S. (1983), Revolution in time, Clocks and the making of the modern world, Cambridge, Mass.: Harvard U.P.

Lever, J. (1956), Creatie en evolutie, Wageningen: Zomer en Keuning. (Transla­tion: Creation and evolution, Grand Rapids: Inter­nat. Publica­tions 1958).

   -, (1973), Geïntegreerde biologie, Utrecht: Oosthoek.

Levin, Ira (1970), This perfect day, London: Michael Joseph

Lindberg, D.C., Numbers, R.L. (eds.) (1986), God and nature, Histo­ri­cal essays on the encounter between chris­tianity and science, Berkeley: Univer­sity of California Press

Mason, S.F. (1992), Chemical evolution, Origin of the elements, molecules, and living systems, Oxford: Clarendon Press.

Minkowski, H. (1908), Raum und Zeit; translation: `Space and Time’, in: A.Einstein et al. (1923), The principle of relativity, London: Methuen.

Orwell, George (1949), Nineteen eighty-four, Harmonds­worth: Penguin

Popma, K.J. (1965), Nadenken over de tijd, Amsterdam: Buijten en Schipperheijn.

Popper, K.R., Eccles, J.C. (1977), The self and its brain, An argument for interactionism, Berlin etc.: Sprin­ger; (1983), London: Routledge and Kegan Paul

Stafleu, M.D. (1970), ‘Analysis of time in modern physics’, Philos­ophia Reformata 35: 1-24, 119-131

   -, (1980), Time and again, Toronto: Wedge; Bloemfon­tein: Sacum

   -, (1985), `Spatial things and kinematic events’, Philosophia Reformata 50: 9-20.

   -, (1986), `Some problems of time - some facts of life’, Philosop­hia Reformata 51: 67-82.

   -, (1988) `Criteria for a law sphere’, Philosophia Reformata 53: 171-186.

   -, (1989), De verborgen struc­tuur, Amsterdam: Buijten en Schipper­heijn.

   -, (1991), `Being human in the cosmos’, Philosophia Reformata 56: 101-131.

         -, (1994a), `De structuur der materie in de wijsbegeerte van de wetsidee’, in: H.G.Geertsema et al. (eds.), Herman Dooyeweerd 1894-1977, Breedte en actualiteit van zijn filosofie, Kampen: Kok, 114-142.

         -, (1994b), `Modelvorming als heuristisch instrument in het weten­schappelijke ontsluitingsproces, Philosophia Reformata 59, to be published.

Van Till, H.J. (1986), The fourth day, Grand Rapids: Eerdmans.









The idea of law 


4. The idea of natural law (1999)


Philosophia Reformata 64 (1999) 88-104



From essence to law


The aim of this paper is to investigate the transition in natural science from the search for the essence of matter to the search for the laws to which matter is subject. Starting about 1600, this transition meant a change of perspective, the introduction of a new metaphysical view of the world. A scientific worldview has at least four components, its ontology, epistemology, logic and heuristic,[1] which I shall discuss with respect to the idea of natural law.

The idea that nature is governed by laws is relatively new. The rise of science in the 16th and 17th centuries meant the end of Aristotelian philosophy, having dominated the European universities since the 13th century. According to Aristotle, four causes, form, matter, potentiality and actuality determine the essence of a thing and the way it changes naturally. Each thing, plant or animal has the potential to realize its destiny, if not prohibited by the circumstances. The aim of medieval science was to establish the essence or nature of things, plants and animals, their position in the cosmic order, and their use for humanity.

Although essentialism is still influential, since the 17th century it was to be replaced by the search for laws. During the Middle Ages it was common sense to distinguish positive law, given by people, from (mostly moral) natural law, given by God, but this was never applied in science. In a scientific context the word law was introduced about 1600 by Brahe (‘the wondrous and perpetual laws of the celestial motions …  prove the existence of God’[2]), Bruno (‘Nature is nothing but the force inherent in the things, and the law according to which they pursue their orbits’[3]), and Galileo (‘Nature … never transgresses the laws imposed upon her.’[4]). Descartes considers laws to be established by God in nature.[5] Leibniz speaks of natural laws as rules subordinate to the supernatural law of general order.[6] For Newton, axiom and law of motion are synonymous.[7]

Kepler was the first to formulate a law as a generalization in the form of a mathematical relation:

1. The orbit of a planet is an ellipse, with the sun in one of its focal points.[8]

2. Each planet traverses in equal times equal areas, as measured from the sun.[9]

Apparently, the first law does not differ very much from the view, accepted since Plato, that the orbits of the celestial bodies are circular, albeit with the earth at their centre. After all, both circles and ellipses are geometrical figures. But circular motion was put forward as being the essential form of celestial motion, not as a generalization from observations and calculations. Astronomers from Hipparchos (2nd century BC) up to Copernicus (early 16th century), have tried to reconcile the observed motions with a combination of circular orbits. In his elaborate analysis of Brahe’s observations, Kepler found the orbit of Mars to be an ellipse, with the sun in a focus rather than at the centre. He assumed this could solve many problems for the other planets, too. The Platonic circular motion was a rational hypothesis a priori, imposed on the analysis of the observed facts. Kepler’s elliptical motion was a rational generalization a posteriori, a mathematical formulation of a newly discovered natural law.

Kepler’s second law contains another novelty. No doubt, medieval philosophers were interested in change. It belongs to the essence of each thing to actualize its potential, but theories of change were never quantitative. Planets were supposed to move at a constant speed. The astronomers knew very well that planets have variable speeds and  applied various tricks to fit the observed facts to the Platonic idea of uniform circular motion. Kepler accepted changing velocities as a fact, connected them to the planet’s varying distance to the sun as expressed in its elliptical path, and established a constant relation: equal areas in equal times. The area law was later shown to be a consequence of the law of conservation of angular momentum.

The introduction of the area law is the first instance of a method to become very successful in natural science, to relate change to a magnitude that does not change, a constant. It means formulating several conservation laws, of energy, linear and angular momentum, electric charge, etc. These laws impose restraints on any changes to occur.

Simultaneously with the increasing emphasis on natural laws the use of essence in scientific language diminished. Galileo criticized essentialism as a play of words. When in his famous Dialogue (1632) the Aristotelian Simplicio says that the cause of fall is known to be gravity, Galileo’s mouthpiece Salviati replies: ‘You are wrong, Simplicio; what you ought to say is that everyone knows that it is called “gravity”’.[10]

In particular Newton replaced the search for the essence, the being or the nature of things, by the question of which laws they satisfy. Newton researched gravity without defining its essence.[11] In Aristotelian philosophy all substances (things, plants, animals and human beings) have the potential to realize themselves. Hence, a substance has a measure of independence over against God.[12] This view collides with Newton’s protestant confession that all things are absolutely dependent on God’s creation and support. He assumed matter to be completely passive, subject to God’s laws. Therefore, Newton rejected the insinuation that he ascribed an active principle of gravitation to material things. In 1693 he wrote to Bentley:

‘You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know and therefore would take more time to consider of it’.[13]

In Newton’s thought essence was gradually replaced by universality.[14] Gravity is not essential, but universal, and universality is the hallmark of a natural law. It is not necessary to know what gravity ‘essentially’ is:

‘And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.’[15]




Scientists usually respond positively to the question of whether natural laws have an existence independent of mankind. Aimed at finding regularities, the empirical method is firmly rooted in the prevalent scientific worldview. Laws discovered in the laboratory are declared universal, holding for the whole universe at all times. With the purpose to study the law-conformity of reality, science takes the existence of laws as a point of departure not to be proved.

Whereas some philosophers deny the existence of natural laws,[16] others acknowledge natural laws not to be invented but discovered.[17] Law-conformity cannot be proved scientifically or philosophically. Its acknowledgement depends on someone’s scientific worldview. This also applies to the view that the natural laws are mutually consistent, antinomies are excluded, as Dooyeweerd states.[18]

Dooyeweerd, too, has a realistic view of laws, which he considers to provide conditions for the existence of everything in reality. But his realism does not imply that the laws have an independent existence. Nothing in reality is independent or autonomous, everything depends on God. Reality is not characterized by independent being, but by dependent meaning, where meaning has the sense of pointing to, giving direction, aiming at.[19] Hence Dooyeweerd takes distance from essentialism, although the way he treats the ‘meaning kernel’ in the modal aspects shows traces of essentialism.[20] Moreover, the laws are mutually dependent as well; there are all kinds of connections between laws.

Because science studies law-conformity and takes the existence of natural laws for granted, it is confronted with the law as a boundary of its activity.[21] Neither science nor its philosophy is able to say anything meaningful about what is hidden behind that boundary. Knowledge of the origin of lawful reality is not gained in a scientific or philosophical way, not even a theological way, but from God’s revelation only. The bible does not provide us with a view on natural laws or natural science; the idea of natural law even hardly existed before the 17th century. The metaphor of the law as a boundary is only intended to call attention to a restriction on scientific activity, and has no other meaning. In particular, the view that God does not restrict himself to proclaiming and preserving laws implies that the laws do not constitute a boundary for God’s interference in his creation.[22]


Ante rem, post rem, in re?


The idea of natural law is a metaphor, which is often taken literally, as a prescription given by God, such as the Ten Commandments. The idea of law as developed during the Renaissance was inspired by the idea that matter has no existence independent of God, but ran the risk of hypostatizing the laws with respect to reality being subject to the laws. By considering the law as the will of God for the creation, the law seems to stand apart from the creation, as if God has called to order an otherwise unordered reality (‘the earth was without form and void’, Genesis 1, 1). This problem reminds one of the medieval distinction between idealists, realists and nominalists with respect to universalia, abstract universal concepts related to essentialia.

Like Plato, the 13th-century idealists Bonaventure, Grosseteste and Bacon, were of the opinion that the observable world is an image of a higher, ideal, invisible but knowable reality. Universals like goodness and justice are inborn. In rank, universals precede the visible world, being ante rem. Aristotelian realists, like Thomas Aquinas and Albertus Magnus, assumed that the forms, the nature of things, can be discovered from observation, all knowledge starting from sensorial experience. The universals are found in being, they are in re. Plato and Aristotle considered the ideas or forms to be eternal, necessary, rationally determined concepts, but the 14th-century nominalists, including William of Ockham, Buridan and Oresme, rejected the logical necessity of the universals, which they considered to be at variance with God’s omnipotence. They stated the world to be contingent, created by God in a certain way, which could have been different. God is not bound to the eternal forms of Aristotle or Plato.

The nominalists appealed to the authority of bishop Tempier of Paris, who in 1277 had condemned a number of Aristotelian theses, assumed to contradict God’s power. For instance, Aristotle stated on rational grounds that the cosmos has necessarily a spherical shape. The nominalists said that the cosmos may very well be spherical, but God could have made it non-spherical as well. The actual shape of the cosmos should be established by observation, not by reasoning alone. They considered universals to   be human inventions. Only individual, concrete things are real. Universals like animal, motion, beauty, are nothing but names (nomen = name), thought up by people, in order to get a rational grip on reality. The universals are post rem, ranked below the things.

With the introduction of natural laws in the 16th century, important shifts in these positions can be observed. The nominalists achieved an increasingly critical attitude towards Plato and Aristotle, more than before relying on their own research. Even more than the realists, the nominalists stressed the relevance of observation as a reliable source of knowledge. Being empiricists, they played an important part in the transition from ancient and medieval thought to the Renaissance and modern science. In its most extreme form, in which only observables have reality and laws are human inventions, nominalism probably never exerted much influence on scientists. Among the philosophers, Kant came close to nominalism. As to their form, he assumed natural laws to be a necessary product of human thought.[23] Positivists like Mach considered natural laws to be logical-economic constructs, intended to create some order in the otherwise chaotic reality consisting entirely of observable phenomena.[24] Hence they considered natural laws to be post rem.

Platonism exerted influence on Copernicus, Brahe and Kepler in the 16th and on Galileo, Descartes and Newton in the 17th century. After his works were printed in 1543, the neo-Platonist Archimedes made a deep impression by his mathematical approach to physical problems, and by his skilful use of idealized thought-experiments. In the 16th century, someone was called a Platonist if, contrary to the Aristotelians, he valued mathematics as a useful instrument in science.[25] To these neo-Platonists or neo-Pythagoreans we owe the mathematization of science. Newton’s use of the word ‘axiom’ as a synonym of ‘law’ springs from the view that science ought to be performed in a mathematical way, more geometrico. The idealistic view of universals (ante rem) is easily recognized in the idea that the laws are commands given by God to the creation, conceived of as an initially unordered reality. Descartes resolved

‘…to speak only of what would happen in a new [world], if God should now create, somewhere in imaginary space, enough matter to make one; and if he agitated the various parts of this matter without order, making a chaos as confused as the poets could imagine, but that afterward he did nothing but lend his usual support to nature, allowing it to behave according to the laws he had established.’[26]

Ostensibly, the 17th-century Aristotelians were the losers, they became the targets of attack by the adherents of new insights. Bacon, Galileo, Descartes, Boyle and many others took distance from the Peripatetics. But the realistic vision on universals, in re, comes close to the implicit worldview of present-day scientists concerning natural laws: reality is intrinsically lawful, and the laws can only be discovered in the facts.[27] The laws cannot be disengaged from reality, they cannot be found by a priori reasoning, but only by empirical research a posteriori. Below, we shall discuss the relevance of the difference between this view and the Neo-Platonic one, that matter is passively subject to laws.

The philosophy of the cosmonomic idea is not unanimous about the position of laws, although it rejects the nominalist view.[28] According to Vollenhoven the law is ante rem, he places the law between God and the ‘subjècte’ (i.e., whatever is subject to law),[29] but according to Dooyeweerd the law is in re. He says that created reality has a law side and a subject side, to be distinguished but never to be separated. Laws are not above reality.[30]

To be sure, Dooyeweerd never used the expression in re. As observed he stresses the absolute lack of self-sufficiency of the creation, to which he does not assign independent being. On the contrary, reality derives its being from the origin, the arche of everything, such that reality, both at its law side and its subject side, is characterized by meaning rather than by being.


