From Logical Systems to Conceptual Populations

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From Logical Systems to Conceptual Populations Stephen Toulmin PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1970. (1970), pp. 552-564. Stable URL: http://links.jstor.org/sici?sici=0270-8647%281970%291970%3C552%3AFLSTCP%3E2.0.CO%3B2-1 PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association is currently published by The University of Chicago Press.

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STEPHEN TOL'LMIN

F R O M L O G I C A L SYSTEMS TO

CONCEPTUAL POPULATIONS

It is hardly news today to report that philosophers of science share a widespread feeling that methods of analysis which have served them well for half a century are reaching the limits of their usefulness. During much of the twentieth century, they have been concentrating on those aspects of science which lend themselves most readily to analysis using the tools of formal logic; they have given detailed, sophisticated accounts of the ways in which the general principles of a natural science are - or might conceivably be - applied to entail statements about its particular phenomena; and they have done much to make clearer the part played in natural science by logical systewis. The resulting debate has been complex and on a high level of abstraction: primitive terms, protocol-statements, hypothetico-deductive systems, inductivism ... verification, falsification, confirmation, corroboration, refutation . . . . From year to year the argument has moved on, and the grounds of debate have shifted. It has all been very exciting. Very exciting, yes: but also oddly inconclusive - and this is where the current malaise begins. On the one hand, the intellectual program on which 'formal-logic-oriented' philosophers embarked around 1920 - what I shall here call the logicians'program for philosophy of science - has been substantially carried through; yet, on the other hand, many urgent questions in the philosophy of science remain entirely unanswered. About the formulation of deductive arguments in science, about the logical relations between singular evidence-reporting propositions and universal hypotheses, and so on and so on, what more is there to be said? By now all the issues have (it seems) been canvassed adizaziseam; what remains to be done in this field is largely intellectual filigree. And, though 'a thing of beauty is a joy forever,' this kind of filigree work is - undeniably - yielding diminishing philosophical returns, while leaving many acute and important problems unsolved. Originally, it was hoped to bring all serious Boston Studies in the Philosophy of Science, VZZZ. All rights reserved.

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philosophy of science within the logician's ambit by sufficiently ingenious extensions. Now, this appears increasingly unrealistic, and nobody is entirely clear where to turn next. My aim hereis to diagnose the sources of this uncertainty, and to suggest an alternative direction of advance. Let me first try to pinpoint the group of problems which most stubbornly resist resolution by formal methods of analysis. In a single word, these problems have to do - in onc way or another - with the reasonableness of science. For some years, logicians invoked a distinction between 'discovery' and 'justification' to sweep these difficulties aside: justification alone was the concern of logic, and therefore of philosophy, while discovery was a matter for psychologists. Then, for a while, there was a counter-attack by Russ Hanson and some others, who pressed the question whether there was not - after all a 'logic of discovery'. Yet this way of posing the difficulties proved, in turn, to be question-begging: if ever a philosophical issue involved a built-in cross-purpose, that did! So, today, the difficulties remain, and our first step must be to try and repose them more adequately. Their crux can be stated quite concisely. The logicians' program for philosophy of science deals with the 'structure' of arguments in which pre-existing concepts are employed or misemployed: employed (that is) correctly or faultily. This structure is analyzed in a formal manner, so that 'good science' is made to appear a matter of doing one's scientific arguing impeccably - i.e, of avoiding inferential blunders, and remaining 'logical'. Inevitably, this approach conceals the distinction between 'logicality' and 'rationality'. For, in practice 'good science' involves not merely doing sums and inferences right - i.e. aright, rightly or correctly. It also, more importantly involves doing the right sums and inferences - i.e. recognizing what particular concepts and forms of argument are relevant and applicableinany problem-posing situation. Correspondingly, scientific failurespringsmost typically from irrelevance or misjudgment in matching ofconceptsto situations, rather than from any subsequent logical blundering. I myself doubt, indeed, whether a logical slip or formal error ever amounts by itself, to a failure of scientific 'reasonableness' or 'rationality'. Instead we need to distinguish sharply between the 'rationality' of of science or scientists and the 'logicality' of scientific arguments. In the actual doing of science, logicality represents a kind of intellectual accountancy: concerned with keeping our inferences neat and tidy, avoiding

