The horseshoe of western science

Tl: THE 'HORSESHOE' OF WESTERN SCIENCE. SO: Journal-of-Indian-Council-of-Philosophical-Research. SPR 84; 1: 41-60 JN: Journal-of-Indian-Council-of-Philosophical-Research ) 1S: 0970-7794 AB: TWO FEATURES MAKE THE "HORSESHOE" AND EXCELLENT METAPHOR FOR THE HISTORY OF WESTERN SCIENCE AND MATHEMATICS: (1) THE HORSESHOE'S SEMICIRCULAR SHAPE MODELS THE EMERGENCE OF SCIENCE FROM MONISM TOWARDS DUALISM, AND ITS MODERN RETURN TOWARDS UNITY. (2) THE LOGICAL "HORSESHOE" OPERATOR (“IF ... THEN") MAKES POSSIBLE THE RULE "MODUS PONENS," AND HENCE WESTERN SCIENCE'S DEDUCTIVE APPROACH (WHICH IS REACHING ITS LIMITS). | PLACE PYTHAGORAS AND VAN FRAASSEN AT THE TIPS OF THE HORSESHOE CURVE, AND DESCARTES AT THE CENTER. vs N

11: NIRMALANGSHU MUKHERJI Field, Hartry (1972), ‘Tarski’s Theory of Truth’, Journal of Philosophy, reprinted in Platts (ed.), op. cit. The page numbers in this paper refer to this reprint. en (1980), Science Without Numbers, Princeton University Press. WILLIAM M. GOODMAN riedman, Michael (1981), ‘Review of Science Without Numbers’, Phi ‚Science, Volume 48, 3. a 12. a, David (1782), ‘Review of Science Without Numbers’, Journal 13: 14. McDowell, John, ‘Physicalism and Primitive Denotation’, in Platts (ed.), op. cit. Mukherji, Nirmalangshu (1983), ‘Against Indeterminacy’, in Humans, Existence, Meaning, (ed.) D.P. Chattopadhyaya, New Delhi: Macmillan. Pravitz, Dag (1977), “Meaning and Proofs: On the Conflict between Classical and Intuitionistic Logic’, Theoria, 1. ~ Quine, Willard (1953a), ‘Two Dogmas of Empiricism’, reprinted in From a Logical Point of View (FLPV), Harvard. 15: ———(1953b), ‘On What There Is’, ELPY. ————(1960), Word and Object, Harvard. a ————(1966a), ‘Truth by Convention’, in The Ways of Paradox, (WP), Cambridge. ————(1966b), ‘Scope and Limits of Science’, WP. ———(1966c), ‘Posits and Reality’, WP. ———(1969a), s ‘Epistemology Naturalised’, , in Ontological Relativi ativit re ————(1975a), ‘The Nature of Natural Knowled ge’ in Guttenplan (ed.), op. cit. ———(1975b), ‘On Empirically Equivalent Systems of the World’, Erkenntnis, 9. ———(1981), Theories and Things, Cambridge. | pe Quine aa and Goodma ns n (1947), ‘Steps Towards a Constructive Nominali minalism’ ’, Journal of Suppe, Fred (1974), ‘The Search for Philosophic Understanding of Scientific Theories? ss de Structure of Scientific Theories, ed. F. Suppe, Illinois. ; arski, Alfred (1956), 5 ‘Concept of Truth in Formalised Lan guages’,hdin Logic, j S tics and Metamathematics, Oxford. van Fraassen, Bas (1980), The Scientific Image, Oxford. University of Waterloo, Canada of Philosophy, ———— (19530), ‘Problem of Meaning in Linguistics’, FLPV. Essays, (OROE), New York. . ———(1969b), ‘Existence and Quantification’, OROE. The ‘horseshoe’ of western science De. À = INTRODUCTION The aim of this paper is to propose a metaphor which can model the course of Western science’s conception of mathematics from the time of the Greeks until the present day. The image chosen is that of a horseshoe (3). Like any trend line that is drawn on the basis of a given set of points, this representation is of course incomplete. It cannot be imagined that all individual philosophers and their philosophies can be neatly and simplistically located within the model employed. Nonetheless, it is the contention of this paper that, as a general pattern, the ‘horseshoe’ image does seem to apply. Moreover, it appears that the model can be used to suggest a new set of interesting questions about the philosophy of science and mathematics. In what sense, then, might the history of philosophy of science be compared with a ‘horseshoe’? The answer is (at least) twofold: on the one hand, it is the horseshoe’s circularity which is of particular interest. If science can indeed be said to have traced some shape through time similar to the horseshoe, then this suggests that its progress has not been linear; but, to the contrary, it has tended to curve back towards its own point of origin. That is, there must be some key respects in which modern trends have tended back towards viewpoints held near the time of Western science’s own emergence. Yet, in keeping with the horseshoe model, one must suppose as well that the initial and the current portions of the ‘curve’ remain separated by a significant gap. This same image of a horseshoe is significant from a second point of view. In symbolic logic, the ‘horseshoe’ is the symbol for material implication, the ‘if. ..then’ relationship. This logical operator plays a central role in the logical rule ‘modus ponens’—a rule which many deem essential for the possibility of deductive reasoning. But it is just this rational, deductive approach—the supplanting, as it were, of myth by reason, and magic and ritual by abstractions and methodology—which characterizes the appearance of Western science among the Greeks.? Given this, the ‘horseshoe’ of logic seems a fitting symbol for the scientific era which was then begun. In the modern era, we find that the power of the rational orientation, symbolized again by the horseshoe of logic, is still strongly felt in science. Yet its sphere of usefulness has already reached its limit. Aware that models, and the conclusions drawn from them, have only limited application (compare, for instance, how the model in which light is a ‘particle’ simply cannot be applied in all contexts), thinkers such as van Fraassen and his contemporaries are al-

THE ‘HORSESHOE’ ready holding back from claims that which may be named or described, provisionally, within their current theories is, by any means, a deductive oortainty But if science is, in this sense, retreating from certainty, it is suggested in h time will be paper presents of the progression of scientific thinking throug ative of provoc antly— import ost and—m e, instructive, essentially accurat new ideas. rationalistic mode of thought. One is reminded, for instance, of Heraclitus Realizing the ‘static nature of concepts and language,’ and thus their inability to convey the true nature of the world, he turned instead to a mode of paradoxical expression; (as when he says, for instance: ‘In the same river we both step and do not step, we are and are not’).* When science, today, speaks paradoxically of waves which are at-the same time not-waves, i.e., er it has in some sense rediscovered this old way of revealing and describing truth; And Just as a horseshoe, if its tips were connected, would no longer be a ho shoe, but a circle; so too, if science were fully to return to that ancient perspective of myth and paradox, it would no longer be based on logic (the ‘horseshoe”), but on some new principle. We begin this discussion, therefore by exploring the birth of mathematical science, represented here by the work of Pythagoras. The radical transitions THE ‘HORSESHOE’ this paper that its new direction is towards a return of some kind to a prein these ideas during the so-called Copernican Revolution will next be discussed; followed by a treatment of modern Western science and its philosophies as represented especially by van Fraassen. On the model of the B Pythagoras appears on the one tip, van Fraassen on the other; and the seienti. 5 revolution occurs at that section of the curve which is midway between the Tip of the ‘horseshoe’: Pythagorean period To discover a time of origin for mathematical thinking would seem an with Pythagoras impossible task. Although, as stated, this paper will begin (c. 570 8.c.), it has been convincingly argued that ‘all the factual mathematical was known many knowledge which is ascribed to the early Greek philosophers auer, in The centuries before’, in Europe and Babylon.® According to Neugeb m, itself, predates Exact Sciences in Antiquity, even the Pythagorean theore Pythagoras by over one thousand years.