The origin of natural laws


During the 17th, 18th and early 19th century, natural laws were generally conceived of as expressions of God’s will. In the preface to the second edition (1713) of Newton’s Principia, Roger Cotes summarized the view of natural laws developed during the 17th century:

‘Without all doubt this world, so diversified with that variety of forms and motions we find in it, could arise from nothing but the perfectly free will of God directing and presiding over all. From this fountain it is that those laws, which we call the laws of Nature, have flowed, in which there appear many traces indeed of the most wise contrivan­ce, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experiments. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of reason, must either suppose that the world exists by necessity, and by the same necessity follows the laws proposed; or if the order of Nature was established by the will of God, that himself, a miserable reptile, can tell what was fittest to be done.’[31]

The flowering physico-theology welcomed each scientific result as a new proof of the existence of a benevolent Creator.[32] The belief in God was increasingly built on the progress of science. In particular the argument of design was popular. The effectiveness and usefulness of nature demanded as an explanation the existence of a suitable building plan and a conscious designer. Both Hume and Kant rejected the argument of design, but their views being purely philosophical exerted little influence on the scientific community. Darwin definitively refuted the argument from design, not because he criticized the idea of God as a prime mover or first cause, or as a principle to explain an ordered creation, but because he explained biotic evolution on the basis of chance events.

Besides, God was required to explain all phenomena that could not be explained by natural laws. Generally, two sources of knowledge of God were acknowledged, the Holy Scripture as word revelation, and nature as creation revelation.[33] Since the end of the 19th century the two appeared to lead to contrary views, and many people started to consider science the competitor of religion, with its own view of creation, fall into sin and redemption. The 20th-century physical ‘theory of everything’ provides the temptation to find God through science.[34] In this view the biblical revelation plays no part anymore. But this pretension is subject to critique, as follows.

The aim of science is to find and explore the laws and their connections, and to design possible applications in concrete reality. Hence, the laws constitute a boundary for scientific activity. The origin and meaning of laws is hidden for science.[35] To assign meaning to reality is a non-scientific task. The search for the origin of laws is meta-physical, meta-mathematical, meta-logical, and even meta-philosophical, because it is religious. It finds its legitimacy and certainty only outside science. The Christian confession, saying that reality (both law side and subject side) is created, fallen into sin, and redeemed through Jesus Christ, is not subject to scientific or philosophical scrutiny, but finds its ground in God’s revelation only.

This belief may serve as inspiration to avoid traps, for instance fear for taboos, or attempts to take a position outside reality, or the temptation to hypostatize any aspect or part of reality. But this belief cannot serve as a starting point for empirical scientific research. Attempts to explain the idea of law and its origin in a scientific or philosophic way are in vain, because science takes the lawfulness of reality for granted. Nevertheless, the idea of law has the pretension to be universal, to hold for everyone under all circumstances. This means that the idea of natural law is not exclusively Christian, it is public. For science it is sufficient to accept the existence of laws as a starting point. Therefore, Christian science does not exist, though it is possible and may be fruitful to be a scientist or philosopher in a Christian context. The idea of natural law arose during the 17th century in a Christian community, it is a gift of Christianity to mankind, but it is not reserved for Christians.


Causality and determinism


During the 17th and 18th century natural laws were considered instruments of God’s government. Therefore law-conformity was easily identified with causality, the laws were considered to be causes, with God as the first cause. Kant and his followers developed this idea.[36] Newton assumed that the natural laws were not sufficient to explain God’s interference with the creation, without his help the solar system could not be stable. When a century later Laplace proved that all planetary movements known at the time satisfied Newton’s laws, the idea that God would correct the natural laws was pushed to the background of theological discussions about miracles. At present, causality is seen as a relation between events, one being the cause of the other, subject to laws. But a law itself is no longer considered a cause.

In the 18th and 19th century, natural laws were often identified with laws of force, interpreted in a deterministic way, as expressed by Laplace’s famous dictum:

‘We ought  … to regard the present state of the universe as the effect of its anterior state and as the cause of the one, which is to follow. [Assume …] an intelligence which could know all the forces by which nature is animated, and the states at an instant of all the objects that compose it; … for [this intelligence], nothing could be uncertain; and the future, as the past, would be present to its eyes.’[37]

Determinism believes nature to be completely determined by unchangeable natural laws, it hypostatizes laws of nature. Determinism has always been an article of faith rather than a well-founded theory, and is now refuted by the discovery of radioactivity and by the development of quantum physics and chaos theory. Scientists agree that things and events are subject to laws leaving a margin of indeterminacy, contingency or chance.




A realistic view of natural laws not only implies their existence, but also their knowability. It is important to make distinction between the laws, which govern nature, independent of mankind from laws as formulated by scientists. We shall call the former natural laws or laws of nature, and the latter law-statements.[38] Newton’s law of gravity is a law-statement, whereas the law of gravity is a natural law ruling the planetary motions. A law-statement is true if it is a reliable expression of the corresponding law.[39] Until the beginning of the 20th century, Newton’s law-statement was considered to be true, but since the acceptance of Einstein’s general theory of relativity, it is considered approximately true. The Newtonian expression is sufficient to solve many problems, and is often preferred because of its simplicity. For a similar reason one may prefer Galileo’s law of fall, which Newton showed to be an approximation of his own statement of the law of gravity.

According to some philosophers, both Galileo’s and Newton’s statements are falsified by Einstein, and therefore have become useless, but scientists have a more liberal opinion.

Indeed, in the context of a theory, being a collection of deductively connected statements, only statements which are asserted to be true can be admitted, i.e., axioms and facts which are accepted to be true and theorems which truth is to be proved.[40] This is a consequence of the law of excluded contradiction. If a theory would contain a statement, which is asserted to be false, the truth of any other statement could be derived. Obviously, this would make the theory quite useless, it proves too much. But the user of a theory has a wide choice of axioms, facts etc. For instance, when studying a falling body, for the law of gravity he is free to choose between Einstein’s, Newton’s or Galileo’s law-statement. He may assume friction to occur or not. For the deductive process the statements within a theory are not allowed to be mutually contradictory, but they may very well contradict statements which are not used in the theory. That is the basis of the use of law-statements and idealizations, which are known to be false, or approximately true.[41]

It has sense to say that a law-statement is true, or false, or approximately true, but it has no sense to say that a law is true.[42] A law is valid or holds for a specified range, which implies a relation to its subject matter. Hence, the meta-physical and meta-logical principle of excluded antinomies, mentioned above, must not be confused with the logical law of excluded contradiction, which only applies in a well-defined logical context, such as a theory.


Criteria for a law-statement


The philosophy of the cosmonomic idea never paid much attention to the question of when a statement has the status of a law-statement,[43] a question that is not easy to answer, as several philosophers have observed.[44] We don’t have a comprehensive concept of law, it cannot be subsumed under more general concepts, but we have an approximating idea of law.

Universality is the foremost characteristic. Each law-statement is a generalization, but not every generalization is a law-statement. ‘All flowers in my garden are roses’ is a universal statement, yet it is a factual statement rather than a law-statement because of the restriction ‘in my garden’. However, it is not easy to give rules for the exclusion of such restrictions. One (disputed) rule is that a law-statement must state something that is necessarily the case, but this should not be understood as a ‘logical necessity’.[45] Clearly, the fact that all flowers in my garden are roses is not necessarily so.

It cannot be required to exclude all specific data in a law-statement. For instance, ‘below 1234 K, silver is solid’ is a law-statement, because being its melting point, 1234 Kelvin is specific for silver. On the other hand, ‘below 1000 K, silver is solid’, although true and universal, is not a law-statement, because the temperature 1000 K is in no way specific for silver and can be replaced by any value between 0 and 1234 K.

The rule that a law holds independent of a certain place or time is much too strong, for the validity of a law is often restricted to certain circumstances, for instance as realized at the surface of the earth since a couple of billion years. The theory of relativity states that natural laws, besides being independent of place and time, ought to be formulated independent of the motion of the frame of reference. This might not be a general criterion for a law-statement, but a consequence of the mutual irreducibility of the physical and the kinematic aspects, providing a restriction on the formulation of physical law-statements only.

In a theory, a law-statement is not only intended to describe a certain state of affairs, it should also enable one to make predictions and explanations.[46] Therefore, it must allow of counterfactuals, it must be able to function in a hypothetical situation which is actually not the case.[47] A disposition, such as ‘glass is breakable’, applies to any glass even if it is not broken. Newton’s first law of motion, the law of inertia, is counterfactual, because bodies on which no forces act do not exist. Its validity can be established only if we apply this law in combination with, e.g., the law that forces can balance each other, which makes the statement ‘If no net force is exerted on a body, it has no acceleration’ a testable consequence of Newton’s first law. The law of conservation of energy, stated as ‘the energy of a closed system is constant’, is counterfactual, because closed systems do not exist, but it has important consequences if applied to real systems. Hence, there is some truth in Cartwright’s proclamation that the laws of physics lie.[48]

Finally, we accept a proposition as stating a law only if it is connected to other law-statements. The law of Titius-Bode should not be called a law-statement.[49] It concerns a regularity in the distances of the planets to the sun, but (apart from the fact that the stated regularity is not very convincing) nobody has ever been able to connect it to other laws.


Law and subject


Carroll observes ‘… if there were no laws, there would be little else…’ no counterfactuals, no dispositions, no causality, no chance, no explanations, no properties.[50] ‘Nearly all our ordinary concepts … are conceptually intertwined with lawhood.’[51]

In ordinary language, a law is seldom distinguished from its subject matter, but in science this distinction is abundant.[52] It is a characteristic of science to disrupt reality, of which the distinction of law and subject is the first instance. But even in science, law and subject cannot be separated; the law is in re. Knowledge about laws of nature can only be achieved by studying its subjects, e.g., in experiments or observations.

If the laws would have existence apart from their subject matter (ante rem) our knowledge of laws could be independent of empirical research. Such was the opinion of the (Neo-) Platonists, who assumed that true knowledge of the laws can be achieved on the basis of intuition and thought, or that knowledge of laws is inborn, and can be recollected by anamnesis. Generally, present-day scientists do not share this view, although some theoretical physicists expect that in the near future natural laws can be founded exclusively on logical and mathematical principles, such as symmetries.




Both Platonic idealism and Aristotelian realism were dominated by the view that the order in the cosmos is primarily rational. This was criticized by the nominalists stating that God’s power cannot be restricted by reason. The cosmos being as it is could have been different. Luther en Calvin shared the nominalist critique of rationalism, but feared that a one-sided emphasis on God’s omnipotence would lead to the idea that God’s acts are arbitrary. In particular Calvin complemented the idea of God’s power with the idea of God’s being faithful to his creation and his laws.[53] The reformers rejected the view that Platonic ideas or Aristotelian forms are logically transparent, but accepted nature to be open to empirical research, in which human thought co-operates with observation and experiment.[54]

The rationalistic views were still shared by Galileo and Descartes, albeit they had a different (i.e., mechanistic) view on what should be considered logically transparent. But Kepler’s and Newton’s laws are not intuitively evident, though derivable from the observed facts by a thorough analysis. A century later, Kant considered the laws of nature again to be ‘principles of necessity concerning the being of things’,[55] attempting to prove Newton’s law from metaphysical principles.

This is related to the supposition that logical laws are a priori valid, and so are the axioms of mathematics which can be derived from logic. However, in the 19th century it turned out that even the axioms of Euclidean geometry, the paradigm of an axiomatic theory, are not exclusively evident and non-Euclidean geometries were developed. The question of whether mathematics is a branch of logic is still not settled, nor the question of whether logic is a priori valid.[56]

The logical-empiricists distinguished logical and mathematical propositions, which are tautologies; empirical statements, being contingent; and untestable or metaphysical statements, considered meaningless. It is quite common to separate thinking and being, as if these two are entirely different, as if thought can be independent of being, as if a thinking human being can place himself outside reality, to study it from a detached position. The philosophy of the cosmonomic idea has a different view, it states that man is part and parcel of the creation, including his thought, and he cannot take a position outside reality, without prejudice. In particular, no creature can take the position of the creator, and scientific knowledge can only be gained from within the creation.

Therefore, human thought is subject to the same kind of laws as the creation as a whole; this is even a condition for the achievement of knowledge. Logical laws are laws for human thought to be considered on a par with laws of nature and mathematical laws. Whereas natural laws are conditions for the existence of atoms, plants, etc., logical laws are conditions for thought. The distinction of empirical versus tautological statements is in this view quite useless.


The justification of law-statements


From the fact that all attempts to justify the existence of natural laws on logical grounds have failed, empiricist philosophers like Van Fraassen conclude that natural laws have no existence outside an epistemological context, there are only law-statements. The logical-empiricists were mainly interested in the question of how law-statements can be justified on empirical grounds. At first being of the opinion that law-statements are nothing else but generalizations of observations, they gradually had to admit that the relation between law-statements and empirical facts is less direct. Popper, who argued that a law-statement could only be falsified, criticized their initial view that generalizations can be verified, i.e., proved by induction. Within a theory, defined as a deductively connected collection of statements, theorems are proved, starting from law-statements and some facts. Theories are tested by comparing its theorems with statements derived from other theories or from observations or experiments. It has become clear, however, that no method is conclusive, there exists no definitive proof of a law-statement. Nevertheless, the methods of science reach a level of certainty that is much higher than any other method to achieve knowledge of laws.

Whereas the logical-empiricists denied the ontological status of natural laws, they maintained the objectivity of law-statements. In that respect, after 1960 they were attacked by the historicists (Hanson, Kuhn, Feyerabend, Lakatos), stating that law-statements are historically determined, and by the social-constructivists (Latour, Pickering), who believe that law-statements are the results of negotiations between interested parties. Both deny the possibility to arrive at objectively true statements about natural affairs.

Realists agree with the logical-empiricists that law-statements are justified if they confirm all relevant facts. If a law-statement is firmly corroborated, it may be considered a true expression of a law.