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formal blunders, doing our sums aright - and all these competences involve employing already existing theories and concepts in accordance with 'established' procedures. The rationality and reasonableness of scientific thinking, on the other hand, have to do with the ways in which the application of existing concepts is extended, or with the ways in which new concepts are developed, in order to solve outstanding scientific problems. And this is a matter, not of following established procedures rightly (i.e. impeccably) but of recognizing what are the right (i.e. relevant) procedures to employ in a new situation, and of devising new explanatory methods and inferences, of kinds that have previously had no scientific use - and a fortiori no 'established' scientific use. In science as elsewhere, that is, man shows that he is acting 'reasonably' and is 'open to reason,' not by his fixed ideas or by his competence in standardized, stereotyped inferences, but by the way in which he extends and modijies his ideas and intellectual skills. To summarize our central problem in a phrase, let me borrow an image from Professor Causey. Analysis in logical terms can give us an instantaneous 'snapshot' of faultless scientific inference, within the scope of existing concepts and methods; but this still leaves us without the 'moving picture' we need if we are to understand the rational procedures by which the scope of science is effectively extended. And this is no accident. For the rationality of the conceptual changes by which new science is made, and the reasonableness of the scientists who make them, could never have been defined or analyzed as matters of 'faultless inference' alone.

This distinction is so elementary that one may want to ask how the problem of rationality or reasonableness, in science ever dropped out of sight in the first place. The prime figure was (I believe) Gottlob Frege. The drive towards mathematical Platonism which has been so powerful in twentieth-century philosophical analysis was triggered by Frege's reaction against the conflation of logic with cognitive psychology. The detailed background to Frege's campaign, in the work of Wundt and the other philosopher-psychologists of the time, would be a first-rate thesis subject for some talented graduate student, but there is room here to deal with only one aspect of the story.

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The point I shall pick on is this. The logicians' program for philosophy of science - and for philosophy generally - had a multiple paternity, and its progenitors were not all of one mind. On the contrary, we can order their interests along a spectrum. At one extreme, the program owed a lot to the example of pure mathematicians: especially to Klein, whose techniques for 'mapping' different branches of mathematics on one another inspired Russell's attempts to 'map' arithmetic onto pure logic, and also to Hilbert, whose mathematical program of 'formalization'gave an impulse to the subsequent campaign of 'axiomatization' in philosophy of science. I11 the center, there was a group of philosophers with a first training in pure mathematics, and mathematicians with philosophical preoccupations, beginning with Frege and Russell, Peano and Vailati. Their concerns were partly internal to mathematics, but they were basically philosophical. In Frege's case, the development of symbolic logic was spurred on by the pursuit of 'pure concepts', untainted by history or psychology, in Russell's by the quest for a genuinely 'perspicuous' language or symbolism, in which the 'true logical forms' of propositions would be immediately evident and explicit. At the other end of the spectrum there stands a third party, comprising philosophers with a first training in physics, together with physicists interested in philosophical aspects of their own work. Hertz and Boltzmann obviously belong in this group; I myself would also include Wittgenstein; and for good measure one might add their most significant forerunner, Immanuel Kant. In writing and talking about the philosophy of science, all these men focussed on the notion of 'representation': a term that English writers have used to translate both Vorstellung - the word employed by Kant, Schopenhauer and Boltzmann - and also Dar~tellungthe variant employed by Hertz, and picked up from him by Wittgenstein. From Kant's Critique of Pure Reason right up to the Tractatus LogicoPhilosophicus, in fact, the central notion in German-language discussions of perception and scientific explanation was this notion of 'representation'. Where ancient Greeks had summarized the task of science in the phrase sozein ta plzainomena, the corresponding nineteenth-century German thesis was that the task of the human mind is to compose a 'representation' of phenomena. The multiple paternity of 'logical analysis' had important - and largely overlooked - consequences, which become apparent if one asks (for