® philosoThus, what distinguishes Pythagoras and the other early Greek invented the phers from their predecessors is not so much that the Greeks by Maziarz ed express as mathematics with which they are credited. Rather, ution was and Greenwood, in Greek Mathematical Philosophy, their contrib process ve deducti and tive especially to discover and emphasize ‘the abstrac on which characin mathematics’, and to begin, thereby, ‘the rational traditi s the Egyptian wherea e, terizes Greek philosophy and science.” For instanc interest in geometry ‘consisted of empirically obtained simple propositions philosopher] areas and volumes, Thales [the earliest recorded Greek wo. about In choosing Pythagoras and van Fraassen as the virtual representatives of their respective ages, I have not meant to imply, by any means, that they and remained the basic part of geometry.’* the work of If this new approach to mathematics was already evident in Yet, Pythagoras’ Thales, it was nurtured and greatly enhanced by Pythagoras. their contemporaries were in full agreement. Rather, it is thought that these particular thinkers come closer to that conceptual path in the history of thought which, according to this paper, represents the overriding trend. With respect, it is felt, to this general theme, almost all of the disputes and en within each given era can be treated as embellishments and minor variations In short, the emphasis of this paper is to present, in outline form, a general schema for a history of philosophy of science (with special emshasis on its treatment of mathematics). For the sake of narrowing its field, it will focus on the outset, the turning point, and the present era of this process. Also, as space — the sketch will be coloured in with limited reference to contemporary Before concluding the paper, some mention will be made of the work of Hartry Field. His work is useful in that it shows, in practice, the limits to the applicability of any model—including the model presented ih this paper. For though, according to the horseshoe image, Field’s contribution belongs maat forcefully to the middle stage (as will be shown), he is, nonetheless, of the present age chronologically. In the attempt to map Field’s ideas ante the horseshoe model, it is believed that both the strengths and inevitable limits of that model will be revealed. It is therefore hoped that the image which this visualized a geometry of simple lines, an essentially abstract subject which has ts of own links with tradition were still quite strong. No less than the adheren search towards the contemporary mystery religions, he too was directing his n belief, underthe discovery of that Divine Soul or God which, in their commo l base, Pythalies the nature of all things. But, although he retained the mystica of the world goras was distinguished by his view that this Divine underpinning could, in fact, be identified with Number and mathematics. secret rituals Like the believers of the mystery religions—for whom their drama—Pythawere taken as the divine re-enactments of the cosmic world nal experigoras too acknowledged the importance of this first-hand ‘emotio atics was not ence of re-union’. Thus, in the Brotherhood he founded, mathem it should be to be taken as simply an area for intellectual study; but, rather, life. That is, for contemplated—as being the central focus for a whole way of whole life; and him the ritual experience was expanded to encompass one’s l unchanging rationa of n platio contem less passion what was required was ‘the .” wisdom of truth, and...[the pursuit] We thus find that, with Pythagoras, mathematics provided a most suitable phy, and from emointerface for the emerging transition from cult to philoso tion to reason.10 To be sure, numerical relations had long played a part in

tic speculations, and their practicality in ‘commerce and everyday social intercourse’ was well known.21 It was left to Pythagoras, howeve r, to observe that every experience of life—in whatever realm—seemed touche d by number Even the harmonies of music, he discovered, can be related to the ratios of die strings which produce the tones. Inspired by observations such as these, Pythagoras saw in numbers both the divine subjects for contemplation, and the basis for a rational understanding of the universe. Since numbers appeared to be the unifying principle behind the varied manifestations of being, they were consid ered divine: and so to ponder them, was a sacred contemplation. Yet, beyond this ficance, the fact that numbers represented the fundam mystical hn. ental principle of the universe, while having properties which can be discovered and vided a basis for rational inquiry about the world. explored, pro- Namely, one could dein about the world by studying the mathematics of which it is comprised.!? However, once the ‘secularization’ of science had becom e more pronounced and sophisticated (i.e., once the departure of science from its own mythological and religious roots became more complete), then this lofty role of numbers could no longer be maintained. To be sure, the sense of awe among thinkers at the properties of number remained for centuries, and still continues Yet, Pythagoras’ assertion that ‘Number is the essence of all things’!3 could not withstand the criticisms which were soon to follow. Nonetheless, many of those arguments which were subsequently made agains t Pythagoras failed to grasp that clear sense of Pythagoras’ own mystic vision, which, 45 sically constructed), the core mystic doctrine of unity had already begun to be lost.1¢ Cornford describes this process, which occurred within as well as outside of Pythagoreanism, as the tendency to dualism.!? Elsewhere in this paper, I have referred to it as a process of ‘secularization’ of science. What this involves, pramially, is the removing of the immanence of divinity from the world. Nature is taken to exist, in some sense, independently of the divine, and to be a subject of inquiry in its own right. In fact, in the extreme example of Aristotle’s self-contemplating deity, divinity has almost ceased to interact with the world at all. To ask, therefore, how Pythagoras’ numbers could serve as causes on earth, is already to assume their separateness from the world described? Yet, it is just this dualistic premiss which Pythagoras himself had denied. However, the distinction between the views of Pythagoras and his ancient critics can by no means be rigidly drawn. For, the tendency towards dualism was already present among the Orphics, by whom Pythagoras was himself strongly influenced. The Orphic religion, in turn, developed from the older mystery religion of Dionysus that believed in the endless cycle of life-deathrebirth. But the rebirth, in their case, was not considered a rebirth for the individual person; the eternal soul was the group soul, not the individual soul.!? By introducing the idea of an individual soul which persists through reincarnation, the Orphics made possible a hope of personal release and redemption; yet, in the process, they divided the unity of Being. had it been Of course, the Orphics too were expressing the impulse of the time. In Finley’s Four Stages of Greek Thought, he describes the cultural process which mystical truth: that one should seek ‘the meaning and nature of the whole in every part.’ For him, this ‘meaning of the whole’ was best expres sed by number; since in every occurrence or phenomenon he found eviden ce of number led to the rational orientation attained in Greece by the time of Plato and Aristotle. As life itself became more diverse, complicated, and individuated, the ‘desire for reasonable decency [in contrast to the ‘irrational’ excitements of the Mysteries] set the tone.’?