by Ivor Leclerc
Ivor Leclerc is Professor of Philosophy at Emory University, Atlanta, Georgia, having previously taught at Glasgow.
The following article appeared in Process Studies, pp. 158-168, Vol. 3, Number 3, Fall, 1973. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
In the past, science and philosophy were separated and apart, each going it alone. Today we face the need for a radical change in this dichotomy, a philosophy of nature where the metaphysical and physical be conjoined.
Earlier, and until about two centuries ago, there had been a main field of inquiry known as philosophia naturalis, the philosophy of nature. Then this field of inquiry fairly abruptly ceased being pursued. It is interesting, and as I shall show, important to us today to determine how and why this happened. It is indeed not difficult to do so, and the main features of this history can be fairly quickly sketched.
In the sixteenth century there occurred a considerable expansion of interest, especially among medical men who were leading scientists and thinkers of the day, in the philosophy of nature, which led to the momentous developments of the seventeenth century. Of particular importance in this process were the steps taken in the first quarter of the seventeenth century, for these had the consequence of the introduction of a new conception of nature, which appeared in a number of books about the year 1620, by Daniel Sennert in Germany, David van Goorle in Holland, Galileo in Italy, Francis Bacon in England, and most fully developed by the Frenchman Sebastian Basso in his Philosophia Naturalis, 1621. This new conception of nature was elaborated and fully explored in the course of the seventeenth century by thinkers such as Descartes, Gassendi, Thomas Hobbes, Robert Boyle, Leibniz and Newton, to name but a few of the most important. Descartes’ Principles of Philosophy (1644) was largely devoted to the philosophy of nature. Gassendi, in a number of books, worked out the theory of material atomism. Thomas Hobbes explored an alternative in his De Corpore. Leibniz, in the next generation, critically and penetratingly examined the theories of his predecessors and developed his own alternative philosophy of nature in a series of monographs, articles, and letters. Newton’s Philosophiae Naturalis Principia Mathematica was published in 1686. Although the work was mainly concerned with the "mathematical principles" of the philosophy of nature, it contained some highly significant philosophical sections, especially the "Rules of Reasoning" at the beginning of Book 3 and the General Scholium at the end of that book. To this must be added the "Queries" at the end of his Opticks. Terse though they are, these philosophical sections not only evidence the depth of Newton’s philosophical reflection, but also adumbrate the philosophy of nature underlying his scientific structure. These writings on the philosophy of nature by these thinkers and others are among the most important works of the seventeenth century.
Quite early Sebastian Basso had seen very clearly that basic to the new conception of nature was a new conception of matter. In this new view matter had come to be conceived as itself substance, in contrast to the previous conception in which matter was only the correlative of form in a substance. The consequence of the conception of matter as itself substance was an ineluctable metaphysical dualism, which had been explicitly accepted by Basso and Galileo and was then systematically developed by Descartes. After Newton the success of the new natural science had become so overwhelming that the acceptance of this dualism was no longer to be withstood, despite Leibniz’s vigorous struggle against it, and in the eighteenth century and onward it reigned completely.
The outcome of this was that the universe was divided into two, one part consisting of matter, constituting nature, and the other part consisting of mind or spirit. The fields of inquiry were divided accordingly: natural science ruled in the realm of nature, and philosophy in the realm of mind. Thenceforth these two, science and philosophy, each went its own way, in separation from the other. In this division there was no place for the philosophy of nature. Its object had been nature, and this was now assigned to natural science. What remained to philosophy was only the epistemological and logical inquiry, which has natural science, but not nature, as its object -- today usually called the philosophy of science. Philosophy of nature as a field of inquiry ceased to exist.
In our time, however, I wish to maintain, the situation has completely changed. The reason for this is to be found in the development of science in the past hundred years. This development has had the consequence that the conception of nature which had originated in the seventeenth century and thenceforward constituted the foundation for science down into this century has now been entirely destroyed. No other conception of nature has replaced it. We today stand in need of a new conception of nature, for this is indispensable to the conception by man of himself and his place in the universe, a conception of fundamental importance to every sphere of man’s life and activity. Moreover, a new conception of nature is requisite for science itself.
Adequately to comprehend the changed present-day situation and especially the necessity of a new conception of nature for science, we must have clearly in mind the scheme of concepts in terms of which nature had been understood. These concepts are matter, space, time, and motion.