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instance) what purpose was served, for the members of each party, by the procedure of axion7atizarion. For pure mathematicians, of course, axiomatization was its own reward. Integrating a set of previously unrelated theorems into an axiomatic system was for them an end in itself, not just a part or means of achieving some further non-mathematical aim. Producing a more comprehensive, powerful and elegant axiom-system was an intrinsic mathematical success, quite regardless of its possible applications, since this was an essential element in the pure mathematician's proper intellectual mission. For a physicist like Hertz, the situation was absolutely different. In axiomatizing the science of mechanics, Hertz's aim was not to bring off a feat of formal virtuosity alone: he was not just a pure mathematician who happened to work in the field of 'rational mechanics'. What Hertz stood to gain from a successful axiomatization was someting substantial within plvsics. Axiomatization was to be the means to a larger end; and that end was the more effective conceptual organization o f p h y ~ i c aunderstanding l - or, as he himself put it, a better Darstellung of mechanical phenomena. Even apart from the central philosophical figures, i.e. Frege and Russell, this difference in attitude is already significant. Just because Hertz regarded the axiomatization of mechanics as a scientific means, rather than as an end-in-itself, it was - for him - only one of several distinct alternatives. Far from anticipating Russell's belief that a 'perspicuous' symbolism would make explicit 'the one true logical form' of propositions, Hertz descr~bedhis own axiom-system as one possible Bild, Darstellung or 'model' among others, whose merits must be judged in competition with its rivals in terms of extrinsic explanatory fruits. When so judged (Hertz saw) his axiom-system might prove superior only in certain contexts rather than others, and for certain purposes rather than others, so he did not have to claim that it was the uniquely meritorious representation of mechanical phenomena. Rather, it was a way of doing one of the jobs of theoretical physics; and for the legitimate purposes of other contexts, it might be proper to employ quite different methods of 'representation' - even Frege's despised 'mental images' or innere Scheinbilder. Hertz was historically ~nfluential,in turn, for two reasons. He was the first, the most lasting, and in some ways the most profound philosophical influence on Wittgenstein, in both his contrasted periods; and in addition the example of his Principles of Mechanics was regularly appealed to, in

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the 1920's and 30's as the prime authority for extending the logicians' program out of the philosophy of pure mathematics into the philosophy of natural science. As it happened, however, the philosophers who had the largest stake in the logicians' program saw Hertz's work through the eyes of mathematicians, rather than of working physicists, and so overlooked the deep differences of aim between (say) Hertz and Peano. Meanwhile, that devotee of Hertz, Ludwig Wittgenstein, was grumbling away in the background - Waismann, for instance, reports him criticizing Frege and Russell for being excessively preoccupied with the application of logical symbolism to mathematical examples - but his protests went unheard and disregarded. The logicians' program for philosophical analysis and philosophy of science accordingly developed in a middle ground, somewhere between the extremes of Klein and Hertz. In both Frege and Russell, the heart of the program was a kind of philosophical reformation. Frege's Begr[ffsclzrift, like Russell's propositional calculus, was intended to serve as the formal core of a disinfected language, and in this language alone 'pure concepts' or 'true logical forms' could be expressed as unambiguously as that reformation required. So for Russell, in direct contrast to Hertz, the propositional calculus was not just one among several alternative ways of getting an intellectual job done - on a par with (say) using mental images. On the contrary, this was to be the central element in the one truly perspicuous symbolisnl -- the symbolism (to use Frege's revealingly Platonist phrase) of 'concepts in their pure form.' At its most ambitious, the resulting philosophical development culminated in the Unity of Science movement of the 1930's, whose methods and principles combined elements from both extremes. On the one hand, its supporters declared that their aims were scientific: the concepts of natural science were to be reorganized on new principles, and integrated into the true corpus of positive knowledge. On the other hand, they treated axiomatization in the spirit of pure mathematicians, as self-justifying, and so as an end in itself. Like Frege and Russell, they saw pure mathematics as providing the formal model for arty perspicuous representation of nature. By adding fresh theoretical terms and definitions (they supposed) we might progressively hope to extend the scope of Russell's logical calculus to embrace not only pure mathematics, but also theoretical physics, genetics, and even - with sufficient ingenuity - physiology and psychology. In this way,

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the specific virtues and merits of pure mathematics were taken as binding on all intellectual disciplines, and most of all on any natural science worthy of the name. (How Plato and Descartes would have cheered!)