° Of those who came after Pythagoras, perhaps Plato came closest to a Pythagorean form of expression when he spoke of the Forms as the unifying principle behind appearances. Perceived as immanent, they serve asimilar mystic role to Pythagoras’ numbers. Yet just as later Pythagoreans allowed their numbers to become crystallized into separate entities—thereby sacrificing the taken into account, might otherwise have made his meani ng transparent. For instance, consider Pythagoras’ aim in relating how the universe unfolded from a central Monad; or else, in affirming that ‘the whole Heaven is harmony and number.’ Throughout, his central purpos e was to express a and hence of the number One, the Monad. In speaking of numbers, he sbs encapsulated the mystical ideas by which alone, in his view, one con tent hend the mystery of the world—as a ‘processional movem ent [of divinity] out of unity into plurality, out of light into darkness.”15 However, many of the criticisms which were later directed against the Pythagoreans assume that a distinction has been made between the in’ the ‘pure’ numbers, abstracted by thought. And, to be sure, to ‘ultimately dry up into mere “concepts” or “logical objects” of thought— immutable still and independent of the subject which knows them, but with- ‘participate out life and power.’ The trend, in other words, was for forms to become simply ‘the relation of logical subject to universal predicate’?! and for numbers to become, as for Aristotle, ‘a mere elaboration of the category of quantity.’ In short, the dualistic tendency was, even then, very strongly in evidence. the later Pythagoreans, themselves, had begun to speak in such terms (as about numbers) as to actively invite criticisms of this sort. Nevertheless atom-like , it should be emphasized that by the time mathematical numbers had been concei this way (i.e., asextended, separate ‘atoms’ of which things are analysis of his mystical concept of participation; and thus allowed the forms “procession of [idealized numbers from] the Monad and [some suppos ed physical] procession which generates the visible world in space.” Thus arise such questions as how the extended number-atoms could possibly be related to, or original aim for unity—even Plato himself succumbed to attempts at rational ved in said to be phy- The turning point: the scientific revolution If any philosopher of the time could be said to represent the essence of the

new natural philosophy and science of the 17th century, Descartes is perhaps the most likely candidate. As aptly described by Westfall in his excellent survey, The Construction of Modern Science, Descartes, with his unshakable faith in reason, uttered the clarion call “for the abolition of wonder by understanding.’ i In the previous section of this paper, it was shown how the tendency towards dualism was inherent in the very emergence of science and rational thinking among the Greeks. But what was latent, or only just developing, at that time reached full maturity in the writings of Descartes. Here, the mind/ body distinction has been made complete; and all traces of the spiritual or psychic have been removed from matter.24 Not only the occult qualities of Scholasticism, and the enspirited nature of Renaissance Naturalism gave way to this new vision, but even the apparently ‘real’ qualities of heat and colour and the rest, proposed by Aristotle, were dismissed ; since even these could not conform within the reigning dichotomy of mind vs. matter.” To be sure, this new philosophy did not arise at once, “full blown’. In fact, the science of the time was characterized throughout by a dynamic tension between the so-called mechanical philosophy which was being created, and a still strong attachment to the Pythagorean tradition in mathematics. This tension, in turn, can be related to the shifting aim and focus of the scientific enterprise itself. According to Cornford, in his talk on the Laws of Motion in Ancient Thought, the science of the Greeks was simply not addressing the same problems as those confronted by modern science. To the contrary, says Cornford, the Greeks lay stress on discovering the essence of what is. Since their science was dissociated ‘from the pursuit of power and wealth,’ they were ‘not bent on influencing future facts to [their own] advantage.’ Thus, he continues, ‘Greek speculation took geometry in particular—that static science—as the pattern and ideal of all knowledge.’ In opposition to the Greeks, however, in Cornford’s account, more modern science is not so much concerned with static existence, ‘i.e., with that which Mill dubs the uniformities of ‘simultaneity among co-existent phenomena’. Instead, commencing with the work of Copernicus and Kepler, science has shifted its emphasis to the study of motion, and the laws of succession; since it is these which give power—the power to predict correctly and to act on the basis of these predictions.?? As Westfall expands this image: the Pythagoreans’ search for order was ‘satisfied to discover exact mathematical description, which it understood as an expression of the ultimate structure of the universe. The mechanical philosophy, in contrast, concerned itself with the causation of individual phenomena’® in order both to vanquish uncertainty, and to provide the basis for prediction and control. But this distinction between the two opposing viewpoints of science, for the Greeks and for the science of the 17th century, is not just the contrast between two ages. In practice, the allure of Pythagorean mathematics still lin- 47 gered, and had its effects in the science of the new era. This explains, for instance, why Kepler, who is renowned for his discovery of the three laws of planetary motion, which we still accept today, held also to diverse speculations (e.g., relating musical harmonies to planetary motion, or regarding the geometric architecture of the universe) which now seem unfamiliar and outdated.” Ironically, Galileo, who helped discover the more modern concepts of mechanics, could not himself resist a return to the more traditional picture of the physical solar system (which was based on that staple of the Pythagoreans, the circle); a picture which Kepler had already discarded as unworkable.?® Even today, this Pythagorean strain can still be detected in science. This ‘throwback’, as Cornford calls it, is evident wherever the laws of science are conceived not merely as statements of causal relations, but in a metaphorical aspect as ‘timeless’, universal properties, inherent in the world”! The advantage of this approach is that if such eternal laws could indeed exist, then, with Aristotle, one might hope that the rest of science could be rigorously explained by deduction from necessary principles. Descartes, in fact, hoped to retain just this privilege by identifying the space of pure geometry with the extended plenum of physical matter—so that certainty could still be possible for scientific knowledge. This hope was dashed in the potent writings of Pierre Gassendi (1592-1655), who affirmed that ‘atoms are extended, but extension is not their essence.’ In short, man cannot hope for certain knowledge of the essence of things (which only God can know).?? The other tip: van Fraassen In the image of this paper, Western science has traced through its history the figure of a horseshoe. Pythagoras, it was said, and the science he represented could be imagined to exist at one of the horseshoe’s tips. The crucial turning point, at the centre of the curve, would lie at about the 17th century during the scientific revolution. Then, with modern science, the other end is reached. The second stage, as shown above, was a science most characterized by an inner dynamic tension. On the one hand, a view of nature was being promoted which sought to explain all phenomena on the basis of solely mechanical interactions. On the other hand, a Pythagorean confidence remained in the role of abstract mathematical formulations to comprehend and accurately describe the phenomena. In this picture, the modern era in science and its philosophy can be described as seeking to resolve the paradoxes of that second stage. An interesting representative of this current era is Bas van Fraassen. Like his predecessors from Stage 2, he identifies his concerns with the ‘facts’. Not for him is talk of essences, or focus on divine intention. Then, too, he shares their attraction to elegant and usually mathematically-based theories which can serve to unify the diverse data. But, to avoid the paradox which befell his forbears when attempting to reconcile these two strains, van Fraassen changes radically the