Reduction of theories


Each theory has a number of basic law-like and factual statements, which cannot be proved within the theory, but serve as starting points for the deductive process. Sometimes the axioms can be proved in a different, more fundamental theory, in which case one says that the former is reduced to the latter. More often than not, the proven theorem in the fundamental theory is not identical to the axiom in the reduced theory, but shows some resemblance. For instance, Newton could derive statements that are very similar to Kepler’s laws but not quite identical. Kepler assumed the sun to stand still, whereas according to Newton the sun moves around the solar system’s centre of gravity. According to Kepler’s laws the planets move independent of each other, whereas according to Newton they influence each other’s motions. Hence, scientists say that Newton proved Kepler’s laws to be approximately true. Because Kepler’s laws were confirmed by observations, this counts as a confirmation of Newton’s theory. Sometimes it is stated that Newton used Kepler’s laws to derive his own theory, and philosophers demur that this cannot be right, because you cannot make use of statements which are proved to be false in the same theory.[57] In fact, Newton first showed that from Kepler’s laws one can find the law of gravity, and next he used that law in a new theory to derive statements which are similar to Kepler’s laws.

Philosophers deny these claims, because they do not accept a proof based on approximations.[58] They also reject the claim of physicists that classical mechanics is an approximation (at low speeds) of relativity physics. They argue that the classical concept of mass (being a constant of the motion of any object) is incompatible with the relativistic concept of mass (being convertible to energy), whereas physicists are content with the observation that at low speeds, relativistic mass is approximately constant.[59]




With respect to the discovery of laws I briefly mention three historically important views. The deductivist view represented by Descartes holds that natural laws must be deduced from clear, intuitively irrefutable principles, from which the laws would derive a rational and necessary character. Descartes knew very well that not every law can be found in a deductive way, and he recognized experiment as a secondary heuristic.[60] Newton pointed out that even the most rational concepts of mechanical philosophy rest on generalizations of experience, and he stressed the contingent character of the law of gravity.[61] This rejection of rationalism, interrupted by a short period of Kantian revival, was reinforced by later developments of science. Repeatedly one had to admit that truths, supposed to be self-evident, were repudiated by scientific research. It appears that the natural laws transcend rational thought.

The inductivist vision, represented by Francis Bacon, saying that natural laws are nothing but generalizations of observations, is at variance with the starting point of science, that natural laws are universal, valid always and everywhere. Generalization never leads to universal validity.[62] Induction needs the presupposition that laws exist, in order to arrive at universal statements of law. Hence, laws transcend human experience.

Popper criticized inductivism, stating that a scientist poses challenging hypotheses, deduces their consequences, and subject them to severe tests with the aim to discover whether or not the hypothesis should be rejected. But Popper underestimates the heuristic significance of experiments. He thinks an experiment has only a place in the context of justification, as a means to test a theory or hypothesis. Popper rightly states that a law-statement is a product of the human imagination, in which experience and rational analysis co-operate. But the laws to which these statements refer even transcend the imagination. In general, the far-reaching consequences of newly formulated law-statements cannot be predicted, and theories are usually much richer than even their inventors could imagine.

Induction, deduction and imagination are powerful means to find law-like propositions, but there are at least three more to be considered: the experimental method, the subject-subject relation, and structural laws.


Isolation of a field of science and the experimental method


More than the logical-empiricists, the historicists were interested in the heuristics of science. Kuhn observes that an important part of normal science is concerned with the solution of problems according to a generally accepted paradigm.[63] Lakatos has become known because of his methodology of scientific research programmes, in which heuristics play an important part.[64]

During the 17th-19th centuries the heuristic of natural science was characterized by the isolation of various fields of science.[65] The shift of emphasis from the essence of things to the laws relating a more or less well defined group of phenomena (electric, magnetic, chemical, thermal, optic, etc.) with their problems and theories turned out to be extremely fruitful. Under the flag of experimental philosophy, natural science made extensive use of the new experimental method, in which phenomena were studied in isolation from the rest of the world. This method relies on the idea that reality satisfies natural laws. An experiment is always performed at a certain place and time with specific instruments and well-chosen specimens, by a single experimenter, whose experimental skills, knowledge and imagination are decisive. Nevertheless, the experimental results are declared to hold for all places, times and comparable materials, independent of the personal properties of the researcher. Therefore, an experiment has to satisfy strict requirements. It must be reproducible by other scientists, using different instruments and materials at various places and times.

The experimental method is an activity transcending passive observation. In an experiment, matter is activated, contrary to Newton’s view that matter is passive.


The subject-subject relation and structures


The heuristic of science relies on the relation of a natural law and its subjects. Without knowing it, Newton laid his hands on a powerful heuristic, to wit, the inter-subjective or subject-subject relation. Each piece of matter attracts any other one by the force of gravity, which according to Newton’s third law is a reciprocal relation. If A exerts a force F on B, then B exerts a force -F on A, action and reaction being equal but in opposite directions. In the investigation of other interactions, Newton’s third law played a leading part. After the middle of the 19th century it was supplemented by the conservation laws of energy and momentum, again expressing subject-subject relations. In the special theory of relativity, Einstein emphasized all motions to be relative, being kinematic subject-subject relations. The rise of biology in the 19th and 20th centuries was largely due to the shift of emphasis from the study of species to the discovery of laws concerning genetic relations.

In the philosophy of the cosmonomic idea the subject-subject relation is a heuristic tool in studying the modal aspects.


Structural laws


Newton’s Neo-Platonic supposition that matter is passively subject to laws is also at variance with structural laws. The realist position, saying that matter is lawful, that each kind of matter has a structure, determining its conditions for existence and its functioning, found favour in atomic physics and chemistry during the second half of the 19th century.[66]

Present-day atoms are far from passive, they are structured and their lawful structure determines in which way they interact with their environment. On a sub-atomic level, too, there is no unstructured matter, not even unstructured energy. In the search for structure, symmetries, transformations and invariances play an important part.[67] The idea that everything in reality is lawful, having a typical structure determining its individuality, constitutes another powerful heuristic, both in science and in the philosophy of the cosmonomic idea.





The introduction and development of the idea of natural law, and the simultaneous downfall of essentialism, is a historical phenomenon, related to the rise of modern science since the 16th century. The idea of natural law as a starting-point for science is truly a metaphysical principle, an unprovable but undeniable part of one’s scientific worldview. The views, that natural laws exist apart from human experience, that law-conformity is a universal trait of reality, that nothing is law-less, that law and subject are intertwined and inseparable, allow us to account for the actual procedures of science, its ontology, epistemology, logic and heuristic. The view of science as an activity bounded by law makes clear that scientific knowledge is restricted to natural laws and to whatever is subject to law, and cannot be gained from any position outside reality. Hence, knowledge of God and of the origin of natural laws is outside the reach of science and its philosophy.


[1] Stafleu, M.D., 1998, Experimentele filosofie, Amsterdam: Buijten en Schipper­heijn, 30-31

[2] Barrow, J.D., 1988, The world within the world, Oxford: Oxford U.P., 59. As a precursor in the 13th century, Roger Bacon used the expression lex or regula  to describe regularity in nature, not divine decrees, see Barrow, 58

[3] Clay, J., 1915, Schets eener kritische geschiedenis van het begrip natuurwet in de nieuwere wijsbegeerte, Leiden: Brill, 42

[4] Galilei, G., 1615, ‘Letter to the Grand Duchess Christina’, in: S.Drake (ed.), 1957, Discoveries and opinions of Galileo, Garden City, N.Y.: Doubleday, 182

[5] Descartes, R., 1637, Discours de la méthode, Oeuvres VI, Paris 1973: Vrins, 41

[6] Leibniz, G.W., 1686, ‘Metaphysische Abhandlung’, par. 16-17, Hauptschriften zur Grundlegung der Philosophie (transl. A.Buchenau, 1904-06), Hamburg 1966: Meiner, II, 156-160

[7] Newton, I., 1687, Sir Isaac Newton's Mathematical principles of natural philosophy (transl.: A.Motte 1729, revised by F.Cajori 1934), Berkeley 1971: U. California P., 13; Newton, I., 1704, Opticks, New York 1952: Dover, 5

[8] Kepler, J., 1609, Astronomia nova; Neue Astronomie (M.Cas­par, transl.), München 1929: Oldenbourg, 34 (Introduction), 267 (chapter 44), 345 (chapter 58)

[9] Kepler 24 (Introduction), 247 (chapter 40). Only later on, these statements became known as Kepler’s first and second law, but in his Introduction, Kepler calls the second one a law.

[10] Galilei, G., 1632, Dialogue concerning the two chief world systems (S.Drake, transl.), Berkeley 1953, 1974, U.California P., 234

[11] Contrary to Popper, K.R., 1963, Conjectures and refutations, London 1976: Routledge & Kegan Paul, 103-107, I don’t believe Newton or Cotes (see below) was an essentialist. More than Newton, Cotes understood that gravity as a force between particles contradicts the neo-Platonic idea of matter being passively subject to laws. On essentialism, see Popper, K.R., 1972, Objective knowledge, Oxford: Clarendon, 194-196; Popper, K.R., 1983, Realism and the aim of science, London: Hutchin­son, 134-137

[12] See Barrow 58; Dooyeweerd, H., 1953-1958, A New Critique of Theoretical Thought, 4 vols., Amsterdam: Paris (henceforward: NC), I, 112-113

[13] Newton, I., ‘Letter to Mr.Bentley’, in: Thayer, H.S. (ed.), 1953, Newton's philosophy of nature, New York: Hafner, 53-54. McMullin, E., 1978, Newton on matter and activity, Notre Dame: U. of Notre Dame P., 57-59

[14] Newton, 1704, 401; McMullin, 8-9

[15] Newton, 1687, 547

[16] Fraassen, B. van, 1989, Laws and symmetry, Oxford: Clarendon, 183; Cartwright, N., 1983, How the laws of physics lie, Oxford: Clarendon

[17] Popper, K.R., 1959, The logic of scientific discovery, London 1968: Hutchinson (orig.: Logik der Forschung, Wien 1934), 438; Popper, 1972, Ch.5; Popper, 1983, 80, 118, 131-149; Bunge, M., 1967, Scientific research, Berlin: Springer, I, 345; Swartz, N., 1985, The concept of physical law, Cambridge: Cambridge U.P., 10-11: ‘the existence of determinate laws of Nature is virtually axiomatic in the contemporary worldview.’

[18] The principium exclusae antinomiae, Dooyeweerd, NC II, 37 cannot be proved by the statement that the occurrence of mutually inconsistent laws would be unthinkable, because human thought itself is subject to laws. Rather, this being unthinkable is a consequence of the said principium.

[19] Dooyeweerd, NC II, 4, 96, 99, 108

[20] Dooyeweerd, NC II, 31: ‘… ‘meaning’ is nothing but the creaturely mode of being under the law, consisting exclusively in a religious relation of dependence on God’. However, instead of defining the meaning kernel as the characteristic law for a modal aspect, Dooyeweerd tries to catch the meaning of each aspect (as well as its anti- and retrocipations to other aspects) in one or a few words, such as ‘discrete quantity’ or ‘continuous extension’. Thereby he easily falls into the trap of essentialism.

[21] Dooyeweerd, NC I, 99-100

[22] Peursen, C.A.van, 1959, ‘Enkele kritische vragen in margine bij “A new critique of theoretical thought”’, Phil.Ref. 24: 160-168, 164. Van Peursen observes that the law can also be seen as the covenant of God with his creation, as a sign of his immanence instead of his transcendence. Dooyeweerd, H., 1960, ‘Van Peursen’s critische vragen bij “A new critique of theoretical thought”’, Phil.Ref. 25: 97-150, 113 agrees.

[23] See Dooyeweerd, NC I, 109

[24] Dooyeweerd, NC I, 110

[25] Koyré, A., 1939, Etudes Galiléennes, Paris: Hermann; Galileo studies, Hassocks 1978: Harvester, 3, 36, 201-202

[26] Descartes, 42; see Westfall, R.S., ‘The rise of science and the decline of orthodox Christianity: A study of Kepler, Descartes and Newton’, in: Lindberg, D.C., Numbers, R.L. (eds.), 1986, God and nature, Histo­ri­cal essays on the encounter between Chris­tianity and science, Berkeley: U. California P.: 218-237. Westfall, 233: ‘Newton’s conception of nature still appears to me very similar to Descartes’s in the dominance of law within it.’

[27] Hübner, K., 1983, Critique of scientific reason, Chicago: U. Chicago P. (orig.: Kritik der wissenschaflichen Vernunft, Freiburg 1978: Karl Alber), chapter 9: when Huygens ‘corrected’ Descartes’ laws of impact, he thereby rejected Descartes’ criterion of truth, to view only those statements as scientifically demonstrated which are claire et distincte when considered in the light of reason. Huygens emphasized his laws of impact to be in complete agreement with experience, not as a matter of fact, but as a matter of method.

[28] Woudenberg, R. van, 1992, Gelovend denken, Amsterdam: Buijten en Schipperhe­ijn, 42-46

[29] Vollenhoven, D.H.Th., 1950, Geschiedenis der wijsbegeerte, I, Franeker: Wever , 25-26; Tol, A., Bril, K.A. (red.), 1992, Vollenhoven als wijsgeer, Amsterdam: Buijten en Schipperheijn, 55, 113

[30] Dooyeweerd, NC I, 96, 508; Dooyeweerd, 1960, 113; Hoeven, J.van der, 1981, ‘Wetten en feiten’, in: Blokhuis, P. e.a. (red.), 1981, Wetenschap, wijsheid, filosoferen, Assen: Van Gorcum: 99-122 and Troost, A., 1992, ‘De tweeërlei aard van de wet’, Phil.Ref. 57: 117-131 endorse Dooyeweerd’s view.

[31] Newton, 1687,  XXXII

[32] Lindberg, Numbers; Brooke, J.H., 1992, ‘Natural law in the natural sciences’,  Science and Christian Belief, 4: 83-103

[33] I believe that God reveals himself only through his written word as the creator and redeemer of the world, and that he is not knowable through nature. The 17th-century project to find the ‘God of the philosophers’ was already critized by Pascal.