Central and basic was the concept of matter, for matter was the physical substance constituting the realm of nature and was thus the principle object of scientific inquiry. Matter was conceived by the philosophy of nature of the seventeenth century as fully "being," that is, as not subject to "becoming"; in other words, matter is, always, and is always what it is. This means that matter is completely without any capability of internal change, either by itself or of being changed by anything else. Matter in itself is entirely unchangeable.
With this conception of matter there is only one possibility for there to be change at all in the realm of nature, and this is that matter is capable of undergoing change of place. But this change of place has nothing whatever to do with matter per se, either in the sense that such change affects matter internally in any way or in the sense that matter could move itself from one place to another. In the modern philosophy of nature this change of place constituted "motion" or "movement." That is, motion could only be change of place, locomotion -- in contrast to the previous conception of motus, motion, which included the kinds of change like expansion and growth in size, and also qualitative change, both of which had been ruled out by the new conception of material substance as in itself changeless. But in this new philosophy locomotion was not necessitated by matter; matter in itself does not need to change place; per se it is completely indifferent to such change. Matter, as Newton explicitly recognized, is movable, but it is incapable of moving itself. This means that the concept of motion is not entailed by the concept of matter and cannot be derived from it. Accordingly in this philosophy motion is a completely independent fundamental concept.
Equally independent are the concepts of space and time. They are not derivative from the concept of matter, since matter per se does not require either space or time. In respect to time this is relatively easy to see, since matter simply "is." That the concept of space similarly is not entailed by matter is frequently not appreciated because of the strong tendency nowadays to confuse the concepts of extension and space, an error of which Descartes, Leibniz, Newton, and also Kant were not guilty. Space and time are required, not by matter per se, but because the new science of physics in the seventeenth century was a mechanics, that is, a mathematical investigation of the locomotion of pieces of matter. For this measurability was requisite, which meant that places and velocity had to be capable of determination. It is this which was provided by space and time, for they, as Newton said in his famous Scholium, are essentially places: "For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is of their essence or nature that they are places; and that the primary places of things should be movable, is absurd."
By the end of the seventeenth century nature was in general conceived as a mechanism, which meant that nature could in principle be completely understood in terms of the motion, i.e., locomotion, change of place, of pieces of matter, usually referred to as "bodies." This concept of body is important, as we shall have occasion to see. In the philosophy of nature which was generally accepted by scientists after the end of the seventeenth century, the concepts of matter, substance, and body were identified.
Even before the end of the seventeenth century it was becoming clear that some revision of this scheme of matter, space, time, and motion was necessary. To Leibniz and Newton it was clear that a pure kinetics, as attempted by Huygens, as well as a phoronomy, as held by Descartes, were untenable. Leibniz and Newton both introduced the concept of force, and in the eighteenth century physics became a dynamics. This entailed that the concept of force take the place of motion in the scheme; motion could be conceived as derivative from force.
The concept of force led to the conception of the interaction of bodies and the attempt to conceive force as derivative from bodies, an attempt to which the notion of gravitational force presented grave difficulties, as Newton had long before clearly seen. In a letter to Bentley he wrote:
It is inconceivable, that inanimate brute matter, should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desire you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.
That in the eighteenth and nineteenth centuries the attempts was nevertheless made to conceive force as derivative from bodies does not necessarily indicate that the thinkers in question were, to use Newton’s words, lacking in a competent faculty of thinking, but rather that implicitly a quite different conception of body was being introduced.