nature of his ‘theories’. For him, the theory has become relative and provisional; and the interests it serves are largely pragmatic. In other words, it might be said that the 17th century dilemma was due to their holding simultaneously to two polarized positions, while yet insisting dogmatically on each. Since its science was so largely a study of mechanics, it was presumed that the world itself was literally mechanical in nature. And, since mathematics owed so much to the ancients for its impetus and development, the original prejudices regarding the meaning and nature of mathematical discoveries were adopted. The conflict arose, essentially, from the uneasy juxtaposition of such vying perspectives. But, nonetheless, these viewpoints can converge, if only they are each interpreted less rigidly—which is to say, in the ‘agnostic’ fashion of van Fraassen. According to the critics of the so-called mechanical philosophers, the latter abandoned in their method that which they themselves put forwardas a guiding principle. Namely, in the interests of disavowing any reliance on occult forces in their explanations (an aim shared in the current era), these older philosophers nonetheless relied on hidden causes and unseen movements of their own. This appears an unacknowledged regression. Some philosophers have tried, as an alternative, to simply remove all reference to the ‘hidden’. van Fraassen, in the opinion of this paper, is more truly representative of the direction of modern science when he permits continued theorization involving the unobserved, but holds back from the ontological commitments which, if made, could embroil him in paradox. What van Fraassen presents as the definitive summary of his own position is the following (italicised in his original text): ‘Science aims to give us theoties which are empirically adequate; and acceptance of a theory involves as belief only that it is empirically adequate.’ To say that a theory is empirically adequate is to say that it ‘saves the phenomena’; i.e., that ‘what it says about the observable things and events in the world is true.” The bulk of his text The Scientific Image is an elaboration and a defence of that position. van Fraassen thus continues the tradition, begun with the scientific revolution, of focusing on the predictive aspect of theories, which enable control and power. The only predictions which could possibly be confirmed or denied are those whose outcomes are seen to be at least partially observable. What goes beyond the observable, from this perspective, may contribute perhaps to a ‘good story’ about what may happen in some predicted situation; yet, ultimately, it is the observable portion alone which can be explicitly ‘watched for’—to discover either that it does in fact occur, or that it fails to. Therefore, many criticisms which have been levelled against van Fraassen’s dependence on the concept of observability can be countered by recalling this purpose, just described, for his employment of the notion. Musgrave, for ins- ‘tance, in his review of van Fraassen, questions whether such ‘a distinction [between what is or is not observable by humans, in general], which is admittedly rough and ready, species specific, and of no ontological significance, THE ‘HORSESHOE’ 49 [can] really bear such an epistemological burden?’*4 That is, he questions whether we should base our inferences regarding what exists on the almost arbitrary consideration of what the physical human species happens to be capable of observing. But in response to this, it must be emphasized that van Fraassen is hardly suggesting that existence is conditional on our ability to observe it; only that if and where existence does go beyond our ability to observe it, then the best one can hope for is speculation—not knowledge. Perhaps an example can make this clearer. Suppose there is a theory which says that in ten hours, the 17th dimension will collapse into the 16th. Since, so far as we know, there is no way in which all, or even some part of this event could be observed by humans, then van Fraassen would need to say that adherence or non-adherence to such a theory is wholly optional. This is not because these dimensions depend on man for their existence, but, rather, since there is no prediction which touches man that can be affirmed or denied on the basis of such speculation about these esoteric states. Contained within the above example is also a clue to van Fraassen’s second claim regarding ‘observables’, which has caused some upset among his critics. It would seem that the line which separates the ‘observable’ from the ‘nonobservable’ is far from clear. Is the image of someone’s knee on an X-ray plate, for example, an ‘observation’ of that kneecap; or is the only true observation involved that of the plate, itself—while the kneecap remains unobserved? van Fraassen, clearly, would favour the first interpretation; and he would say that what counts as an observation is determined by the accepted current body of theory. Since, in the present case, the accepted theory of X-rays confirms the correspondence between its images and that which is imaged, it is therefore sufficient to see the exposed plate in order to say that one has observed the features shown therein, as well. The complaint about van Fraassen’s answer is that it seems to involve one in a vicious circle: On the one hand, as already described, van Fraassen seeks to tie all theories back to tangible observations. Now, in turn, it seems that what is ‘observable’ is itself determined by some given theory. Surely, say some, this displays a basic circularity in van Fraassen’s account.% This paper would argue, however that this second objection to van Fraassen’s use of observables is, like the first, somewhat off the mark. For consider again that image of a theory which predicts the collapse of higher dimensions. As originally expressed, the theory was unsupportable in van Fraassen’s terms, since, so far as we know, it was said, the claims the theory makes are not subject to observation. But, for the sake of the present argument, let us now suppose that the theory includes also the following assumptions: 1. The 16th and 17th dimensions, though not subject to direct experience as such, do nonetheless have observable effects. 2. For instance, they do determine the relationships that hold between our phenomenological perceptions of colour and the corresponding wave-