[34] Hawking, S., 1988, A brief history of time, New York: Bantam

[35] Popper, 1983, 152-153: the origin of natural laws is a mystery.

[36] Clay

[37] Lap­lace, P., 1814, Essai philosophique sur les probabilités; A philos­ophical essay on probabilities, 1951, New York: Dover, 4-5

[38] ‘Law-like sentence’ according to Goodman, see Hempel, C.G., 1965, Aspects of scientific explanation, New York: Free Press, 265. Swartz, 4, 11, calls laws of nature ‘physical laws’ and law-statements ‘scientific laws’. In physics, many other expressions are used for law-statements, like Pauli’s principle, SchrØdinger’s equation, Gauss’s theorem, Einstein’s postulates, and Fermi-Dirac statistics.

[39] Nominalists would say that a law-statement is true if it confirms to observable facts. Realists would call this a criterion for the truth of a law-statement.

[40] Stafleu, M.D., 1987, Theories at work, Lanham, New York, London: U.P. of America, chapter 1.

[41] Swartz,  chapter 1

[42] Both Swartz, 3, and Carroll, J.W., 1994, Laws of nature, Cambridge: Cambridge U.P., 22-23, state a law of nature to be a (true) proposition, which I believe to be a categorical mistake.

[43] But see Hart, H., 1984, Understanding our world, Lanham: U.P. of America, chapter 1-2, on universality.

[44] Nagel, E., 1961, The structure of science, New York: Harcourt, 48; Hempel, 264-278, 291-293, 335-347; Van Fraassen, 25-38 discusses a dozen possible criteria.

[45] Swartz argues extensively against the necessitarian view of laws (maintaining that all laws are necessary, they express what must occur in particular circumstances), favouring the regularist view (laws express only what does occur) . See also Carroll, 24-25. Swartz, 37-38, mentions and dismisses a third and older view, the prescriptivist one that laws have been issued by God. It appears that none of these views can be proved, and the choice between them depends on one’s scientific worldview.

[46] Stafleu, 1987, chapter 2

[47] Nagel, 51; Hempel, 339; Swartz, 68, chapter 8; Carroll, 4

[48] Cartwright, 3: ‘But fundamental equations are meant to explain, and paradoxically enough the cost of explanatory power is descriptive adequacy. Really powerful explanatory laws of the sort found in theoretical physics do not state the truth’. According to Swartz, chapter 1, virtually all law-statements are false.

[49] Nieto, M.M., 1972, The Titius-Bode law of planetary distances, Oxford: Pergamon

[50] Carroll, 3, 6-10

[51] Carroll, 9-10

[52] Carroll, 3

[53] According to Calvin, God is neither subject to laws, nor arbitrary: ‘Deus legibus solutus est, sed non exlex’, see Dooyeweerd, NC I, 93, 99

[54] Deason, G.B., 1986, ‘Reformation theology and the mechanistic conception of nature’, in: Lindberg,  Numbers: 167-191

[55] Kant, I., 1786, Metaphysische Anfangsgründe der Naturwis­sen­schaft, Leipzig 1900: Pfeffer, 5: ‘Gesetze, d.i. Prinzipien der Nothwendigkeit dessen, was zum Dasein eines Dinges gehØrt.’

[56] Jong, W.R. de, 1982, ‘Logika en rationaliteit’, Phil. Ref. 47: 134-154

[57] Stafleu, 1987, 108-112

[58] Popper, 1972, 197-202; Popper, 1983, 139-144, 148. For a critique, see Finocchiaro, M.A., 1973, History of science as explanation, Detroit: Wayne State U.P. 180-188, 196-198

[59] Kuhn, T.S., 1962, The structure of scientific revolu­tions, Chicago: U. Chica­go P., 99, 101-102

[60] Descartes, 63-64

[61] Newton, 1687, 398-400. Newton’s ‘Rules of reasoning in philosophy’ represent his heuristic in condensed form.

[62] Van Fraassen, 22

[63] Kuhn, chapters 2-4

[64] Lakatos, I., 1970, ‘Falsification and the methodology of scientific research programmes’, in: Lakatos, I., Musgrave, A. (eds.), Criticism and the Growth of Knowledge, Cambridge: Cambridge U.P., 91-196

[65] Stafleu, 1998, hoofdstuk 1

[66] Popper, 1972, 196-197; 1983, 137-139

[67] Van Fraassen, 1, who apparently does not recognize the law-character of symmetries etc.





 The idea of law



5. Components of a critical realistic scientific worldview (2002)

 with special attention to the status of laws


(not published before)


A worldview is shared by a group of scientists during a historically determined period. The physicists’ worldview may differ from the biologists’. In the first half of the twentieth century the dominating worldview differs from that in the second half. It concerns a complex of usually not provable, often normative, now plausible and then controversial conceptions about the presuppositions and methods of natural science.[1]

The study of diverse worldviews belongs to philosophy, sociology and history of science.[2] Because characters as well as their relation frames are clusters of laws, I shall especially pay attention to the status of natural laws.[3]

Instead of giving a definition that would determine the essence of a worldview, I am looking for a norm, a rule that a worldview should comply with. It should represent a viewpoint with respect to at least six subjects, six components together constituting the scientific worldview.

1. In broad lines, a worldview states how the world is composed and how it changes. This is the ontolo­gical component, the context of being and becoming (section 1).[4] Conceived of as clusters of natural laws, do characters exist independent of human experience?

2. The worldview determines what sources of knowledge and what problems are acceptable. This is the epistemolo­gical component, the context of knowledge (section 2). Is it meaningful to distinguish characters in an ontological sense from the scientific formulation of our knowledge of characters?

3. The logical component of the worldview concerns what is accepted to be an explanation or a proof, the context of justification (section 3). An important part is played by theories, in which scientific formulations of laws occur. Theories serve to clarify concepts, to make connections, to derive propositions, to solve problems and to systematize our knowledge. Is there a theory available for each scientifically investigated character? When is a law statement true?

4. In the context of discovery the view of the world determines the choice of one’s heuris­tic, the art of finding law conformities, of theories and of solutions to problems, in short, the methodology of scientific research (section 4). Regarding characters, on the one hand experiments and observations come to the fore, on the other hand the use of models. Are characters manifest? How are they discovered?

5. The knowledge of characters opens up many opportunities for exploration and exploi­tation. How are natural laws applied in technology and society? This subject, related to the ethics of scientific research, is too comprehensive for a single section, hence will be left out of discussion. In the context of application I shall only deal with the distinction of natural laws and norms (section 5).

6. The final component concerns the context of the origin and of meaning. What is the origin of characters? And what is their meaning? I have discussed this part of the world view elsewhere.[5]

Of course it is impossible to summarize all scientific worldviews in a single paper. In several respects my relational philosophy corresponds with ‘critical realism’.[6] Other views will be mentioned cursorily.


1. Do characters exist?


In the history of atomic theory, up till 1900 the dominant positivist view was that an atom was merely a model, because only directly observable and measurable properties were considered to be real. Phenomena were emphasized, not characters of things or processes. In his first design of a model for a gas (1860) Maxwell was very reluctant to admit the reality of atoms. Only in his Theory of heat (1871) he accepted the atomic hypothesis.[7] In the German debate between positivist energeticists (Mach, Ostwald) emphasizing thermodynamics on the one hand and realistic atomists (Boltzmann, Planck) who put forward statistical mechanics on the other hand, philosophic arguments prevailed. But shortly after 1900 the scientific community accepted the existence of invisible atoms and sub-atomic particles, not because of philosophical arguments but on physical and chemical grounds. These concern the investigation of the electron, radioactivity, atomic and molecular spectra and Brownian motion. The discussion about quantum physics stimulated instrumentalism for some time, but at the end of the twentieth century in physics and chemistry a realist view is dominant. In biology too, positivist views of heredity, evolution, the concept of a species and the behaviour of animals (behaviourism) are replaced by more realistic ideas.

This mainly concerns ‘entity realism’, concerning the existence of things and events that are not directly observable.[8] The fact that the boundary of what is observable shifts because of new observation technologies complicates the discussion about this point.


The existence of natural laws is controversial

The ontological component of the worldview does not only concern the existence of things or events that are not directly observable. It also requires a standpoint about the question of whether reality (independent of human knowledge) is lawful. Law conformity cannot be proved scientifically. Whether someone recognizes the existence of laws depends on his or her worldview. This also applies to the not provable, hence metaphysical statement that the natural laws are consistent, that antinomies are excluded.[9]

The empirical method, presupposing regularity and directed to its discovery, is strongly anchored in the dominant worldview. Scientists respond implicitly in the affirmative to the question whether natural laws exist independent of human beings. They do that by declaring the laws found in the laboratory to hold for the universe, for all times and all places. They consider the laws of nature to be universal. Natural scientists studying the lawfulness of reality accept its existence as a starting point that can neither be proved nor avoided.

Nominalist philosophers deny the existence of natural laws,[10] realistic philosophers recognize that scientists do not invent natural laws but discover them.[11] Similar views can be found with scientists reflecting on their subject. Besides, some mathematicians defend a Platonic vision.[12]


Are the natural laws ante rem, in re, or post rem?

The discussion about the status of natural laws is comparable with the medieval controversy about the universalia, i.e. abstract, general concepts, related to the earlier mentioned essences.[13]

Followers of Plato, the idealists of the thirteenth century, like John Bonaventura, Robert Grosseteste and Roger Bacon, assumed that the observable world reflects a higher, ideal, invisible but knowable reality. The general ideas like beauty and justice are inborn. The universalia transcend the observable world, they are ante rem (before being).

Their realistic contemporaries Thomas Aquinas and Albertus Magnus were adherents of Aristotle. They believed that the forms, determining the essence of the things, could be discovered in reality by observation. The universalia are situated in being, they are in re.[14]

The fourteenth century nominalists William of Ockham, Jean Buridan and Nicolas Oresme resisted the logical necessary nature of the universalia. Whereas Platonists and Aristotelians considered the ideas or forms to be eternal, necessary, rationally determined concepts, according to the nominalists the universalia are invented by people. General concepts like animal, motion, or beautiful are merely names (nomina, hence nominalism), thought up by people, in order to make it possible to get some insight into the multifaceted reality. The world consists of individuals, of concrete things. The universalia are post rem, coming after the things that have prior existence.[15]

By their actions the nominalists achieved that scientists after 1300 became more critical toward Plato and Aristotle and started to pay more attention to their own research than to reading and interpreting ancient texts. Even more than the realists, the nominalists stressed observation as a source of knowledge. Nominalism is first of all anti-rationalistic, more inclined to empirism. It played an important part in the transition from ancient and medieval thought to the Renaissance and modern science with its empirical streak. In its most extreme form, in which only observations have reality and people invent laws, nominalism probably never found many adherents among scientists. Among philosophers David Hume and Immanuel Kant are considered nominalists, Hume because he denied the reality of causal relations. According to Kant the natural laws are products of human thought because of their form, whether necessary or not. The positivists like Ernst Mach considered the natural laws to be constructions of thought post rem, intended to create a logical and economical order in an otherwise chaotic reality entirely consisting of observable phenomena.[16]

In the sixteenth century neo-Platonism still exerted an important influence on Copernicus, Kepler and Brahe, and in the seventeenth century on Galileo, Descartes and Newton. The Platonist Archimedes, whose works were printed for the first time in 1543, made a deep impression because of his mathematical approach of physical problems and by idealized thought experiments. In the sixteenth century somebody counted as an adherent of Plato if he (contrary to the Aristotelians) valued mathematics as a tool for science.[17] To these neo-Platonists (also called neo-Pythagoreans) we owe the mathematical approach to physics. Their idealistic opinion of the universalia (ante rem) is easily recognizable in their view that the laws, preceding the (initially unordered) reality, are God’s commands imposed on the creation. Newton’s use of the word axiom as a synonym for law of nature is a consequence of the view that science should operate in a mathematical way, more geometrico.

Romanticism, German Naturphilosophie and related currents around 1800 were probably the latest expressions of idealism in science. In the idealist morphology Goethe, Owen and others sought for an archetype of a proto-plant or a proto-animal, conceived of as an idea, not a common ancestor.

The neo-Platonic idea that matter has no existence apart from God inspired the idea of natural law developing during the Renaissance. However, it took along the risk to separate the laws from concrete reality. By conceiving the law as the will of God for the creation the law seems to stand apart from the creation, as if God orders an unordered reality (‘the earth was without form and void’, Genesis 1, 1) by giving his laws. This view appears to be more Platonic than biblical.

Neo-Platonism was a reaction to Aristotle’s natural philosophy, in which every thing has certain autonomy, matter realizing its form by its potential and activity. The Aristotelians were the apparent losers, during the Renaissance they were the targets of attacks by the adherents of new insights. Bacon, Galileo, Descartes, Boyle, Newton and many others considered themselves neo-Platonists, taking distance from the Aristotelian ‘peripatetics’. But already in the seventeenth century the neo-Platonists met with some opposition.[18]


Critical realism is the best fit to scientific practice

Yet the realists’ vision on the universalia, in re, appears to be the best fit to the implicit view of present-day scientists about natural laws. According to this view reality is intrinsically lawful. The natural laws take part in reality. Kepler did not find his laws by rational arguments prior to facts (a priori), but by making generalizations (a posteriori) from prior empirical research.

This realism concerns both generally valid laws and specific characters. If we say that the earth is larger than the moon, or that the sun has a distance of 150 millions km from the earth, or that the earth moves around the sun, or that an atomic nucleus attracts an electron by an electric force, or that a plant descends from another plant, or that a dog observes a cat, we intend to express a reality that is subject to regularity. Likewise, the structure of a mathematical group, a spatial figure or a harmonic oscillation, the composition of a molecule, the function of the roots in a plant or the nervous system in an animal are considered realities which character is open to empirical research.