A most important development was that the concept of force led to the field concept in the nineteenth century. I shall quote C. F. von Weizsäcker’s excellent brief exposition of this development:
The field concept was the product of a study of forces active between bodies, under the influence of a wish to surmount the dualism of body and force. Forces acting at a distance seemed to be rigidly and unchangeably attached to bodies. Faraday maintained the doctrine of a field as a reality independent of bodies, equipped with its own inner dynamic. Then followed the hope of explaining the field as a particular body, the "æther," spread through the whole of space. . . . This was wrecked by the special theory of relativity. In addition the concrete structure of electrodynamics remained dualistic in its distinction between "ponderable matter" and the "electromagnetic field." The distinction matter-field is but a new form of the old distinction of body-force. (EN 147, my translation)
If we then consider the general theory of relativity, it becomes clear how very far contemporary physics is from the basic concepts of the eighteenth century. Again I shall cite von Weizsäcker:
The general theory of relativity was developed from the physics of fields and knows no action at a distance. Through its fusing of the field of force with space it has turned space into a physical object in the full sense of exercising action and suffering effects. . . . Consistently with this Einstein sought to resolve the remaining dualism of matter and space by conceiving matter as an attribute of space, the particles being singularities of the metrical field. (EN 149)
Little indeed remains in this of the former scheme. Although the words matter, space, time, and motion continue to be used, they now have completely different meanings. Take the concept of space. In the general theory of relativity it has, as von Weizsäcker has said, become a "physical object in the full sense of exercising action and suffering effects." But what exactly does "physical object" mean? If it means "the object of physics," then this is not anything new or special, for space has, since the seventeenth century, always been an "object" of physics. But this is not what is meant here, for von Weizsäcker said, "a physical object in the full sense of exercising action and suffering effects." Clearly what he means here is a substance, a res. That is to say, in this theory space has become the physical existent or substance. Einstein himself saw how close this position is to that of Descartes with his one res extensa. In the philosophy of Newton, however, space was definitely no substance; for Newton there was only one substance, matter. In Einstein s theory, on the contrary, space has become substance, and not only one substance among others, but the true physical substance, from which matter is derivative.
To see how Einstein has arrived at this position it is necessary to take into consideration a particular development after Newton. In the eighteenth century space was conceived by increasing numbers as some kind of existent, a conception which Kant correctly completely rejected as an "Unding." Nevertheless space continued implicitly to be conceived as some kind of existent or substance. One important reason for this is that after Kant there no longer existed the discipline, the philosophy of nature, to subject this conception to critical scrutiny. Thus it has come to be possible for Einstein in this century to conceive space not simply as a substance but as the true physical substance. The question must, however, be raised whether Einstein’s true physical substance is to be conceived as "space" at all. Certainly his physical existent or substance is extended, but not everything which is extended is to be identified with space. Further, in the classical eighteenth century doctrine of space, space was conceived as a container, in which the physical material substances exist and move, itself, however, neither affecting the substances nor being affected by them. But this conception of space has been completely abolished by Einstein. What he calls space is no more a container than is Descartes’ res extensa. And further, Einstein’s space both affects and is affected by matter. With that complete difference in conception, how appropriate is it to continue to use the term "space" in the contemporary theory, and can it be done without danger of confusion? It seems to me that much confusion has indeed ensued.
In Einstein’s theory we also have a concept of matter completely different from that of the earlier philosophy of nature. In the latter conception, as we have noted, matter was a full being, in itself unchangeable. Not only in Einstein’s theory but in general in contemporary physics, what continues to be spoken of as "matter" is something which, by contrast, is "in becoming" an existent which is active, producing effects by its acting, and itself suffering effects, these effects being internal changes in the entities affected. It is clear that in the contemporary theory we do not find the concept of matter as formerly understood. More precisely stated, nothing of the previous conception of matter remains in contemporary physics; every feature of matter as formerly understood has been completely abandoned.
To continue to refer to these entities as "matter," as "particles" (i.e., of matter), can have serious consequences. I shall take only one example, but it is an important one. We have noted that in the earlier philosophy of nature the concepts of matter and body were equivalent. Macroscopic bodies are composites of a mass of material particles which, right down to the smallest atomic (indivisible) particles, are still bodies. Consequently in classical physics it was completely indifferent whether, in experiments concerning the laws of motion, bodies of (say) 10 kilograms, or 1 kilogram, or 1 milligram are used. The laws of motion hold for all bodies, however large or small. Consequently, although the laws of motion are not empirically verifiable with individual atoms, it is consistent to assume the laws, empirically verified with compound bodies, as equally applying to the final constituent bodies, the atoms, and therefore that the routes of individual atoms in motion are exactly determinable. Now since about 1900 it has been established not only that what had been taken to be atoms, i.e., not divisible, are in fact compounds but also that the classical laws of motion do not hold for the sub-atomic constituents, which display variations in their motion, so that their paths are determinable only by statistical probability. In fact, all the laws of sub-atomic physics are statistical probabilities.
This difference in respect of laws of motion could be significant of a fundamental difference in the kinds of entities respectively involved. The presupposition has, however, continued that the newly discovered constituents must themselves he material bodies -- they are spoken of as "particles" or "elementary particles," that is, of matter. For "particles" (little parts) are parts of something, and the something of which they are parts is body or matter. This presupposition is strengthened by the adjective "elementary," for an "element" means a final, not further divisible constituent, it being not further divisible not because it is impossible to divide it but because further division would result in its ceasing to be a "part," that is, of the same kind as, that of which it is a part. Accordingly an elementary particle of matter must be matter; an elementary particle of a body must itself be a body. Thus the very terms used carry the presupposition of the sub-atomic constituents as bodily, that is, they are implicitly conceived as having the properties and characteristics of bodies.