lengths of light, which can be independently measured. 3. Thus, when the 17th dimension collapses into the 16th, as is predicted, an observable effect will be that when the familiar colour ‘red’ is perceived, the measured wavelength of light which corresponds will be increased times pi (compared with the previously expected measurement); and so, too, for all the colours, the corresponding frequencies will be increased times pi. The addition of such further assumptions to our imagined theory draws attention to these two important points, which bear on problems raised above: (1) Let us assume that, at the predicted time, the change in correspondences between perceived colours, on the one hand, and the measured wavelengths of these same colours, on the other, actually occurs; or, rather, let us assume that the holders of our imagined theory assert this change to have been made. What could they point to in order to support their claim? Clearly, they would describe the work of those experimenters who have actually seen certain colours, and read certain numbers from the dials and monitors of their test apparatus, in some specified order. To be sure, it is their theory itself which has said which numbers the researchers should expect to see on their displays (namely, in this example, those numbers which are roughly 3.14 times larger than the numbers which they would formerly have expected from otherwise similar experiments made prior to the dimensional collapse). This, then, expresses the sense in which the theory determines the role for observation. It says where to look, and what to be watching for. Yet there is nothing in this which should be problematic for van Fraassen. If, for whatever reason, theory predicts the appearance of certain numbers, at certain times, on particular display devices, the bottom line of confirmation or disconfirmation still rests with the very human-dependent question: ‘But did the researchers actually see those expected numbers, or did they not?’ (2) The same example helps, also, to show the way in which the realms of ‘observation’ can expand in theory-related contexts; though, always, it is bound to the final criterion (vague as it may sometimes be to define) of what the actual human being can confront and recognize. As of now, we presume, there corresponds with each colour we perceive a certain wavelength of light. To affirm this is to embrace a certain theory—a theory which is supported every time the ‘seeing of some colour’ and the measurement of its anticipated wavelength are conjoined. Once we accept this theory that affirms a certain constant conjunction of what is (or could be) perceived with what is (or could be) measured, there is a readily understood sense of ‘observe’ in which the direct experience of the one conjunct can be taken automatically as a case of ‘observing’ the presence of the as-yet unseen member of the pair. So, for instance, we may say a star is ‘red’, based on a direct observation only of a reading of its wavelength from a meter, though perhaps no one has actually ever perceived its alleged ‘red’ colour in their visual field. Or again, THE ‘HORSESHOE’ 51 we say we have observed a kneecap upon inspection only of its X-ray exposure without (fortunately) feeling the need, every time, to first cut through the flesh and look directly. Have we really observed the ‘red’ star or the kneecap? Well, what we have done is ‘as good as’ having observed it, provisional upon our continued acceptance of the theories which conjoin these phenomena to those we have literally experienced in a direct sense. But our example shows what can happen when one of these provisionally accepted theories is overturned (as when the expected relationship between colours and wavelengths is allegedly altered). Clearly, this reveals the tentative nature of all such indirect observations; and shows, once more, how consistency with strictly direct observation is the more fundamental test. The essence, then, of van Fraassen’s case is this: the crucial test for any theory is its compatibility over time with observed phenomena. In dispute, ‘observation’ must be taken in its crudest (though vague) sense, as what a human can actually perceive (such as e.g., ‘red’ or ‘the displayed representation of the number 112’). In practice, however, a far more expansive sense of observation is permitted; provided only the theories and presumed associations on which this observational method is based are not, in the given context, being questioned. If these premisses are questioned, the disputants must fall back to observations they can agree on—with direct reports of literal experiences comprising the last resort. (It should not matter that what, exactly, a ‘literal experience’ is, is unclear; provided the disputants themselves can reach a tentative agreement on the subject.) Having thus summarized van Fraassen’s position at some length, it next remains for this paper to relate it more fully to the general flow of the history of philosophy of science. In particular, it must be shown that his views can be appropriately mapped onto the ‘second tip’ of the horseshoe image—the position reserved for the thinkers of the ‘modern era’. SUPPORTING MODERN TRENDS As the reader will recall, this paper has suggested that the emergence of Western science involved at its outset a tendency towards ‘secularization’. That is, the pre-scientific emphasis on ritual interaction with nature was progressively diminished in favour of an increased attempt to stand back from it for understanding, and, eventually, for control. This trend, described also asa tendency towards dualism, reached its climax with the scientific revolution, when the mind of the observer and the matter under study were seen as rigidly distinct. Yet, since ultimately man, his culture, and his reason are themselves also a part of nature, i.e., of that which is under study—this strict dichotomy of mind vs. matter, of scientist vs. his subject, could never really be supported. Once the divinity of mathematics passed from favour as part of this dualistic tendency, it was never clear exactly where or how to classify its content. Who could deny the close kinship of mathematical and deductive thinking with the activity of the mind? Yet, if mathematics were simply of the mind, would this

53 not abandon nature to randomness and chance disorder? Once Descartes had principles could be relied on just as surely as for Pythagoras or Descartes. failed in his attempt to enforce a strict and conveniently necessary parallel between mathematics and the actual geometrical properties of the extended unibecause, in the final analysis, it has in fact been constructed from them. verse, it became the pressing problem for all future philosophy of science to resolve this unpleasant dilemma. It is thus that van Fraassen has been chosen in this study to represent the current stage in this historical development. In him, mathematics has completed its transition from its divine station with Pythagoras, through its uneasy period of co-existence with mechanical philosophy, to finally (and in answer to the post-cartesian problems); an essentially pragmatic role. But, in the process, a new sort of unity has been restored to science from the forceful dualism That is, we can know the world conforms to these rational principles precisely Perhaps, it might seem that these schools, if any, are antithetical to the viewpoint of van Fraassen. How, then, can van Fraassen be said to speak on behalf of modern philosophy of science in general? The reply is that, although the constructivists definitely aim to restore a place for certainty, which van Fraassen himself has finally abandoned, they nonetheless contain within themselves the seeds for their own collapse. Once this occurs, they tend to merge within the general ‘modern’ perspective, represented by van Fraassen. Kant, himself, acknowledged that, barring total scepticism (that is, avoidof its past. For, since, in current science, both mathematical formulas and physical particles alike are postulated—not as certainly existing, but as being effective for certain specific explanations—the need for holding rigidly to the ing the premiss that nothing external really exists), there must remain a cerold divisions between their realms is breaking down. And, in the age of science built up from man’s own logical framework; one can therefore never know the thing itself. This suggests that the accounts we give of our experienced environment are provisional upon our own adoption of a certain logico-mathematical framework. But, in the current era, when there have been shown to be possible alternative mathematics and logics, the relativity which was inherent but hidden in this constructivist outlook has now become apparent. For, which mathematics is to be chosen for our constructions? That is, with where particles have also become waves, perhaps the