The reality of relations, things and events (whether or not observable) cannot be separated from their law conformity. It makes no sense to speak of distances without having a metric. It is meaningless to debate the reality of quarks or genes without considering the laws to which they are subjected. In that respect entity-realism falls short. Electrons are discovered at the end of the nineteenth century and further research revealed their properties gradually. An entity realist will not deny that electrons existed even before their discovery, having the same properties that we ascribe them now, and probably this applies to every sober scientist. But then it is inconsistent to recognize the subjective existence of electrons apart from human experience, but deny the existence of the laws to which they are subjected.

Nominalists denying the existence of electrons including their law conformity independent of human experience will have trouble interpreting scientific theories about the astrophysical evolution. It would be consistent if they denied the possibility to establish that such an evolution has taken place in fact. They take a position comparable to that of extreme creationists, stating that God created the fossils together with the earth, such that it appears that the earth is much older than the supposed age of 10.000 years or less.

If questioned many scientists will take an agnostic attitude towards the existence of natural laws apart from human experience. In fact, this is not a scientific but a philosophical question. Scientific practice accords with critical realism, providing the best philosophical explanation for the empirical and theoretical success of twentieth-century science (including its technological applications). This explanation assumes that science represents reality in a fair and adequate (but not perfect or complete) way.


Whether a natural law holds is determined by other natural laws

Among other things, critical realism implies that science should never absolutize any law. Natural laws are mutually coherent and they do not hold independently. Each assumption about law conformity is always open to renewed critical research in new circumstances. Maybe not a single natural law holds absolutely. The law of conservation of energy is restricted by Heisenberg’s relations, the second law of thermodynamics by statistical fluctuations, and the translation symmetry of a crystal by its finite dimensions. Physical and biotic characters are only realizable if circumstances permit.

Such restrictions are lawful themselves, they mean that reality is full of laws that cohere with each other, that relativize each other, but also reinforce each other. An unavoidable consequence is that we shall never know the natural laws completely. That is the subject matter of the next section.


2. Knowledge of characters


The epistemological component of a scientific worldview points out which problems are relevant, what sources of our knowledge are available to solve our problems and which hypotheses are acceptable. The theory of characters is critical and realistic, it assumes that scientific theories about characters concern the world as it is. It assumes that the world is knowable according to mutually irreducible relation frames, playing an important part in the primary, secondary and tertiary typification of characters. It is an empirical theory, deriving its knowledge from the results of the various sciences. It is not dogmatic but critical, amenable to corrections. The next question is from which sources the sciences receive their knowledge.


A natural law should be distinguished from its formulation

The epistemological component of the scientific worldview concerns the human knowledge of reality. A realistic view on natural laws implies that the laws exist as well as that they are knowable. It is important to distinguish between laws that govern nature independent of human beings from laws as formulated by scientists. I shall call the first natural laws and the second law statements.[19] Newton’s law of gravity is a law statement having a function in various theories, whereas the natural law of gravity determines how planets move. The question is whether Newton’s law statement adequately represents the natural law of gravity. Until the beginning of the twentieth century the answer to this question was affirmative and Newton’s law statement was called true.[20] Since the acceptance of Einstein’s general theory of relativity we assume that Newton’s law statement does not strictly agree with a natural law, although in many cases the difference with Einstein’s formulation is so small that Newton’s law statement is considered to be approximately true. In practice it is often favoured because it is easier to manipulate than Einstein’s theory of gravity. In fact, this applies to the even simpler formulation by Galileo as well.

Different equivalent formulations of the same laws occur frequently in science. The character of number sets (see sections 2.1-2.3) can be axiomatized in various ways, and quantum mechanics has several representations.


Criteria for a law statement are not readily available

The question of when a proposition may have the status of a law statement is not easy to answer.[21] We do not have an all-encompassing concept of a law. Laws cannot be grasped in terms of more general concepts; at most we have an approximate idea of laws.[22]

Each law statement is a generalization, but a generalization does not always refer to a natural law. The generalization ‘all flowers in my garden are roses’ is not considered a law statement because of the restriction ‘in my garden’, but it is not easy to define such inadmissible restrictions. A law statement should not be restricted to a stipulated number of individuals, place or time. Moreover, relativity theory states that physical laws ought to be formulated independent of a specified state of motion. But whether a natural law holds may depend on specified circumstances, like temperature or the presence of oxygen, and circumstances depend on time and space. This difficulty may be overcome by mentioning the circumstantial conditions in the formulation of the law.

A statement pretending to represent a natural law is not merely a description of a state of affairs. It ought to be instrumental in predictions and explanations as well. It should admit of ‘counterfactuals’, capable of functioning in hypothetical situations that are in fact not the case.[23] Besides stating what actually happens, a law ought to state what would happen if certain conditions are fulfilled.[24] In that case a law states a disposition, and we have seen how important dispositions are for the theory of characters. For instance, ‘glass is breakable’ applies to a glassy object that is not broken. Newton’s formulation of the law of inertia ‘Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it’ is counterfactual as far as bodies on which no forces act do not occur, for gravity is everywhere. The validity of the law of inertia only comes to the fore in combination with other laws, for instance with the law that several forces may balance each other. The statement ‘If all forces on a body balance each other, it continues in its state of rest, or of uniform motion in a right line’, is now a testable consequence of the law of inertia. Likewise, the law of conservation of energy (‘for each closed system energy is constant’) is a counterfactual, because closed systems do not exist. But the law is relevant for systems that are not closed as well, for the net input of energy must equal the increase of the system’s total energy. Hence there is some truth in Cartwright’s statement that the (general) laws of science lie.[25]

Arbitrariness, too, should be avoided in a law statement. The statement ‘below 1234 K silver is solid’ as a part of the character of silver is an adequate representation of a natural law, for 1234 K is the melting point of silver. The statement ‘below 1000 K silver is solid’ is just as universal and true, yet it does not represent a natural law, because the value 1000 K is arbitrarily chosen and exchangeable by any other between 0 and 1234 K.

Next we accord a proposition only the status of a law statement if it is not isolated but has a demonstrable connection to other accepted law statements. The law of Titius and Bode should not be called a law.[26] It concerns regularity in the planetary distances from the sun, but (apart from the fact that this regularity is not very convincing) nobody has ever succeeded in connecting it to other natural laws. It has been suggested that the stability of the solar system depends on the formulated rule, and if that turns out to be true it may yet receive the status of a law statement. The implicit but not provable supposition that natural laws form a coherent whole apparently belongs to the scientific worldview.

Conversely, a law statement may be derivable from other ones, for a law is not irreducible as such. For instance, the conservation laws are reducible to lawful symmetry relations.

Finally, the standpoint that a law statement should universally hold with respect to a specified set of subjects or objects should be interpreted carefully if it concerns statistical laws, e.g. the laws for radioactivity. The statement that radium-226 has a half time of 1600 years says that in a specimen after 1600 years half of the radioactive atoms have decayed. This statement is tested so well that we may safely call it a law statement. If we would formulate the same law for a single atom, we get a probability statement: for all radium atoms, an individual atom has a chance of 50% to decay within 1600 years. This statement cannot be tested, but it is acceptable because it agrees with the earlier formulation that is testable.


Laws presuppose subjects

About the importance of laws Carroll observes: ‘… if there were no laws, there would be little else …’[27]: no counterfactuals, no dispositions, no causality, no probability calculus, no explanations, no properties, no understanding of things.[28] ‘Nearly all our ordinary concepts … are conceptually intertwined with lawhood.’[29] Ordinary parlance seldom distinguishes a law from its subjects, this only occurs in science.[30] It belongs to scientific practice to disentangle reality, and thereby the distinction of law and subject (what is subjected to the law) is extremely important.[31] But even science cannot separate them, because a law expresses itself in its subjects, it is in re. We can only have knowledge of a law by researching individual subjects, for instance in observations or experiments.

If a law would have a separate existence (ante rem) our knowledge of laws could be independent of the research of subjects. This is the view of the (neo-) Platonists, assuming that knowledge of laws is possible based on intuition and deep thought, or that the knowledge of laws is inborn, capable of emerging from the subconscious mind by interrogation. Usually, scientists do not share this view, although some theoretical physicists expect that in the near future it will be possible to base natural laws on logical and mathematical principles, such as symmetry. Since the seventeenth century natural science is empirically inclined, it finds and tests law statements by observation and experiment, sustained by reasoning and computation.


Natural science rejects ratio as well as revelation as sources of knowledge

Being empirically inclined, natural science rejects two sources of knowledge categorically. The first is human ratio, being accepted as one of the most important instruments of achieving knowledge, but not as an autonomous source of knowledge. Besides Aristotle even Descartes still believed that scientific knowledge should start with clear and well-distinguished ideas, being self-evident. Newton criticized this rationalist view, and in his Principia he set the tone for an empirical method. In philosophy rationalism is still alive, but in science it belongs to the past. Of course a scientist makes use of his thinking ability and of theories as logical instruments that he develops himself. But a scientist is not bound to a certain type of instrument to achieve his goal. He observes reality, manipulates it in an experiment and transforms it in technology, being instruments of research as well.

Second, the prevailing science rejects the revelation in the form of the Bible or the Koran as authoritative sources of knowledge for scientific research, albeit that they inspire many scientists in their search for truth. This rejection already started in the seventeenth century, when the Royal Society at London decided not to discuss theological problems. Yet natural theology influenced science well into the nineteenth century and it still plays a part in discussions about evolution theory. Only in the twentieth century the scientific community consensus arrived at a consensus about the non-admissibility of sources invoking an authority that is not open to independent scientific research. Of course, each historical document may serve as a source of knowledge, e.g. about astronomical observations performed in past centuries, if these are open to the same kind of critical research as is common with respect to present-day data.

The two rejected sources of knowledge have in common that they take a stand outside the empirical reality. They are both foundationalist, if by foundationalism one understands the view that science is founded by irrefutable truths. By its method science restricts itself to experience that can be achieved from within the cosmos. Scientific experience is fallible and imperfect. It requires continuing critical research.


The research of characters is controlled by problems

Each measurement, each calculation, each observation, each change of a theory, is intended to solve a problem. Each form of knowledge is an answer to a problem. Important sources of knowledge for scientific research of characters are observation and experiment. An important source of knowledge for mathematics is human imagination, which should neither be underestimated for natural scientists. Scientists get much knowledge from each other, from their memory or that of their colleagues, and from the collective memory consisting of books, periodicals and data files. The mutual discussion, oral, written or electronic, is an important source of scientific insight. Because of the interlacement of characters and the possibility to project relations on each other, a large amount of division of labour is possible and fruitful. Biologists make use of the results of chemists, who in turn profit from physical insights, and all natural scientists apply mathematics.



3. The truth about characters


The logical component of the scientific worldview concerns argumentation. For the delivery of proofs theories are the most important instruments. A theory is a man-made artefact.[32] With each scientifically investigated character corresponds at least one model in the form of a theory. For each character to be investigated a scientist devises a theory, in which he or she formulates the character’s laws and deduces their logical consequences. In the empirical research of the character this theory plays an instrumental part.


A law statement requires proof

What kind of proof justifies the formulation of a law? As successor to the positivism of Mach and others logical-empirism dominated the philosophy of science during the first part of the twentieth century. It was especially interested in the question in which manner scientifically found law statements can be justified on empirical grounds. Law statements were considered to be generalizations of observations functioning as universal statements in a theory. The most important problem was how to determine whether these statements are objectively true or false. Popper took a special position. He denied the possibility to verify statements and in stead posited that each scientist ought to make bold conjectures, next attempting to falsify them.[33] Science only progresses by trial and error. The difference between Popper and the logical-empirists is less than Popper assumes and scientific practice steers a middle course. Absolute certainty about law statements cannot be achieved, but the empirical method of the natural sciences is capable of leading to a high degree of certainty that cannot be achieved in any other way. In this process falsification of universal statements plays a part as well as verification of facts. Besides the empirical proof resting on conclusions drawn from observations and experiments one accepts as a test the agreement with other accepted law statements, according to the metaphysical principle that excludes antinomies (see section 2).

A theory derives a law statement from one or more other statements. Sometimes this concerns a proposition that functions as an axiom in another theory. Sometimes the proven statement turns out to be slightly different from the earlier law statement that was accepted as an axiom. Based on his laws of motion and of gravity, Newton proved that Kepler’s laws are approximately true. The approximation is so good that physicists are inclined to say that Kepler’s laws are reducible to Newton’s. Historists like Hanson, Kuhn, Feyerabend and Lakatos reject this claim, because they do not accept a proof by approximation to be valid. They also contest the view, generally held by physicists, that Newtonian classical mechanics is a good approximation of the theory of relativity, this time arguing that concepts like mass would have different meanings in the two theories. This follows from the fact that mass according to Newton is a constant, whereas according to Einstein it depends on the state of motion.

Although the logical-empirists sometimes expressed themselves negatively about the existence of natural laws, they held fast to the objectivity of law statements. After 1960, this view drew fire from the same historists who assumed that scientific insights are historically determined, and from the social-constructivists (Bloor, Barnes, Latour) who (in short) stated that scientific insights come about by negotiations between interested parties.[34] Both historists and social-constructivists underestimate the possibility to arrive at objectively true statements about nature, in particular about the lawfulness of nature. Clearly, what one accepts as proof depends on the worldview one adheres to.


Logical discussion is subject to norms

Logic implies making distinctions and connections subject to laws. One of the most important logical distinctions is that between the truth and the falsity of a statement. Therefore the most general function of a theory is to prove that a statement is true or false.

With respect to logical laws, too, it makes sense to distinguish between subjects and objects. A logical subject is a human being who argues, a logical object is that what the reasoning is about, for instance in the form of a statement. The logical subject-subject relation can be described as a discourse, as deliberation or discussion between partners who try to achieve agreement by argumentation. They ought to stick to the logical norm that it is allowed to contradict others but not oneself.

This formulation deviates from the current law of excluded contradiction, stressing a subject-object relation. Again the logical law is a norm for the thinking subject, but now it concerns an object: a statement or a theory should not contain contradictions. However, the received formulation neglects the subject-subject relation, in which contradiction plays an important part. Whoever forbids contradiction appears to be authoritarian. An interdiction of contradiction, conceived of as an interdiction of a difference of opinion, leads to an untimely end of a discussion. But who in a discussion is caught to contradict himself runs the risk of losing the debate.