But this presupposition is definitely open to question. We have here a philosophical problem. A macroscopic body is a composite, but so is any microscopic body, down to that which is still called an "atom." The question has to be raised whether the constituents of a composite body necessarily have to be conceived as being bodies. Stated generally, is it necessary that the constituents be "parts," i.e., of the same kind, having the same character or property, as that of the composite? That there is no necessity in this had been clear to Leibniz in the seventeenth century -- and also to Aristotle in antiquity. Leibniz strongly opposed the assumption and developed a theory of body, and matter, as composite, with the constituents entities of a very different kind, explicitly nonmaterial. But despite Leibniz the presupposition has ruled down to the present day. It seems to me that in contemporary science, not only in physics but also in chemistry, biochemistry, biophysics, and in biology, the continued implicit acceptance of this presupposition is having restrictive consequences.
For if the sub-atomic constituents are not particles, little parts, i.e., little material bodies, but are nevertheless implicitly conceived as having bodily characteristics, in particular as having as a basic feature that of locomotion, change of place, it would not be surprising if difficulties ensue. For example, corporeal locomotion is continuous, but in contemporary physics quantum characteristics, i.e., discontinuity, are well established. But the presupposition nevertheless continues that the motion of the sub-atomic constituents is essentially locomotion, change of place -- sub-atomic physics is dominantly a quantum mechanics.
But if the presupposition entailed in the terminology of "elementary particles" be rejected, and we accept the possibility that in the sub-atomic realm we have entities of a quite different kind, then a number of important consequences open up. It could then be the case, for example, that locomotion pertains properly only to compounds, bodies, and that the changes involved in the constituents are something quite different and far more complex. Thus if it be taken that the sub-atomic entities are not in themselves unchangeable -- which surely is one definite outcome of contemporary physics -- but rather that they are acting entities, then clearly we have a kind of change, i.e., that which is involved in "acting," which is not reducible to, or derivative from, change of place, locomotion -- though change of place could be derivative from it. Thus locomotion could be analyzed as an abstract, derivative feature, essentially pertaining to bodies. The kind of change, motion, in the sub-atomic realm would. be something else. In this realm Whitehead, in Science and the Modern World (chapter 8), distinguished a kind of change which he termed "vibratory organic deformation" in addition to that which is "vibratory locomotion," but, as he later came to see, even these are derivative from a kind of change, motion, which is still more fundamental. Clearly it is necessary that the whole concept of motion be entirely rethought.
The main point I am concerned to make is that considerations such as these are of direct relevance to science. This means that it becomes of the highest significance to know what kinds of entities we are concerned with, for the inquiry into the kind of change is not possible in dissociation from the question of the kinds of entities. It is to be noted, too, that contemporary physics displays an interesting contrast to the earlier, so-called classical physics in respect of the entities with which it is concerned. In the earlier physics all the entities were alike, material bodies. They could differ in size, structure, and composition, but they were of one single fundamental kind, matter. But contemporary sub-atomic physics has revealed a number of entities of different kinds. This makes the question of the nature of the entities with which it is concerned all the more acute. And this raises the further issue, namely, by what procedure the answers to these questions as to the nature of the entities and the nature of motion are to be arrived at.
In respect of this one thing must be clearly recognized. This is that these considerations and questions transcend the realm of science; with them we are in the realm of philosophy -- admittedly philosophy which is very close to science, but philosophy nevertheless, whether it be engaged in by scientists themselves or by those who are primarily philosophers. In other words, we have philosophy here which once again has nature as its object. In our time, I wish to maintain, the development of science has come to require of philosophy as one of its most important tasks the resumption of the inquiry into nature.
With regard to this task, however, philosophy today faces singular difficulties. First, for the past two centuries philosophy has not had nature as its object at all, with the result that the entire problematic, the range of issues involved as well as that of method, has been lost. A second kind of difficulty is constituted not simply by philosophy’s having been for two centuries essentially a philosophy of mind or spirit; the difficulty is contained in what emerged into clarity when this kind of philosophy reached its maturity with Kant’s Critique of Pure Reason, namely, that on its basis the Ding an sich remained inaccessible, unknown and unknowable, on the other side of the great metaphysical divide. But it is precisely the physical Ding an sich which is required to be the primary object of the philosophy of nature.