only supportable approach is to reduce, along with van Fraassen, one’s commitment to the dualistic view. But even if van Fraassen’s views can be plausibly related to an historical pattern of development in the philosophy of science, many readers may yet object to this paper’s selection of van Fraassen as the special ‘representative’ of the ‘current position’ in that field. Unfortunately, there is not enough space here to fully justify this choice. (At least a book would be required to fully elaborate all the issues and debates which have occurred in the modern philosophy of science, and to clearly demonstrate convergence on a single view such as van Fraassen’s.) Instead, what will be offered here is a somewhat eclectic comparison of van Fraassen’s position with a few other modern views, in order to show their common, basic similarity in key features. Perhaps the earliest expression of the theme here attributed to the modern era in science was provided by David Hume in the 18th century. Famous for his arguments that no one has ever seen a ‘cause’, but only the ‘constant conjunction of two objects’, he calls it merely the result of ‘custom or habit’ ‘to expect the one from the appearance of the other.”% What this leaves as the role for sound philosophy is to avoid dogmatism, and to confine itself ‘to such subjects as fall under daily practice and experience.”#’ Such a view is clearly compatible with van Fraassen’s more recent injunction that a scientific theory can only be judged on the basis of how it tallies with experience; van Fraassen, like Hume, takes a pragmatic attitude to all that exceeds this limit. In reaction to this initial statement of a position akin to van Fraassen’s, tain externally existing ‘stuff’, the ‘noumena’, about which nothing specific can be known. All descriptions of the known world are already constructions which mathematical or logical framework should we model the world; since, by definition of the case, we cannot know the world itself apart from the models we choose? Once the constructivist viewpoint is confronted with such questions, then it soon becomes obvious that even their views tend to merge within the van Fraassenean ‘agnosticism’ of our time regarding the possible ‘truth’ of accepted theories. Ironically, van Fraassen sees his second main adversary, after the positivists, as the so-called realist schools. Perhaps the classical spokesman for such schools is C.G. Hempel. In this author’s view, however, van Fraassen’s attempt to maintain a polarity between his own view and that of his other contemporaries seems essentially shallow, and hinges on trivialities. Hempel, no less than van Fraassen, acknowledges that ‘we can never establish with certainty that a given theory is true, that the entities it posits are real. But, that is not to disclose a peculiar flaw in our claims about theoretical entities, but, to note a pervasive characteristic of all empirical knowledge.’ In other words, Hempel is in full agreement with van Fraassen that, regarding things empirical, certainty is simply not possible. But, once this is acknowledged, the socalled distinction between Hempel’s realism and van Fraassen’s view collapses the constructivist schools (including, e.g., Kant, and the 20th century positivists) attempted to restore certainty to reason and to mathematics, and, thus, to the following: to rational deductions about the world. The key to this attempt was to consi- HEMPEL: If my theory says that unobservable entities, ‘A’, exist, then, if der the world of experience, itself a construction, built up by the mind on its own mathematical. deductive principles. Therefore, it was felt, these latter that theory is true, I would of course be committed to believing also in the existence of A’s.% But since, of course, I can never be certain that this

55 theory is correct, I am never quite certain about the existence of A’s, either. work of shared ideas, as because, in a very real sense, his ideas are a sort of VAN FRAASSEN: If my theory says that unobservable entities, ‘A’, exist, throwback to an earlier time. In particular, the thrust of his arguments appear then, even if I totally accepted the theory, I would not consider myself committed to believing also in the existence of A’s. So, even if I accept the theory, I am never quite certain about the existence of A’s. to belong more appropriately to the time of the scientific revolution and Des- So where is the great distinction between these two positions? Clearly, neither claim that mathematics and numbers are expendable (in his words, ‘conservative’)*! for the pursuit of science. That is, whatever science needs to express van Fraassen nor Hempel would acknowledge the existence of entities which are posited only in theories which they do not accept. But, suppose they share the acceptance of some given theory which happens to purport the existence of unobservables. Would one of these thinkers be more committed to the existence of these objects than the other? No. Hempel would hold back, because no such theory can be believed with certainty; while van Fraassen would likewise refrain from belief, in his case saying that theory-acceptance does not entail such ontological commitment. The outcome, in terms of what is or is not believed on the basis of accepted theories, is essentially the same for both thinkers. Further parallels with van Fraassen’s ideas can be found in the work of Israel Scheffler. In his Anatomy of Inquiry, for instance, he speaks in ways which complement van Fraassen’s notion that a theory itself determines what are its observables. Scheffler holds the events we select to confirm or explain a theory cannot be looked upon as simply ‘raw’ happenings, but always too as events-described-as-P. That is, the theory itself must indicate which features ofP). Ss present in some event, (if it is to be characterized as such an instance In short, although these few examples could hardly be called a ‘proof’ they do help to illustrate how the current views in the philosophy of sbienee tend to have a great deal in common. If van Fraassen has been chosen as the spokesman for this era, this has only been to provide a point of focus for this study. As illustrated above, many other thinkers have had valid points to add to this essentially common view. FIELD AND THE HORSESHOE MODEL Throughout, this paper has tried to present the history of the philosophy of science as a smooth transition from Pythagorean towards van Fraassenean perspectives. Hopefully, at least the nature of an overriding trend has been expressed, though the variety and richness of published opinion on the subject can hardly be captured in a single such account. For instance, there has been in each period a diversity of schools and doctrines— which, even if they expressed some common themes, had nonetheless some sharp disagreements with each other. With Hartry Field, however, we see evidence of another type of diversion from the pattern here presented. He is distinguished from his other modern contemporaries not so much by holding to another view within a common framecartes than to the present debates. It is therefore useful to take a special look at Field’s proposals to see how they can be mapped onto our present model. The essence of Fields’s arguments in his Science Without Numbers is a or demonstrate can be accomplished without the employment of numbers. Thus, though mathematics may provide a useful tool, the existence of its entities need not be at all acknowledged. Ironically, it is Field’s strong attitude towards mathematics which places him so out of step with his peers. His general set of beliefs is not particularly distinct from common views. For instance, Kemeny, in his excellent work A Philosopher Looks at Science, virtually paraphrases Field (though writing twenty years in advance of him) when he says of the scientific method: ‘it starts with facts, ends with facts, and the facts ending one cycle are the beginnings of the next cycle.’42 Where does mathematics fit in? For Kemeny, no less than for Field, mathematics is an extension of pure logic. From facts we induce theories; mathematics, as simply a convenient shorthand for logic, helps us to deduce predictions from these theories; and these predictions are verified or refuted by reference to other facts.