Apparently logic concerns ‘thinking about …’, stressing the subject-object relation. Who wishes to give priority to the subject-subject relation observes that logic concerns persuasion, argumentation and discussion between two or more logical subjects, attempting to achieve agreement about something about which initially disagreement existed. In this way they bring about a rational order in their environment. This may occur in a direct, informal way or in an indirect, formal way with a theory as an intermediary.


Each theory functions in three logical relations

As a logical instrument a theory is a product of human formative labour, it is an artefact. The formation of theories is part of human culture and has a history. It functions in three logical relations:

In a logical subject-object relation a theory is an instrument between the logical subject (the user of the theory) and the logical object, for instance a character. Each theory has both a logical form and a non-logical content. To the latter category belong observations, for instance. A theory only contains statements, but such a statement may concern an observation.

In a logical subject-subject relation, i.e. an argument, a discussion or a debate, a theory functions as proof. The participants in the debate have to agree about the starting points and methods of proof (otherwise the discussion makes no sense), and must try to convince each other about matters of initial disagreement.

The participants in the debate are bound to logical rules or laws. A theory is indirectly subjected to these rules, and therefore functions in a logical law-subject relation.

In all three relations logical subjects are involved. We cannot consider theories apart from the people using them. Strictly speaking a theory itself is not a logical object (unless we think about a theory) but a logical instrument.


In science truth is relational

In a theory about a character, law statements rather than natural laws have a function. Hence, for a theory it is not necessary that a law statement strictly corresponds to a natural law. Often a law statement representing a natural law approximately is sufficient. For the law of gravity one may use Galileo’s, Newton’s or Einstein’s formulation, but not two of them simultaneously, because logically they contradict each other. The user of a theory has a large freedom in choosing his starting propositions, as long as these do not contradict each other.

Concerning law statements a relational realist philosophy may discern at least four kinds of truth.[35]

1. In a logical subject-subject relation the participants in the debate stipulate (often tacitly) which starting points they take for granted. This is a conventional conception of truth. Such an agreement may be hypothetical (‘suppose that Goldbach’s hypothesis is true’), or may rest on long time scientific research (‘according to the law of conservation of energy …’), or appeals to an authority (‘according to Einstein all motions are relative’), or it makes a choice (‘let us start from Euclidean geometry’). With respect to a theory the truth of axioms rests on a convention, not on evidence like Aristotle assumed. A conventionalist absolutizes the conventional conception of truth, not accepting other kinds of truth.

2. In the logical context of a theory law statements are true or not true, tertium non datur. This concerns the logical conception of truth: a proposition is true if it follows from statements accepted to be true by the users of the theory. Logical truth is a relation between statements, depending on the theoretical context. The same statement may be true in one theory and false in another one. Who absolutizes the logical conception of truth may be called a logicist.

3. According to scientists a law statement is often only approximately true.[36] Now they do not mean a logical truth but an epistemic truth, i.e. the agreement (hence a relation) between a law statement and a natural law. Epistemic truth concerns the question of whether our knowledge of a law is adequate. The fact that epistemic truth is not directly testable[37] provides the nominalists with an argument against the existence of natural laws. Some realists absolutize the epistemic conception of truth, believing that every theoretical statement should have a counterpart in reality and assuming that besides law statements natural laws themselves can be true.[38] Critical realists accept that an epistemic truth has a provisional nature and is always subject to criticism and revision. Clearly, it makes no sense to assert that a natural law is true, rather it holds on a certain domain.

4. The epistemic agreement between natural law and law statement can only be tested by means of a fourth relation, the agreement between a law statement and one or more statements about facts. This is the empirical conception of truth, absolutized by empirists. Only because of an empirical truth it is possible to establish whether our knowledge of natural laws is adequate. An empirical truth too is tentative, because we can never know all facts and our insight in facts is limited and fallible.[39]


For each theory consistency is a norm

A theory must satisfy the law of excluded contradiction, that is a norm for its users. Within the context of a theory a statement and its logical contradiction cannot both be true. The restriction within the context is very important. In different theories statements may occur that contradict each other, but within a theory this is not admissible. From a combination of a statement and its denial any proposition can be proved, and the theory would lose its effect.[40] A theory ought to be consistent, devoid of contradictions. A statement in a theory that is considered false within the theory’s context, is already a contradiction. Therefore, one has to assume that the unproven starting propositions in the theory are true in a logical sense. Only then we can maintain that every proposition that has been proved by logically valid means is true, just as true as the theory’s unproved starting propositions.[41] Hence, logical truth is relative to the theory to which it concerns. Logical truth is contextual, dependent on the context of the theory. Theoretical reasoning has a relative meaning.

The consistency of a theory rests on the logical truth of statements, not on their epistemic truth. If Euclidean geometry is consistent, this does not exclude the consistency of non-Euclidean geometries. Presumably, classical mechanics is consistent, but the epistemic truth of its axioms is refuted by the theory of relativity and quantum mechanics. Only for quite simple theories consistency can be proved, but such proofs are not available for arithmetic, Euclidean geometry or classical mechanics.[42] Hence, consistency is not a fact but it is a norm: in no theory a demonstrable contradiction is admitted.

The statement that only true statements are admissible in a theory is therefore not intended to proclaim some kind of absolute truth. We don’t even need to believe that all statements are true. We accept their truth only for the sake of the discussion, for instance, in order to be able to solve a problem. Theories are instruments producing proofs. People use theories to achieve unanimity about statements they keep for true. Somebody says ‘let us assume that, …’ and the discussion can only proceed if the other participants agree to accept this proposal, even if temporarily.

Users of theories are free to determine their context and within this context to decide what they want to accept as true. Often, in a theory one accepts statements that are known to be false or merely approximately true in another context. In a theory about planetary motion we assume now that the earth is point-like and then that it has a perfectly spherical shape, although we know that both statements are contradictory to each other and both false. The subjunctive method, the use of counterfactuals, statements known to be false outside a given context, is so general and fruitful, that we cannot afford to overlook it. It is important for discussions about characters as well, because our knowledge of characters is often restricted to a model, even if we know it to have little resemblance to reality.


The logical character of a theory rests on deductive ordering

What is a theory? The Greek word theoria (related to our word theatre[43]) means something like contemplation, but the earliest Greek philosophers already related theoria to rendering proofs, to deductive reasoning.[44] Foundationalists suppose that a theory must start from known and generally accepted truths or evidences, others assume that a theory should start from new and bold conjectures, through reasoning leading to verifiable or falsifiable conclusions. Neither the movement from the known to the unknown nor that from the unknown to the known is exclusively characteristic of a theory.

As far as the logical structure of a theory is concerned, I propose the following definition: A theory is a deductively ordered set of true statements.[45] Some of these statements are accepted to be true, serving to prove the others to be true as well. Hence it is not just a collection of statements, but one characterized by its deductive ordering.[46] It means that each statement in the set is directly or indirectly connected to all other ones, through a deductive argument, a deduction. This leads automatically to a criterion to decide whether a statement belongs to a theory. A statement belongs to a theory if and only if it takes part in the deductive process in the theory.[47]

Proof is not only subject to the above mentioned principle of excluded contradiction, there are much more rules, like syllogisms, modus tollens, modus ponens, argumentum ad absurdum and complete induction.[48] Circular reasoning is a method of proof that is generally rejected, yet much applied. The paradigm of a theory is Euclidean geometry, but there are not many sciences that bother to follow this enlightening example. What I described as a theory is a model, an idealization. The daily practice of scientists is far less formal than the given definition of a theory suggests. In science arguing is almost as informal as elsewhere. However, the formal definition is needed in order to investigate the logical structure of a theory.[49]

For instance, the definition teaches us that a theory is not a narrative. A story is a set of statements, too, giving a description of a state or an event without proof, without making deductive connections. It demonstrates how something could have been or could have happened. In particular about biotic evolution narratives are told, e.g. about the emergence of living beings, the manner by which a species adapts itself, or how humanity evolved from the animal kingdom. As long as it is clear that a story does not provide a proof there is no objection to stories. A narrative may clarify or elucidate things, even theories.


Theories are useful for the research of clusters of laws

Some propositions in a theory are law statements; others referring to individuals are data. Therefore a theory is a suitable instrument to investigate clusters of laws like characters and their relation frames.

A theory about a character (like that of hydrogen atoms) or about a relation frame (like that of thermodynamics) must not be confused with the character or relation frame itself. First, this would be a category mistake. A theory is not a cluster of laws but a set of statements. Second, natural characters and their relation frames are not invented but discovered by people, whereas a theory is a human product. Third, each theory has an approximate nature; its statements represent reality imperfectly. Often this comes about because our knowledge is limited, but sometimes we apply consciously simplifying propositions, in order to facilitate the solution of problems. For a theory is not only intended to connect statements in a logical sense.

The primary logical function of a theory is to prove propositions starting from axioms characterizing the theory, from propositions derived from other theories and from data. But a theory is an instrument to achieve a certain goal as well, and this goal is generally speaking not logically determined. Non-scientists use theories as well, in daily life, in technology, in the application of justice, in politics, arts and journalism. In the investigation of characters, the aim of a theory is to identify and make connections, to predict and to explain, to solve problems and to process information. As a logical instrument a theory is a historically determined artefact and the formation of theories is a historical process. The formation and use of concepts, statements and theories requires the availability of language. These are six secondary functions, related to projections of the logical relation frame to the relation frames preceding the logical one. I have discussed these secondary functions elsewhere.[50]


4. Scientific research of characters


The next component of the scientific worldview is heuristics, the art of finding solutions to problems and to formulate laws, the method of science. Heuristic is derived from the Greek word heurèka, I have found. Heuristic is related to the history of science, to the scientific opening up of reality, extending the horizon of human experience. Scientific research is like an exploration expedition changing reality. Science and technology are closely tied and there is no need to argue that technology has changed our environment enormously. Without instrumental technology, natural science would never have achieved its present level.[51]


Natural laws are transcendent in several ways

With respect to the discovery of natural laws I shall shortly review five visions.

According to the view represented by René Descartes and other rationalists, law statements follow from clear, intuitively irrefutable principles, being rational and inescapable.[52] Isaac Newton pointed out that even the most rational assumptions of the mechanical philosophy depend on generalizations of experiences. He stressed that his formulation of the law of gravity was contingent.[53] Later developments in science confirmed the contingency of natural laws and contributed to a weakening of foundationalist rationalism, recognizing that many statements conceived to be self-evident are not tenable. Clearly laws transcend rational thought. But rationalism is tough. The resistance to the duality of waves and particles in quantum mechanics originates from the rationalist view that something cannot essentially be a wave and a particle at the same time.

The second view, represented by Francis Bacon and other inductivists, assumes that law statements are merely generalizations of observations. This is contrary to the assumption that natural laws are universal, holding always and everywhere, transcending all observations being bound in time and space. The problem of inductivism is that generalization of experience alone never leads to universality.[54] Only the assumption that laws exist together with induction may lead to acceptable formulations of natural laws. But the supposition that laws exist can neither be proved by induction nor by deduction. Natural laws transcend experience.[55]

Karl Popper criticized inductivism by stating that a scientist poses bold conjectures, deriving consequences and testing them in order to find out whether the conjecture is warranted.[56] Law statements spring from the imagination of people in a process making use of experience and rational analysis. But the laws to which these statements refer even transcend human imagination. In general, the far-reaching consequences of newly formulated law statements are not predictable. A fruitful theory solves more problems than was intended by its designer.

As a fourth view I propose that natural laws be in re. Being unbreakably connected to matter, laws can only be found in the cosmos itself. Metaphorically the laws form the upper side of reality, transcending everything else. People are bound to laws as well and are unable to transcend them. We know only one universe of which we are a part. We live in it and cannot escape from it, even in our imagination, thought or research. Scientists investigate the world from within, meeting the natural laws as an upper boundary.

Finally it may be observed that scientific research is not always directed to nature, but to artificial situations as well, in experiments and in instruments, meaning that science transcends nature. The theory of waves and oscillations is found by studying musical instruments, pendulums and oscillating strings. Electromagnetism is mainly concerned with artificial circuits. Many elementary particles only exist in particle accelerators. Research of stars, of living cells and of the nervous system is only possible using advanced apparatus.

Induction, deduction and imagination are powerful means to find law statements, but all three stress too much the significance of theories in scientific practice. It is a typical philosophical prejudgement to assign theories a more important role than other instruments of research.[57] However, a large part of scientific practice in laboratories, observatories and the field do not concern testing of theories, but exploring reality, in particular the investigation of characters, their relations to other characters and their possible applications.


A research program consists of a sequence of models

A model summarizes the scientific knowledge of a character. For practical reasons we often present a character simpler than it is, for instance to explain it to others, or because calculations are only possible in a simplified model. Bohr’s atomic model is an example. A model is often descriptive; it may even be literally a picture, for instance a diagram of the double helix structure of DNA. But in science a model is foremost a theory and in the investigation of characters models play a heuristic part.

The word model has several meanings. As a consciously simplified theory about a character a model meets the demands and abilities of its designer. The model must allow of being applied, it should not be so complicated that it has no use. The problem to be solved determines the complexity of the model. Therefore the model agrees in a restricted way with the character concerned, it is known to be imperfect. It abstracts from details not needed to solve a given problem.

But being a scientific model it has a certain abundance as well, containing more details than will be necessary in the end, because beforehand it is not known which details will lead to a suitable solution. The model should be complicated enough to address interesting problems as well as simple enough to make their solutions possible.