How then in the circumstances today is philosophy to proceed to take up its task of making nature again an object of its inquiry? flow is the problematic of the philosophy of nature to be recovered? Certainly there can be no one single way, and many should be attempted. One way is to approach it from the side of natural science, that is, trying to get at the philosophical problems as they are seen to arise in scientific inquiry. This is the way followed by some thinkers, for example, A. N. Whitehead in a series of books, The Principles of Natural Knowledge, The Concept of Nature, and Science and the Modern World; by Milic Capek in his The Philosophical Impact of Contemporary Physics; and by C. F. von Weizsäicker in his recent Die Einheit der Natur, as well as other books of his -- this list is intended as illustrative, not exhaustive. A survey of the attempts following this way reveals an appreciable difficulty in being able to disentangle the philosophical from the scientific issues and to move further than merely formulating the contemporary scientific developments in rather general, as opposed to specifically scientific, terminology. Whitehead’s success in recovering the problematic of the philosophy of nature has been the most considerable, but his writings unfortunately have been far from easy to understand, moving as they were not only in unfamiliar territory but in an unfamiliar terminology, the latter devised in an attempt to free himself from inherited presuppositions, at first epistemological and later also metaphysical. By the time he wrote Science and the Modern World, he had come to see that the basic issue was that of the physical existent, how it was to be conceived. The contemporary scientific development had made completely untenable the conception of the physical existent as in itself changeless, individually self-complete, each physical existent in no intrinsic relationship to any other. The very contrary emerged as the case; the physical existents act and suffer effects. This for Whitehead brought the philosophical problem of relations to the fore:
It must be remembered that just as the relations modify the natures of the relata, so the relata modify the nature of the relation. The relationship is not a universal. It is a concrete fact with the same concreteness as the relata. The notion of the immanence of the cause in the effect illustrates this truth. We have to discover a doctrine of nature which expresses the concrete relatedness of physical functionings and mental functionings, of the past with the present, and also expresses the concrete composition of physical realities which are individually diverse. (AI 201)
But this could not be achieved without explicitly tackling as fundamental the problem of the nature of the physical existent. This is what Whitehead undertook in his major and most difficult work, Process and Reality, subtitled "An Essay in Cosmology," the term "cosmology" there being a synonym for "philosophy of nature." This work contains his most extensive and most profound analysis of the problems of the philosophy of nature. It should be emphasized, what is sometimes liable to be overlooked, that Whitehead’s recovery of the problematic of the philosophy of nature would not have been possible without his having gone back extensively to earlier philosophy, especially Greek and that of the seventeenth century.
This suggests another way of approach to the philosophy of nature, complementary to the one we have been discussing, that is, from science. This alternative way, one which I have followed in my The Nature of Physical Existence (Allen & Unwin, in the Muirhead Library of Philosophy, 1972), is to seek to recover the problematic of the philosophy of nature though a study of the philosophy of nature in past periods, particularly those in which it has been vigorous. The sixteenth and seventeenth centuries are of especial value in this respect. Not only was this a period of fundamental change like that in which we are living, but it was one in which the thinkers advancing the new conceptions particularly well understood the problems at issue. For they had to develop their theories in opposition to the dominant Aristotelianism. Although they rejected the particular Aristotelian doctrines, they gained from their detailed study of Aristotle a singularly good grasp of the fundamental issues involved in the philosophy of nature. This way of approach, especially by the inquiry into the sixteenth- and seventeenth-century thought, has two other advantages. One is that by securing a thorough understanding of that period from which the entire modern development in science and philosophy derives, we shall be in a better position to assess the present. Secondly, such an inquiry can be of appreciable value too in disentangling the philosophical and the scientific issues, respectively, and by distinguishing them, clarifying their interconnection.
I should like here briefly to discuss one issue, especially prominent in the seventeenth century, which seems to me to be of particular significance for the present. This is the problem of the status of the mathematical and its connection with the physical. I have here used the adjectives "mathematical" and "physical" as nouns in the attempt to avoid implicit presuppositions. I have posed the problem as that of the status of "the mathematical," not of "mathematics." "Mathematics" is the name of a particular science, a branch of systematic inquiry. The question can be raised as to the object or objects of mathematics, and various answers to that are possible and have been maintained. The point I wish to bring out is that the answer to that question involves the problem of the physical. That is, the philosophy of nature is necessarily implicated.