*? The van Fraassenean emphasis on confirmation-by-facts reveals the modernity of this view; and Kemeny has already made clear his own assessment of the ultimate ‘conservativeness’ of mathematics. In fact, we are reminded here, of the modern emphasis—which van Fraassen also employs—on models in scientific theories. Like the mathematics described by Kemeny, models (according to Hesse in her Models and Analysis in Science) are required to make theories predictive.“ Even if verification depends on discreet observations, a theory must somehow contain within itself a basis for deciding where next to look—for what to expect. Strict logicomathematical deduction from accepted theory is one such basis, though by no means the only one.*® So what is Field’s point in insisting that numbers have no existence? In the present phase of science, surely, there is no need to devote a book to such a subject. Since numbers are not observables as such, they must be considered parts of those theories or models which are alleged to connect our observations into some more or less unified picture. In this respect, their status is no better or worse, no more or no less ‘real’, than that of quarks or the fourth dimension. Since the role they play is provisional, in any case, in agnostically-held theories, there simply seems no point in focusing on them (as opposed to other unobservables) for special exclusion from our ontology. In the second phase of the ‘horseshoe’, however, there would have been reason for concern: and it seems that Field’s attitude is largely an inheritance

from that period. At that time, when the dichotomy between mind and matter was in its heyday, the role of mathematics was indeed a sore point. If it belonged on the mind side of the barrier—and surely it must—then how could its role in the explanation of the movements of objects be accounted for? When questions such as these were still in vogue, Field’s contributions would have been most welcome. (Notice, by the way, that his examples are drawn primarily from Newtonian physics—which is science of the second stage, not today’s.) Field’s solution: ‘Though it is convenient to employ mathematics in scientific explanation, all reference to mathematics can, with effort, be removed; and, thus, the ‘matter”side of our rigid dichotomy can remain untainted by mind, in the form of numbers.’ This would seem, no doubt, to have been an excellent solution for this problem, for those involved at the second phase of the horseshoe; but, for today, unfortunately, the problem itself seems anachronous. 57 cal on certainty became more tenuous, as matter itself was seen as mechani hope and devoid of its own intelligence. In our own era, a great deal of this for certainty has been simply abandoned. Thus, it might be said, there has been somewhat of a return to the attitude of Heraclitus —according to which it might be preferable, in some respects, to acknowledge one’s limits by employing paradoxical, but useful and non-dogmatic, models, rather than insisting always on a literal adherence to some one perspective. In short, this paper has completed its attempt to briefly trace the history of philosophy of science in the image of a horseshoe’s curve, and to clarify philoand support that model. In the course of this discussion, a number of utions contrib Den how r discove sophers have been quoted or described to reflect the general theme of some stage within the ‘horseshoe’. i Of course, the presenting of this model proposes at least as many questions as it (hopefully) solves. For, let the model be drawn as shown below: CONCLUSION AND AFTERWORD A model for interpreting the history of the role of mathematics in the philosophy of Western science has now been drawn. According to this model, the philosophy of science has traced a horseshoe-curve through time. The emergence of this ‘horseshoe’ with Pythagoras and the other Greek scientists can be seen as the rise not so much of the content of what we now recognize x? time Pythagoras as Western science and mathematics, as (more importantly) the emergence Descartes of that rational and deductive orientation which has since been characteristic of the scientific enterprise. From what has just been said, one of the two interpretations intended for DUALISM MONISM the horseshoe image of this paper can be derived. As mentioned in the introduction, the ‘horseshoe’ is perhaps the one symbol in logic mostch aracteristic of the deductive mode of thought (since it represents the ‘if...then’ operator employed in modus ponens). So, from this perspective, to say that the period in Western science from Pythagoras to the present day has traced out the curve of a horseshoe is to say that, in that period, reliance on the deductive mode of logic has been a central feature in the corresponding science. But, again, as mentioned in the introduction, the horseshoe image can be seen in another way. For, to trace a horseshoe pattern is to begin a return, at some point, towards the place of origin. We have seen, in this paper, a number of respects in which science has, indeed, curved ‘back’ in this way: (1) With Western science began a trend towards dualism. By the time of Descartes, this tendency had reached its extreme possibility, with the rigid mind/body distinction. By van Fraassen, a return has indeed begun, as theories blend waves with particles, and define to large extents their own observables. (2) Also, science began with a search for certainty. Pythagoras, indeed, focused nearly all his attention on the certain numerical relations which underlie the manifestations of nature. With the scientific revolution the oracn van Fraassen Kant THE HORSESHOE OF WESTERN SCIENCE The philosophers indicated are taken to hold increasingly dualistic views ted as the the further to the right they appear on the figure. Time is represen the emerfrom e) progression of the horseshoe curve (approximately clockwis ore exHow—m gence of Western science. Where is the curve heading next? plicitly—should individual thinkers be placed on the curve? What does the philosopher, vertical distance between points represent (if anything)? Is there a to point onding or at least a general philosophical period or position, corresp own Kant’s to x (which is ‘opposite’ from Kant)? What is x’s precise relation possible for s views? These, and many like these, are the sorts of question research which the model is intended to suggest. the To close this paper, the reader will be left with a question: If indeed model for the horseshoe image of the philosophy of science provides a useful be Annatar and nenerac af thie field then what can we exnect with regard to