For the research of characters it is necessary that each model can be replaced by a new one, suited to solve new problems. The method of successive approximation approaches a complicated character in a sequence of models, such that each step is feasible as well as testable, and such that each model teaches how to make the next step. Each model refers to phenomena fit to show whether the model works, within which limits it works, in which respect it does not work and in which way it should be corrected. In the succession of models one often finds a change of roles. Something serving as an explanation (an explanans) in one model may become a problem, something to be explained (an explanandum) in a later model. Sometimes successive models are planned in a research program.[58]

Lakatos made clear that such a research program only works if both a positive and a negative heuristic are present. The negative heuristic defends the hard core of the program against external attacks, attempts to refute a model. Because the model is consciously simplified, refutation is never difficult; each model is ‘born refuted’. The negative heuristic ought to make clear that refutations of this kind are irrelevant. The positive heuristic points out how the program generates new problems, solving them by devising new models. A research program achieving no more than warding off external attacks degenerates. But it is progressive if it is fruitful in solving its own problems.

The model as an imperfect representation runs the risk to be overestimated in realism and underestimated in positivism. Extreme realis­m requires that a model in all details corresponds to the character concerned and that the sequence of increasingly complicated models approaches it more and more. Positivists would counter that a character apart from our knowledge is not knowable, hence the requirement that a model resembles a character is not verifiable and should be rejected. As usually steering a middle course, science applies the norm that experiment or observation should test each model, within boundaries given by the model itself.

In the past people required a model to be graphic. But models in twentieth century science are no more graphic. This leads to a distinction of scientific from didactic models, which should still be graphic. For many nineteenth century physicists a model could only be accepted if it was mechanical.[59] After physics was forced to abandon the mechanist worldview this requirement fell into disuse as well.

A practical demand is the availability of sufficient data to construct and test a model of a character. A research program aims at acquiring such data, but there is no warrant that it will succeed. Some problems remain unsolved for lack of data. This applies in particular to historical events, if the necessary data are lost. In the theory of evolution this may concern the problems of the emergence of the first organisms, of eukaryotes, of differentiated plants and animals and their sexuality, if fossils provide insufficient data to construct testable models furthering research. Models in a research program differ from speculative models about how things could have happened. For the aim of a heuristic model is to promote research, not to satisfy curiosity by hypotheses that cannot be tested.


In empirical science a specimen is a model for a character

The word model is also used for a specimen or a sample taken from a class of similar things or events. In a publication the author describes the properties of the investigated specimen, not because the individual experiment would be very interesting, but because it is a representative example of the character discussed. Science demands experimental results to be reproducible. By studying different specimens of the same character scientists should find the same results. The used specimen is a model for all other specimens that in comparable situations should lead to the same results.

Empirical research is always exemplary. The selected specimen, acting as a model, displays the lawfulness that one wants to study. The investigator assumes that law conformity exists, that it is reflected in the observable properties of his specimen and that he can find law conformity in his experiment.

According to an inducti­vist philoso­phy, popu­lar during the nineteenth century but strongly contested in the twentieth century, one finds law conformities by generalization (induc­tion) of a number of similar observations. Much experimental research is not induc­tive in this sense. Often, an investigator restricts himself to a single specimen, having good reasons to assume it to be a suitable model. The only reason for repeating the research is to find out whether the specimen is sufficiently representative.

Research of a single specimen is not sufficient if one wants to investigate the variation allowed by a character. In that case the specimen is replaced by a sample, selected such that the acquired results are suitable for statistical processing.


5. The application of characters in freedom and responsibility


The view that technology is applied science appears to be contradicted by historical facts, demonstrating that scientific knowledge depends on the development of corresponding technology.[60] The scientific acquirement of knowledge is strongly dependent on technical apparatus. Moreover, technology itself is an inspirational source of problems. This includes the investigation of characters. On the one hand science applies technical means to explore characters, on the other hand technology uses scientifically achieved results to exploit characters.

In this section I shall only comment on the distinction and relation between natural laws and norms. My comments concern the way people deal with characters being clusters of natural laws. Norms cannot be demonstrated scientifically but they play an important part in science and technology. Hence, they belong to the scientific worldview. Science and technology are not free of norms and values.


Responsibility characterizes human activity

Physical things and events, plants and animals are determined by a character, a cluster of specific laws to which they are subject and by which they are distinguished from each other. Human beings do not have a character in this sense. They are not first of all characterized by a cluster of specific laws, but by an entirely different relation to laws. People are conscious of regularities; they know laws, formulate existing laws and devise new laws. People are able to formulate laws as law statements and to analyse them logically, to develop new characters and to implement them according to their own insight.

For a human being laws are not always compelling, not imperative. Besides natural laws, norms hold for people, who have a certain freedom to decide whether to act according to a norm or not. Contrary to animals, people are responsible for their behaviour. The norms developed by humanity itself condition human responsibility, the way people satisfy the laws. Men and women recognize their calling to bear responsibility in freedom, to justify their actions, because they have knowledge of good and evil.


People experience good and evil

The notion of good and evil stood at the cradle of humanity. For physical and chemical things, plants and animals, natural laws are imperative. The fact that animals are capable to learn means that they have a sense of regularity (see section 7.5). Besides having knowledge of laws, people have the disposition of considering them to be normative. Besides lawfulness, humanity distinguishes good and evil in the animal world and its environment.

An example is the phenomenon of illness of plants and animals. As such, illness is a natural process, one man’s meat is another man’s poison. Only from a human point of view illness is evil. A man or a woman feels the urge to combat illness of plants, animals and human beings. Also the struggle for life achieves a normative sense only in humanity. In the organic world death and extinction are as natural as germination and development. Only people take care.

An animal accepts the world as it is, as a given fact, but people try to improve the world. Men and women feel the calling to combat evil that they recognize in the living world including humanity. People experience a responsibility for the world, for plants and animals, and for humanity itself. This notion of being called to responsibility forms the heart of human existence and culture.

This philosophical statement implies that the evolution of humanity from the animal world cannot be explained biologically or psychologically. At a philosophical or scientific level it can only be ascertained that human beings have a sense of responsibility. The answer to the question of the origin of this sense and to whom a human being has to be responsible, depends on one’s religion or worldview. The answer may be the confession that God created the world, including man as his image, his deputy, loaded with responsibility. But the denial of this confession depends on a worldview as well. Science and philosophy have nothing to add to that.


Sometimes science handles natural laws as norms

Mathematics and science make it their task to study characters in their natural state, not as norms but as laws, imperatively applicable to natural things, events and processes. Yet mathematics and science cannot escape to handle laws as norms. The choice of a co-ordinate system is not arbitrary, but subject to the norm that it reflects the symmetry of the problem situation. The uniformity of kinetic time constitutes a norm, both for scientific use and for the construction of clocks. All scientific instruments are subjected to norms of accuracy and reproducibility, besides the norm that what they measure corresponds to natural laws. Also for logic norms apply, see section 3. In the development of theories a much-applied norm of parsimony for concepts and statements is called ‘Ockhams razor’.

This concerns the application of laws in the exploration of characters, i.e. human activity concerning natural characters.


The technical development and application of characters is entirely normative

The development and application of natural things and processes for human use we call technics and its science is called technology. Purely use of makeshifts occurs in the animal world as well. Birds build nests, foxes burrow holes, beavers build dams, ants milk aphides and primates use sticks as tools. But people do that on a much larger scale, with an uncomparable creativity.

The discovery and investigation of the possibilities that nature offers is part of science, but in technology research is directed to and normed by practical applications. Technological research leads to the opening up of the dispositions of natural characters, which are not spontaneously realized. For instance, this concerns the production of synthetic materials satisfying specific requirements. Humanity invented many processes as well, starting with the use of fire for the preparation of meals, followed by cultivating plants and animals in agriculture and cattle breeding. A next step is the invention and application of technical apparatus. The invention of the wheel is the proverbial example. Designing is an important phase in any technical production process.

The implementation of inventions requires an infrastructure of a governing organization, of commerce and travel, of education and instruction, of industry and communication networks.

In technology the effectivity of the means to achieve one’s goal is an objective measure. Besides there are norms of economy, safety, liability, design, clarity of instructions and simplicity of operation.

[1] Laudan 1977, 58: ‘Every practicing scientist, past and present, adheres to certain views about how science should be performed, about what counts as an adequate explanation, about the use of experimental controls, and the like. These norms, which a scientist brings to bear in his assessment of theories, have been perhaps the single major source for most of the controversies in the history of science, and for the generation of many of the most acute conceptual problems with which scientists have had to cope.’

[2] On the history of the idea of natural law, see Stafleu 1999.

[3] In Stafleu 2002, I proposed to rename Dooyeweerd’s ‘modal aspects’ into ‘relation frames’, and his ‘structures of individuality’ into ‘characters’. Both are clusters of laws. The universal laws in each relation frame concern general subject-subject relations and subject-object relations. A natural character I consider to be a specific cluster of natural laws, determining a class of individuals and sometimes an ensemble of possible variations. Characters of artefacts contain norms besides natural laws. Because characters are sometimes misinterpreted as essentials, it is relevant to show that the theory of characters is at variance with essentialism.

[4] Since Reichenbach (1938), ‘context of justification’ and ‘context of discovery’ are standard expressions in the philosophy of science. I invented the other four. Niiniluoto 1999, 2 mentions six problems for scientific realism, that more or less agree with the first five of my components of a scientific worldview: ‘Ontological: Which entities are real? Is there a mind-independent world? Semantical: Is truth an objective language-world relation? Epistemological: Is knowledge about the world possible? Axiological: Is truth one of the aims of enquiry? Methodological: What are the best methods for pursuing knowledge? Ethical: Do moral values exist in reality?’

[5] Stafleu 2002, §8.4.

[6] For a recent review of critical realism (Popper, Bunge, Putnam and others), see Niiniluoto 1999 or Psillos 1999.

[7] Maxwell 1860; 1871, chapter 22.

[8] Psillon 1999, 255-258. The realistic criterion for the existence of, e.g., physically qualified things is not that they are observable, but that they can interact with other things, see, e.g., Hacking 1983, 21-24. Cartwright 1983, essay 4, accepts the reality of causes, not of laws.

[9] The principium exclusae antinomiae, see Dooyeweerd 1953-58, II, 36-49 cannot be proved by the proposition that the occurrence of inconsistent laws is unthinkable, for thought itself is subject to laws. This being unthinkable is rather a consequence of the principium.

[10] Van Fraassen 1989, 183.

[11] Popper 1959, 438; 1972, chapter 5; 1983, 131-149; Bunge 1959, 22; 1967b, I, 345; Niiniluoto 1999, 133; Swartz 1985, 10-11: ‘the existence of determinate laws of Nature is virtually axiomatic in the contemporary worldview.’ Omnès 1994, 506-531 pleads for a ‘total realism’ with respect to mathematics, science, logic and epistemic. ‘Science is possible and it meets such a great success because there is an order in the universe.’ (ibid., 528).

[12] Penrose 1989, 97, 112-113, 158-159. Brown 1999, chapter 2. Putnam 1975, xii, 69-75, calls himself an Aristotelian realist regarding the existence of mathematical objects. According to Shapiro 1997, 6, structuralism in the philosophy of mathematics is a variety of realism. He distinguishes ante rem (Platonic) structuralism from in re (Aristotelian) structuralism (ibid. 84-85). Structuralism differs from essentialism by stressing relations: ‘The essence of a natural number is its relations to other natural numbers’ (ibid. 72).

[13] Stafleu 1999.

[14] Sometimes the (neo-) Platonists are considered extreme realists. The Platonic vision on laws is also called ‘transcendent’, the Aristotelian one being ‘immanent’, see Niiniluoto 1999, 28-29.

[15] Sometimes one distinguishes conceptualists (the universals are mental constructs) from nominalists (the universals are lingual constructs, or do not exist at all).

[16] Mach 1883, §4.4; cp. Dooyeweerd 1953-58, I, 110.

[17] Koyré 1939, 3, 36, 201-202.

[18] According to Hübner 1983, chapter 9, when correcting Descartes’ laws of collision, Huygens rejected Descartes’ criterion of truth of accepting as scientifically proved only those statements that are clair et distincte, if seen in the light of reason. Huygens stressed that his laws of collision agree completely with experience, not only as a fact, but in particular as a method.

[19] Bunge 1959, 249; 1967a, 44. Achinstein 1971, 1-2. ‘Lawlike sentence’ according to Goodman, see Hempel 1965, 265. Swartz 1985 calls natural laws ‘physical laws’, and law statements ‘scientific laws’. A law statement cannot always be identified with an axiom in a mathematical sense, i.e., a proposition that cannot be proved in a given theory. In natural science the word ‘law’ is used even in case it can be derived from other laws.

[20] Here I speak about truth as agreement between a law statement and a law. Often truth is interpreted as agreement between a law statement and facts, see section 4. This agreement is sometimes difficult to find, because law statements are simple and generalizing, whereas facts are complicated, see Cartwright 1983.

[21] Nagel 1961, 48; Hempel 1965, 264-278, 291-293, 335-347; Achinstein 1971, 2-18; Van Fraassen 1989, 25-38 discusses a dozen possible criteria.

[22] This is not an expression of idealism, because it does not concern the status of natural laws, but our knowledge of laws, which is always incomplete.

[23] Nagel 1961, 51; Hempel 1965, 339, 377; Carroll 1994, 4; Griffiths 1999, 216. A counterfactual or contrary-to-fact conditional is something that is not the case (e.g., if this piece of copper were heated, which is not the case, it would expand). A subjunctive conditional is a condition that can be realized (e.g., all copper expands if heated). In both cases a disposition (of copper) is expressed.

[24] Bunge 1959, 35.

[25] Cartwright 1983, 3: ‘But fundamental equations are meant to explain, and paradoxically enough the cost of explanatory power is descriptive adequacy. Really powerful explanatory laws of the sort found in theoretical physics do not state the truth’. See Swartz 1985, chapter 1. Indeed, the fundamental laws are far away from concrete reality, and to make a suitable description, prediction or explanation of a complex phenomenon often requires a complicated reasoning, as Cartwright illustrates with many examples. But the conclusion that the fundamental laws cannot be true is too fast. For, Cartwright does not demonstrate that these laws are superfluous for the argumentation, or contrary to the phenomenological generalizations that she assumes to give an adequate description, prediction or explanation.

[26] Nieto 1972; Barrow, Tipler 1986, 220-222.

[27] Carroll 1994, 3.