The seventeenth century was a time when the importance of mathematics for the inquiry into nature, the physical, impinged with particular force. This was the outcome of a development which had its roots in the late medieval revival of Neoplatonism, in which Nicolaus of Cusa played a determinative role. From him derived the conception of the universe as a mathematical structure, which was taken up by Galileo and a number of other thinkers in the seventeenth century. But the entire issue had to be subjected to close scrutiny, which it was by thinkers like Descartes, Gassendi. Hobbes, Leibniz, and Newton among the chief. The issue can be most satisfactorily put as the question of the status of the mathematical. Galileo, and Descartes following him, identified the mathematical and the physical. For Descartes the physical existent was res extensa. This was not an existent which, in addition to other properties, was also extended -- as was the case in Gassendi’s matter. For Descartes the very essence of the physical res was extensiveness; it existed as extensive; its extensiveness constituted its being. That is, this res in essence was geometrical extensiveness and nothing else. Descartes conceived the other existent, res cogitans, as the mental counterpart of the physical extensiveness; cogitatix in its purest form was mathematical, that is, it was the conceiving, the mental grasping, of what in the other res was the extended mathematical. This is why for him the knowledge of pure mathematics was the knowledge of the essence of physical existence. It was not at the level of pure thought, therefore, that the metaphysical dualism presented Descartes with difficulties in respect of mathematical knowledge of the physical.
What constituted a real difficulty for his contemporaries and thinkers of the following generations was that Descartes’ identification of the physical and the mathematical made material atomism impossible. Gassendi and Newton both saw that the only way to save material atomism was to separate the mathematical entirely from the physical. But that made acute the problem of how there can be mathematical knowledge of the physical if the physical be entirely devoid of mathematical features. Gassendi did not see this problem very clearly. Newton and Leibniz, however, did, and both produced complicated and subtle solutions. Newton’s was to ground the mathematical in God’s activity in respect of matter. Leibniz rejected this way as a Deus ex machina, but his own theory of a pre-established harmony did not strike his contemporaries as all that different. In the eighteenth century two alternatives were developed. The first, not philosophically very coherent, was to regard space as the object of geometry. The second was the revolutionary doctrine of Kant, conceiving mathematics as grounded in the mind, a mental construction. The former doctrine continued in favor in the nineteenth century and was thought to be strengthened by linking it with field theory. The entire position, however, was undermined by the discovery of non-Euclidean geometries. So Kant’s position came into increasing acceptance and today is dominant. But the fundamental difficulty with this doctrine is that according to it the object of mathematical investigation, in mathematical physics, for example, must itself be a mental construct. The physical existent remains on the other side of the metaphysical gulf, unknowable.
This century has seen great prominence given to the problem of the foundation of mathematics. Most of this inquiry is rooted in the basic Kantian position of mathematics as a mental construct. In this tradition too stood the great work of Russell and Whitehead, Principia Mathematica. Whitehead was to have written the fourth volume of the work, on geometry. It never got written, at least not as a part of that work. For Whitehead had come to see the need to face the crucial issue of how geometry applies to the physical, as Victor Lowe has pointed out. This meant the necessity to get into the philosophy of nature, recovering its problematic, the long road leading finally to Process and Reality, which has developed a new position bringing the physical and the mathematical once again into close relationship.
This problem of the connection between the physical and the mathematical is one not merely of philosophical interest; it is one of the greatest relevance and importance for science, more particularly at the present time, which is why Whitehead, himself a scientist, made this problem central to his endeavor.
I have given Whitehead some prominence in this paper, not because I am concerned to propagate his particular doctrine -- I have myself come to some appreciable differences from him -- but because he has seen most clearly the need in our time for the philosophy of nature, particularly for science, and because he has gone furthest in recovering the problematic of the philosophy of nature and has produced the first major philosophy of nature in response to the changed situation resultant from the scientific developments of the recent period. But, just as in the seventeenth century, other such philosophical schemes will need to be produced. However, as in the seventeenth century the various later theories were not produced independently of each other but came to be developed by working through, and in divergence from, the first great attempt at a philosophical structure built upon a profound insight into the problems at issue, namely, that of Descartes, so in our time the new efforts which are required in the philosophy of nature will need to come to terms with the pioneering work of Whitehead.
EN -- C.F. von Weizsäickcr. Die Einheit der Natur. München: Hanser, 1971.