WILLIAM M. GOODMAN its future? Will it, perhaps, complete its cycle in the direction of its origin; and, if so, what would this mean? To answer such questions, even if possible, would be clearly beyond the scope of this paper. What follows is not intended as a rigorous argument. Since the case for this paper’s claims has already been presented and defended above, all that remains is to offer, as an afterword, the following two quotes, each of which suggests a vision of where the next steps of science may lie. Whether these contain some truth, or whether some more traditional path will be followed, it is perhaps too soon to say. But since the trends revealed in this paper suggest that science is not likely to remain stagnant, but is changing in its form and content, it is felt a fitting close to present these thoughtful views. FRITIOF CAPRA (The Tao of Physics): The age-old tradition of exploring complex structures by breaking them down into simpler constituents is so deeply ingrained in Western thought that the search for these basic components is still going on. There is, however, a radically different school of thought in particle physics which starts from the idea that nature cannot be reduced to fundamental entities, such as elementary particles or fundamental fields. It has to be understood entirely through its self-consistency, with its components being consistent both with one another and with themselves. This idea. .. is known as the ‘bootstrap hypothesis.’ CARL JUNG (Preface to Wilhelm’s Translation of the J Ching): My position in these matters is pragmatic, and the great disciplines that have taught me the practical usefulness of this viewpoint are psychotherapy and medical psychology. Probably in no other field do we have to reckon with so many unknown quantities, and nowhere else do we become more accustomed to adopting methods that work even though for a long time we may not know why they work... The irrational fulness of life has taught me never to discard anything, even when it goes against our theories (short-lived at best) or otherwise admits of no immediate explanation. It is of course disquieting, and one is not certain whether the compass is pointing true or not; but security, certitude, and peace do not lead to discoveries.47 Notes Regarding this interpretation for the usefulness of models in suggesting further questions for research, compare Mary B. Hesse, Models and Analogies in Science, p. 8. Edward A. Maziarz and Thomas Greenwood, Greek Mathematical Philosophy, p. vii. Warren A. Shibles, Models of Ancient Greek Philosophy, p. 44. Heraclitus (49aFr), in Walter Kaufmann, ed., Philosophie Classics: Thales to St. Thomas, p. 19. Ibid., p. 35. Maziarz and Greenwood, pp. 7 and 9. | we Ibid., p. 7. Specu Western of Origins the in Study À F 2 Een nd, From Religion to Philosophy: lation, pp. 198ff. Ibid. Maziarz and Greenwood, p. 12. Ibid., p. 17. Aristotle (Metaph. 987a) in Kaufmann, p. 389. Cornford, p. 207. Ibid., p. 209. Ibid., pp. 212f. Ibid., | p. 213. in the Greek Philosophers, had Caird, The Evolution of Theology Cornford, pp. 194ff. pp. 84f. John H. Finley, Four Stages of Greek Thought, en Cornford, p. 255. 138. Maziarz and Greenwood, p. Modern Science, p. 30. Richard S. Westfall, The Construction of Ibid., p. 31. Ibid., pp. 31f. Thought, p. 17. F.M. Cornford, The Laws of Motion in Ancient Ibid., pp. 15f., 20. Westfall, p. 1. Ibid., p. 12. Ibid., p. 18. p. 20. | Cornford, Laws of Motion, pp. 22f. Westfall, p. 40. (Oxford: Clarendon, 1980), p. 12. 2 Bas C. van Fraassen, The Scientific Image Scientific Realism’, Philosophical Quavs. Empiricism Alan Musgrave, ‘Constructive eon Wis 32 (July 1982): 265. of Philoso Journal Image, Scientific The Fraassen: van 35. oe ‘Bas C. | 79 (May 1982): 278. and Concerning the Understanding Human 36. ur ee Enquiries Concerning Principles of Morals, p. 43. 37. À : ce, pp p . 80f.801. hilosophy 0.of Natural Science, The Philosophy .G. Hempel, 38. le which variables the of function a being Ber this an of ontological commitments also Willard Van Orman Quine, From a are bound within an accepted theory, see Logical Point of View, PP. 12f. D. 59. Israel Scheffler, The Anatomy of Inquiry, p. 13. Numbers, Without Science Field, H. Hartry 41, p. 85. Science, at Looks 42. John G. Kemeny, A Philosopher Ibid., p. 86. 43. , D. 19. 44, see also: (a) Martin H. ee on models, and their potential employment, 45. Philip J. Davis and Reuben (b) and 11; p. Models, and A.P. Rollett, Mathematical p. 78. Hersh, The Mathematical Experience, 1976), pp. 301f. 46. Fritjof Capra, The Tao of Physics, or Book of Changes, p. XXXIV. 47. Carl Jung, Foreword to The I Ching:

BIBLIOGRAPHY > 4 vol 10. of 1 heology in the Gr eek Philosopher ‘S. Glasgow: James Capra, F ritiof, (9 7 6), The Tao of Ph VSICS. UK, I ontana/Collins . > LelÿlesEy > Y.: Purpose of man in the tradition of Indian orthodoxy S.P. BANERJEE igion to Philoso hy: A Study à phy in the O rigi igins of West estern University of Calcutta, Calcutta Cornford, ne F.Ml (1931), aieThe Laws of of Motion Motion in i Ancien I t Thought. Cambridge: Cambridge Cundy, H. Martin and A. P. Rollett, (1957) Mathe matical Models. Oxford: Clarendon Press. j Davis, Philip J., and Hersh Reuben. (1981), The Mathematical Experience. Boston: Houghton Miffin. Field, Hartry H., (1980), Science Withou t Numbers. Princeton, N.J.: Princeton University Press. : Finley, John H., (1966), Four Stages of Greek Press. Thought. Stanford, Cal.: Stanford University Friedman, Michael., ‘Bas C. van Fraassen: The Scientific Image.’ Journal of Philosophy 79 (May 1982): 274-283. 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Philosophical Quarterly 32 (July 1982): 262-271. Neugebauer, O. (1952), The Exact Sciences in Antiquity. Princeton, N.J., Princeton Unive rÀ sity Press. Quine, Willard Van Orman., (1980), Fr a om Logical Point of View. Cambridge, Mass. : Harvard University Press. Scheffler, Israel., (1963) The Anatomy of Inquir y. N.Y.: Alfred A. Knopf. er Schlesinger, e G., (1974) bn Confir de matir and Confirmabili11ty. Oxford: Clare ndon Press. Ancient Greek Philosophy. London: Visi Le gees oa es (1980), The Scientific Image. Oxford nn he en » Richard oP S., ( (1971), ), The Construction je of Modern2 Scienc Sci e. N.Y., John ; Wiley and I The attempt at explaining the mainspring of philosophical systems has been an interesting endeavour in philosophy. Until recently, it has been almost a common place in the subject to hold that philosophy starts either with the problem of nature, taken to imply objectivity, or of man, signifying subjectivity. That man himself is a combination of both or that nature includes man also has not been totally unknown, but in the matter of laying emphasis, this is forgotten and it has been laid either on the one or on the other. The early western thinking seems to have started with the problem of nature or the world. The Greek thinkers started wondering on the ultimate stuff of the universe and so, they are legitimately claimed to have also been the first scientists. It cannot, however, be an exclusive affair restricted only to nature. Some have naturally mused on the nature of mind (nous) and the masterminds on the nature of human knowledge and values especially Socrates, Plato and Aristotle. In the case of Indian philosophy, it seems to have started the other way round. The seer of the Rg Veda has wondered at the natural objects, but the centre, which has prompted him to explain or utilizethem, has been man himself. To unfold the mystery of human nature, to clinch the essence of man, has been the primary motivation of the traditional Indian systems. Atmanam viddhi (know thyself) is the key-word of Indian philosophy. And this knowledge, as developed through the Vedas, the Upanisads, and other systems based on them, is not a mere epistemic affair. Knowing is for being; they interpenetrate. The dichotomy between thought and action, between the knower and the agent, is transcended in the concrete being of man. It is the full man in his perfection (Moksa) that is the object of quest for the Indian systems. It is for the realization of man’s true self, it is for his liberation that thought, feeling and action converge. This philosophical motif makes no rigid distinction between philosophy and religion. Philosophy is that of human existence or being; so, it is religion in practice and action. Dharma (a synonym for religion) is that which sustains a man—it is the philosophy of life. Philosophy and religion supplement each other. They tend to fuse together to depict the true nature of the concrete man, who not only thinks but acts and feels too. With all its diversities and dimensions, life is one. Science of Dharma is the master science of life.