[28] Carroll 1994, 6-10.

[29] Carroll 1994, 9-10.

[30] Carroll 1994, 3.

[31] Hart 1984, xxi: ‘…I consider the correlated pair of ordered world and world order to be the most fundamental relationship which philosophy needs to treat.’

[32] Stafleu 1987.

[33] Popper 1959, 1963.

[34] Cole 1992, 5: ‘Nature does not determine science; instead, they say, the social behavior of the scientists in the laboratory determines how the laws of nature are defined.’ For a criticism, see Niiniluoto 1999, chapter 9. For the social aspect of science, see Galison 1987, 1997; Ziman 2000.

[35] Comparable remarks can be made with respect to the truth of statements about individual things or events and their relations. The biblical concept of ‘truth’ points to a relation as well, namely the road to God.

[36] Giere 1988, 106: ‘Yet the failure of philosophers to explicate a viable notion of approximate truth must not be taken as grounds for concluding that approximation is not central to the practice of science.’ In science the concept of  (in) accuracy of measurement results and law statements based on them play an important part.

[37] The epistemic truth of law statements is relatively testable by comparing various statements of the same law. Accepting Einstein’s theory of relativity, Galileo’s and Newton’s law statements of gravity can be shown to be logically false, but approximately true in an epistemological sense.

[38] Swartz 1985, 3 and Carroll 1994, 22-23 state that a natural law is a (true) statement. In my view this is a categorial mistake. Contrary to a law statement, a natural law is not a proposition.

[39] By a fact I understand a state of affairs about which there is reasonable agreement among the participants in a discussion. Reasonableness requires a certain amount of objectivity, resting for instance on observations and measurements, one does not achieve facts by organizing a democratic vote. However, the identification of facts with observations is too strong, for observations need interpretation and for the establishment of facts theories are equally indispensable.

[40] The statement ‘if a then b’ is logically equivalent to ‘either a is false, or b is true’. Now if we accept both a and not-a, b is always true. Hence, a contradiction allows of proving any proposition. See Popper 1963, 317-322.

[41] Therefore Aristotle held that the unproved premisses or axioms of a theory ought to be evidently true. In the course of history, this foundationalist view turned out to be untenable.

[42] Sometimes relative consistency can be proved: if Euclidean geometry is consistent, then some non-Euclidean geometries are consistent as well.

[43] Crease 1993 is of the opinion that in particular experimental science has the character of a theatre.

[44] Often the word theory is restricted to a single unproved statement, a hypothesis, compare Popper 1959, 59: ‘Scientific theories are universal statements.’ Popper 1983 identifies on page 33 a theory with a hypothesis, but on page 113, 178 and 292 with a deductive system.

[45] Stafleu 1987, 15. The characterization of a theory by deduction implies a restriction. Logic as the science of reasoning, in all its functions and appearances, concerns much more than the use of theories. Deduction means deliverance of proofs, drawing conclusions from premisses, which is what theories are about. But reasoning does not merely use deductions, and scientists, too, are not exclusively theoretically-deductively involved.

[46] Braithwaite 1953, 12, 22. Bunge 1967a, 51-54; 1967b, I, 381. In fact, a theory is only a partially ordered set.

[47] Bunge 1967b, I, 391. In a mathematical sense the mentioned criterion means that the set is ‘closed’ or ‘complete’ with respect to deduction. In 1931GØdel (see GØdel 1962) proved that each theory satisfying some minimum conditions contains statements that cannot be proved or disproved within the theory. With respect to theories concerning characters the relevance of GØdel’s theorem appears to be marginal.

[48] What someone accepts to be proof depends on his worldview. For instance, L.E.J.Brouwer and other intuitionists only accept a proof if it can be finished in a finite number of steps, rejecting proof by complete induction. Brouwer also rejected proof based on double negation, proof by negative demonstration, and proof from the excluded third (tertium non datur).

[49] The structuralism of, e.g., Sneed 1971 is a formal approach to mathematical and physical theories making extensively use of the theory of sets. See also Torretti 1999, 408-417, who considers Bunge 1967a to be a forerunner of this type of structuralism.

[50] Stafleu 1987, 2002.

[51] Hacking 1983; Galison 1987, 1997; Giere 1988.

[52] Because by no means all law statements can be found by deduction, Descartes recognized experiment as a secondary heuristic, see Descartes 1637, 63-64.

[53] Newton 1687, 398-400. Newton’s ‘Rules of reasoning in philosophy’ represents his views on heuristics in condensed form.

[54] Van Fraassen 1989, 22.

[55] Popper 1959, 424; Niinniluoto 1999, 175.

[56] Popper 1959, chapter X; 1963, chapter 1; 1972, chapter 1. Popper underestimates the heuristic significance of experiments. He only assigns the experiment a function in the context of justification, as a means of testing a theory or a hypothesis.

[57] Franklin 1986; Crease 1993, 2-6; Galison 1987, ix: ‘Despite the slogan that science advances through experiments, virtually the entire literature of the history of science concerns theory’. Hacking 1983, 149: ‘Philosophers of science constantly discuss theories and representation of reality, but say almost nothing about experiment, technology, or the use of knowledge to alter the world’.

[58] Lakatos 1970, 1978; Lakatos, Musgrave (eds.) 1970; Howson (ed.) 1976.

[59] Cp. Kelvin 1884, quoted by Brush 1976, 580: ‘I never satisfy myself until I can make a mechani­cal model of a thing. If I can make a mechanical model, I can understand it.’

[60] Harwit 1981.


The idea of law



6. Laws, subjects and objects (1980,1919)


(Time and again, 1980, revised 2019, section 1.6)


We have now covered enough ground to justify our use of the word ‘subjects’ to designate things which, perhaps, are more commonly referred to as ‘objects’.[1] In fact, the linguistic use of these words is more original than the modern scientific and philosophical practice.

For example, consider the following question: Is it possible to speak of modal, universal, biotic laws which are valid for all kinds of subjects, regardless of their typical structure? Initially, it would seem that a stone is not subject to biotic laws. In order to answer this question adequately it is helpful to distinguish between ‘subjects’ and ‘objects’. In the philosophy of the cosmonomic idea, subjects are actively or directly subjected to a certain law, whereas objects, in contrast, are related to the law only passively or mediately. This implies that objects receive their creational meaning from the subject to which they are related by a subject-object relation. Thus a stone cannot be a biotic subject. Only organisms can be subjects to biotic laws. But atoms and molecules, rocks and sticks, may function as biotic objects within the sphere of some biotic law. For example, a bird’s nest, as a subject, is subjected to only mathematical and physical laws (it has mathematical and physical ‘subject functions’). As a bird’s nest, however, it can be understood adequately only as a biotic ‘object’; the nest has an objective biotic qualifying aspect. The bird’s nest receives its true objective biotic meaning through its relation to a bird, which is a biotic subject.[2]

The distinction of subject and object is not limited to typical structures of reality. Subjects and objects also appear on the modal side of reality. The path of a moving subject is a kinetic modal object since the path itself is motionless; and the state of a physical subject is a physical modal object since states do not interact.

A point has no dimensions and could have been considered a spatial object if extension were essential for spatial subjects. However, a relation frame is not characterized by any essence like continuous extension, but by laws for relations. Two points are spatially related by having a relative distance. The argument ‘a point has no extension, hence it is not a subject’ reminds of Aristotle and his adherents. They abhorred nothingness, including the vacuum and the number zero as a natural number. Roman numerals do not include a zero, and Europeans did not recognize it until the end of the Middle Ages. Galileo Galilei taught his Aristotelian contemporaries that there is no fundamental difference between a state of rest (the speed equals zero) and a state of motion (the speed is not zero).[3]

It is correct that the property length does not apply to a point, any more than area can be ascribed to a line, or volume to a triangle. The difference between two line segments is a segment having a certain length. The difference between two equal segments is a segment with zero length, but a zero segment is not a point. A line is a set having points as its elements, and each segment of the line is a subset. A subset with zero elements or only one element is still a subset, not an element. A segment has length, being zero if the segment contains only one point. A point has no length, not even zero length. Dimensionality implies that a part of a spatial figure has the same dimension as the figure itself. A three-dimensional figure has only three-dimensional parts. We can neither divide a line into points, nor a circle into its diameters. A spatial relation of a whole and its parts is not a subject-object relation, but a subject-subject relation.[4]

Whether a point is a subject or an object depends on the nomic context, on the laws we are considering (nomos is Greek for law). The relative position of the ends of a line segment determines in one context a subject-subject relation (to wit, the distance between two points), in another context a subject-object relation (the objective length of the segment). Likewise, the sides of a triangle, having length but not area, determine subjectively the triangle’s circumference, and objectively its area.


It is also possible to speak of subjects and objects in an epistemological context. In this case, however, only man can be a subject, since things, events, plants, and animals always remain objects of scientific or common thought. The latter can only function as subjects in an ontological context. As we have already noted, during the first half of the 20th century epistemology has taken priority over ontology in the dominant western philosophies. Since the Renaissance the ground motive of western thought has been the relation of freedom and nature – i.e., the relation of human thought and activity, and its natural object.[5] In developments of the past four or five centuries, the natural subjects have become increasingly objectified. Whereas they retained an independent existence, determined by their spatial extension or mechanical interaction in the philosophy of René Descartes, Isaac Newton and Gottfried Leibniz, natural subjects were denatured, in principle, to unknown ‘Dinge an sich’ in Immanuel Kant’s thought. In modern positivistic and phenomenalistic thought they became mere appearances. Occasionally existentialistic circles have tried to restore nature in a purely individual relation of man and his environment. Paralleling this development, natural laws were reduced to mere epistemic ordering principles, whether a priori and unavoidable (Kant), merely economic (Ernst Mach), or conventional (Henri Poincaré).

These developments are reflected in our modern terminology. Today we generally speak of natural objects, even when we discuss their subjectivity to natural law. The modern view is strongly oriented towards a completely functionalistic view of reality, in which the modal aspects considered as universal modes of thought are the dominant principles of explanation. In this respect, post-Renaissance philosophy differs sharply from Greek and medieval philosophies, which were usually dominated by a typicalistic view, most clearly exemplified in Aristotle’s form-matter scheme.[6]

For Christian philosophy there is no need to absolutize any modal aspect, or any typical structure or relationship. At its foundation lies the acknowledgement that the creation is not independent of its Creator. On the one hand, there is no ‘substance’ which exists independently of law, and, on the other hand, all natural subjects exist as creatures (being and becoming) under the laws. Because they are all subjected to laws, all subjects point to the Lawgiver: ‘Meaning is the mode of being of all that is created.’[7] This implies that natural subjects acquire their full meaning only if, in addition to their subject functions, all of their object functions are also opened up in their relation to humankind. In this relation natural subjects receive their full religious meaning since, in his relation to God, humanity is the religious centre of the creation.


The distinction of subject and object enables us to achieve a clear insight into the terms ‘objectification’ and ‘objectivity’. In humanistic thought everything which relates to sub-human subjects is referred to as ‘objective’. As a result, the demand for an ‘objective science’ has acquired an entirely confused meaning. It is sometimes understood as being ‘intersubjective’ or ‘public’. In this case one distinguishes between individual (subjective) experience and public (objective) experience.[8] In other contexts objectivity is identified with universal validity or law conformity. In the philosophy of the cosmonomic idea, the meaning of the word objective is clear: objectivity means a representation of modal and typical states of affairs referring back to earlier modal aspects. Objectification is made possible by the existence of retrocipations on these earlier aspects, and the opening up of the latter’s anticipations. The problem of objectification, which may be termed the sixth aim of science, shall occupy much of our attention. Spatial points, which refer back to the numerical modal aspect, enable us to find an objective numerical representation of spatial magnitudes and relative positions (chapter 2). The path of motion, referring back to the spatial modal aspect, provides us with an objective representation of the motion of a kinetic subject (chapter 4). Similarly, the state of a physical system allows us to objectify the system’s interaction with other systems (chapter 5).

For physics, objectification means a representation of physical states of affairs in mathematical terms, in  particular the projection of physical relations on kinetic, spatial or quantitative ones. It is frequently said that mathematics is the language of physics,[9] as if it were a merely linguistic matter. The real state of affairs is more complicated than this metaphor suggests. The modal aspects, which precede the physical aspect and form the subject matter of mathematics, are universal aspects of the full creation, including physically qualified things and events. It is impossible to account for physical functioning without including the earlier relation frames in one’s analysis.




[1] Dooyeweerd NC, II, Ch. 5.

[2] Dooyeweerd NC, I, 42-43. Because of the distiction of subjects and objects, one should the term ‘subject side of reality’ understand as ‘subject-and-object side’, but for short I shall stick to the usual ‘subject side’.

[3] Galileo 1632, 20-22.

[4] In a quantitative sense a triangle as well as a line segment is a set of points, and the side of a triangle is a subset of the triangle. But in a spatial sense, the side is not a part of the triangle.

[5] Dooyeweerd NC, I;1965; for the subject-object relation in humanist philosophies, see. Dooyeweerd NC, II, 367 ff

[6] Dooyeweerd NC, II, 12; Jaki 1966, Ch. 1.

[7] Dooyeweerd NC, I, 4.

[8] See. e.g. Popper 1934, 44ff, but also Kant 1781, A, 820, B, 848; for Popper, objectivity of scientific statements lies in the fact that they can be intersubjectively tested, which implies that the described phenomena should be reproducible. See also Margenau, Park 1967, who enumerate the following ‘meanings of objectivity’: ontological existence (‘the objective reality behind perceptible things’); intersubjectivity; invariance of aspect (‘objectivity must be assigned to those properties which are, or can be made, invariant’); scientific verifiability (‘Constructs which satisfy the metaphysical requirements as well as the stringent rules of empirical confirmation are called verifacts, and verifacts are the carriers of objectivity in the domain of theory’). The ‘metaphysical requirements’, e.g. Occam’s razor, economy of thought, logical fertility, simplicity, are discussed in Margenau 1950, Ch 5; 1960.

[9] cf. Galileo, in: Drake (ed.) 1975, 237, 238.