So much for the historical background: let me now come to my diagnosis. For too long, I claim, philosophers of science have been blind to the differences between rationality and logicality. As a result, they have restricted their attention to those aspects of scientific investigation which can be construed in formal terms, as involving logical systems and strict inferences; and they have been unable to give an account of those other aspects which - while 'rational' enough, in all conscience are non-formalizable. Hence the present impasse in the philosophy of science over the rationality of conceptual change, and also the resulting malaise. This has happened chiefly (I believe) through following too devotedly the philosophical example of Frege and Russell, who have led logic-oriented philosophers to interpret one ofthe means of natural science as its essential end. In some cases deliberately, in others unthinkingly, these philosophers have identified the creation of logical systems, which is one valid intellectual technique in science among others, with the conceptual organization of understanding, which is its more general goal. Yet, while the creation of logical systems has an unquestionable place in the conceptual organization of understanding, these two activities cannot simply be equated. Logical systems can be created for many different purposes, in the context of many different intellectual activities, or none: a formal network of theorems would not cease to be 'mathematical' (to cite an example of Wittgenstein's) just because its only application was to determine the patterns on a piece of wallpaper. Logical systems become 'scientific', in short, only through being given a scientific application: only through being put to use, that is, within the conceptual organization of scientific understanding. It is one thing then to consider logical systems for themselves, and in their own right: it is another thing to consider them as the intellectual instruments of a natural science, with all its specific concepts and problems. And this brings us to our next important point. As wellas distinguishing between rationality and logicality, we must also take care to distinguish between the intellectual content of an entire science, and that

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of any single theory employed in that science. In suitable cases, the content of any one theory or 'conceptual system' can perhaps be represented by a 'logical system': though it would be a mistake - even here - to equate the resulting logical system with the conceptual system which it is used to represent. (The 'systematicity' of a conceptual system is that of a semantic domain, like that which is established when we segment the color-space into 'red', 'green', 'blue', etc., not that of a formal or syntactic structure.) But the content of an entire 'science' can be cast in a strictly logical form only in quite exceptional circumstances. Normally, any particular science will comprise numerous co-existing, logically-independent theories or conceptual systems, and it will be nonetheless 'scientific' for doing so. In this respect the dominant influence of Newtonian mechanics, or an example of what a science should become, has been unhappy and misleading. One might even argue that Ernst Mach's book, The Science of Mechanics, was ill-named, since mechanics as such is not 'a science', but rather an analytical instrument employed within the science of physics. Hertz and Mach were in fact both writing just at the moment when Newton's physical mechanics was in process of crystallizing into a branch of pure mathematics: the branch known today oddly by my standards - as 'rational mechanics'. And the crucial distinction, between mechanics as a branch of pure mathematics and as an instrument of physical science, was made very nearly explicit by Hertz himself, when he set out his argument in two parts - the first concerned with the inner articulation of mechanical theory alone, the second with its application to actual empirical situations. Granted this distinction between a science and ~ t component s theories, we can take one further step away from the present impasse. Any particular science (I have said) normally comprises an aggregate of logicallyindependent theories and concepts. The scientists working in that field may, in certain special cases, be moving towards a situation in which all its concepts are organized into a single integrated 'conceptual system'. But - pure geometry and rational mechanics apart - that is normally a long-term goal rather than an actuality and, when it is realized, the theoretical system in question is then trembling on the verge of becoming - in turn - a branch of pure mathematics. In the meantime, 'axiomatizing' remains a formal possibility, as an exercise in logic, but there is no scientific occasion - and no scientific profit - in pursuing it.

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To go further, there may even be a certain scientific loss incurred as a result of premature axiomatization. For there is normally a great deal of logical 'slip', 'gappiness' and even inconsistency, between the constituent concepts and theories of an entire science; and - as Professor Shapere has emphasized elsewhere -this very 'logical gappiness' is one thing that helps to define the characteristic conceptual problems of a science and so powers its rational development. In quantum electrodynamics (to cite Shapere's example) we must at present assume, for certain purposes, that an electron has zero radius while, for other equally legitimate purposes within the same science, we must assume that it has non-zero radius. For pure mathematicians, this situation would be catastrophic. For physicists, it is at worst unsatisfactory; a challenge, and a source of conceptual problems. If they could find a way of circumventing this contradiction, their scientific understanding would be improved; but for the moment, if they have to live with it, they know how to do so.

So much by way of criticism of the logicians' systematic ideal; let me now propose a counter-description of science which does better justice to our working conceptions of scientific rationality and reasonableness. Consider a natural science not as a tight and coherent logical system, but rather as a conceptual aggregate or 'population', within which there are - at most localized pockets of 'logical' systematicity. The whole problem of scientific rationality can then be restated in new terms. And I shall here indicate, as concisely as I can, how this change of standpoint opens up a fresh line of attack on some outstanding problems in the philosophy of science. We may begin by remarking that, within any particular natural science, numerous different explanatory procedures, concepts and methods of representation are normally current, as means of fulfilling the proper intellectual missions of the science concerned. Between some, but only some, of these concepts and procedures there are formal or 'logical' links - as there are, for instance, between the Newtonian concepts of 'force', 'mass' and 'momentum'. (If there are these formal links, that is because the terms in question were introduced at one and the same time, for one and the same purpose, and so interdefined.) Meanwhile, alongside these systematically-related concepts and procedures, there will normally

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be others that are logically independent of, and even logically at variance with, one another. (These co-existing and independent sets of concepts and procedures will commonly have been introduced at dzfferent stages in the development of the science.) An adequate analysis of 'rationality' and 'reasonableness' in science will then require us to study: (i) the various possible non-formal relations between the co-existing concepts, explanatory procedures and methods of representation circulating in each of the different natural sciences, and (ii) the ways in which, in each field of science, conceptual problems arise and are recognized as such. As Shapere's example indicates, logical incoherence in the assumptions of a science is one source of conceptual problems among others; but scientists most frequently recognize other, nonformal conditions as giving rise to conceptual problems, and these call for a more careful analysis than they have yet had. Once we have seen how the proper intellectual missions of any science serves to define its outstanding problems, the next task is to study the activity of conceptual innovation by which scientists do their best to meet the intellectual demands of those problems. Often enough, these demands taken as a whole are irreconcilable. Improved understanding in one respect can be obtained, only by paying a price in other respects; and it is a matter for the nonformal theoretical judgment of scientists to decide what intellectual gain justifies what intellectual price. Even where there is no conflict of interests, there will normally be several competing proposals - or 'conceptual variants' - all designed to help us improve our scientific understanding in the field concerned; and it is again a matter of critical judgment to determine which of these variants does most to improve our understanding. So at this point we need to study the manner in which - and the criteria by reference to which -these choices between rival conceptual variants are made. Once more, this is not a formal matter, to be described in terms of the 'logical articulation' of the concepts and propositions in question; rather, it has to do with the ways in which those concepts can be applied, extended and/or modified, in the interest of better scientific understanding - with the ways (that is) in which rival variants can yield more effective procedures of explanation or techniques of representation. Let me put the issues that arise about the rational development of

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scientific concepts in a nutshell. (1) Any natural science employs a repertory of concepts and explanatory procedures which, at any stage in its history, goes only part way towards fulfilling its current intellectual missions. (2) The gap between the legitimate goals of the science and its existing explanatory capacities defines a reservoir of outstanding theoretical problems. (3) Alongside the established repertory of concepts and procedures, there is a pool of conceptual variants or 'possibilities' which are under discussion as candidates for incorporation into the repertory of 'established' concepts and procedures. (4) A definitive conceptual change results from the agreed selection of certain theoretical innovations from this pool of variants, as best meeting the intellectual demands of the current theoretical situation. (5) This selection is made with an eye to numerous and partly conflicting criteria of choice. (6) These criteria vary from science to science, and from epoch to epoch within any given science, being determined by developing intellectual missions of the science in question. About this group of issues, three things must be said in conclusion. I n the first place, they all raise matters of substance rather than of form. The spec& intellectual missions governing the research programs of the various natural sciences are defined in terms that respect the special aspects of external nature with which they deal. They cannot be specified in terms of universal formal features, like entailment, inconsistency and elegance. The same is true of the shortcomings that define the outstanding problems in a science, and of the intellectual requirements to be met before conceptual variants can become established. These, in turn, depend on the substantive tasks of the particular science concerned. As for the resulting changes in the theories and explanatory procedures of the science, these generate new populations of concepts and propositions, whose relations to their predecessors are even less formal or 'systematic' than the interrelations between the co-existing sets of concepts and propositions current in a single cross-section of its development. (At most, successive phases in the historical development of a science are linked by partial analogies, like those laid down in the 'correspondence principle', which relates quantum-mechanical and classical interpretations of corresponding physical phenomena.) In the second place, it is precisely these non-formal questions about conceptual change in the sciences that have most stubbornly resisted

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answering within the limits of the logicians' program for philosophy of science. If we wish to give an adequate account either of the historical development of a science, or of the sense in which the intellectual choices involved in this development are 'rational', or of the manner in which scientists display their 'reasonableness' in the course of making those choices, our analysis will have to be very different in kind from those that philosophers of science have become accustomed to during the last 50 years. Such an account cannot be given in formal, still less in quasimathematical terms. For the steps by which the conceptual and explanatory repertories of the sciences develop are - by their very nature -populational rather than jormal. Their aim is to devise explanatory techniques which meet the specific intellectual demands of particular scientific problems; and questions about their 'rationality' or 'reasonableness' are concerned with how far and in what respects, they actually succeed in meeting those demands. Finally, the study of conceptual populations is not only a necessary supplement to the study of logical and propositional systems, it is the prior and more fundamental task for philosophers of science to undertake. Unless we already have accepted a certain set of concepts as valid, applicable and/or relevant to our scientific inquiries, we are not yet in a position toforrnulate any propositions at all, still less to investigate their interrelations. And only in the last few years have we come to realize how far we are, in any field of science, from having any 'uniquely rational' or universally acceptable set of concepts or presuppositions to start with. That is why the analysis of scientific rationality must focus, in our generation, on the problems of conceptual diversity and conceptual change. The main unsolved problems in philosophy of science accordingly raise questions less about 'probability' and 'formal adequacy' than about intellectual ecology, and Professor Causey's 'moving picture' of the historical development of the sciences will have to be an evolutionary one. It will involve us in looking at the changing concepts of science as elements not in static 'theorems' but in developing theories, with an eye not to their current 'implications' but to their extended applications. And it will consider the rational procedures adopted by scientists as reflecting the nature of their externally directed tasks: these being, not to formulate a logically-impeccable system of 'unified science' continuous with symbolic logic and pure mathematices, but rather to improve our intellectual grasp

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over the world of nature in whatever manner, and by whatever means, the actual demands of all their varied problem-situations may suggest or require. I do not, of course, underestimate either the intrinsic difficulties involved in actually carrying through this new line of philosophical attack, or the temerity involved in encouraging other philosophers of science to move in what must, for them, be a novel and unfamiliar direction. But a moment comes when the only thing left to do is to be blunt and direct. So, as one who has always been more interested in the historical processes and rational procedures of conceptual change than in the logical articulation of static formalisms let me simply present my three central theses. (a) A man shows his rationality not by the ideas he actually holds, but by the manner and the circumstances in which he is prepared to change his ideas: this is as true in science as anywhere else. (b) An adequate account of the rationality of conceptual change, like an adequate account of organic evolution, will avoid any sharp distinctions between different kinds of change (normal, revolutionary etc.), aLld explain all historical changes in science as the varied outcomes of one and the same set of factors working together in different ways. (c) Talk about logical systems, and about the timeless deductive relations within such formal systems, has served its purpose in the philosophy of science. The most serious outstanding problems in the subject- about the rational development of scientific ideas, and about the reasonableness of scientific procedures - require us to think, instead, about conceptual populations, and about the temporal sequences of conceptual variation and selective perpetuation by which these populations develop. There may be no such thing as a logic of discovery; but conceptual change in science certainly has its characteristic rationale. And we shall learn more about the rationality of scientific development from five years' study of 'intellectual ecology' than we shall learn from 'inductive logic' in a century.

Michigan State University