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Problems, truth, and consistency
DISCUSSIONS LARRY LAUDAN” PROBLEMS, TRUTH, AND CONSISTENCY IN A RECENT article in this Journal,’
Husain Sarkar posed some fundamental challenges to my version of a problem-solving methodology of science. Sarkar’s essay consists both of criticisms of some of my formulations of that model and of constructive recommendations about ways in which that model might be fruitfully amended. Some of his criticisms are cogent and some of the recommendations are highly useful; but in certain respects, he has mistaken my ambitions and in several cases his criticisms will not sustain detailed analysis. Above all, Sarkar is concerned to get truth back into an account of the scientific enterprise. As I understand his position, he is generally sympathetic to a pragmatic and problem-solving approach to scientific inquiry, but believes that such an approach, to be coherent, must assign a central role to the quest for truth in the scientific enterprise. He finds my analysis wanting chiefly (but not exclusively) because I do not represent science as the search for true theories. Indeed, virtually all of his criticisms, and most of his counterexamples, are designed to show how central a role considerations of truth play in an account of science. In Progress and Its Problems (hereafter: PIP), and several more recent publications,* I have been puzzling with one of the paradoxes that confounds contemporary philosophy of science. In a nutshell, it amounts to this: the possibility of exhibiting science as a rational activity seems to depend (given our understanding of rationality in general) on our showing: (a) that there are certain aims or goals of scientific inquiry and (b) that the methods of theory assessment and appraisal used in science can be shown to conduce to the achievement, at least partially, of those goals and aims. Unless an appropriate ends/means relation can be established between the aims of science and its *University of Pittsburgh. Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A. ‘H. Sarkar, ‘Truth, Problem-Solving and Methodology’, Studies in Hisrory and Philosophy of Science 12 (1981). 61-73. ‘See especially ‘A Confutation
of Convergent Realism’, Phibsophy of Science 48 (1981), 19 - 49; ‘A Problem-Solving Approach to Scientific Progress’, in 1. Hacking (ed.), Scientific Revolutions (Oxford, 1981); and ‘The Philosophy of Progress’, in I. Hacking (ed.), PSA 1978, Vol. 2. Stud. Hist. Phil. Sci., Vol. 13, No. 1 pp. 13 - 80, 1982.
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methods, we will be in no position warrantedly to assert that science is a rational activity. This much is uncontroversial: goal-directed activity which chronically fails to further the relevant goals is a paradigmatic instance of irrationality. Almost as uncontroversial is the claim that the methods presently used in the sciences do not, so far as anyone has been able to show, lead to the formulation of theories which are true, verisimilar or approximately true. We would like it to be otherwise, of course; but few if any philosophers of science would claim themselves to be in a position to show that the methodological repertoire of contemporary science includes methods which can be shown to lead us closer and closer to true theoretical accounts of the physical world. It takes little ingenuity to put these two points together and to realize that they lead to this staggering conclusion: insofar as, and to the extent that, the aim of science is the formulation of true (or ever more nearly true) theories, then we have no grounds for viewing science as a rational activity. Because we have not documented the appropriate sort of ends/means linkage necessary to justify an attribution of rationality to science - conceived as the search for true theories - I have suggested that it might be as well to leave questions of truth outside of our account of the aims of science. My project in PIP was to explore whether, with respects to goals or aims other than securing true theories, science might turn out to be a paradigmatically rational activity. The strategy of Sarkar’s essay is to exhibit that, despite my efforts to read truth out of the axiology of science, my own problem-solving model requires me to fall back on truth as a goal of science. Virtually all of his specific arguments, including the three which I shall examine below, involve efforts to show that my account is incoherent unless we imagine that the scientist aspires to the truth. The first point to note is that Sarkar’s strategy is itself fundamentally ad hominem. Even if it were the case that the model I have articulated required the inclusion of truth among the aims of science, that would in no way count against the argument briefly summarized above which seeks to show that the search for true theories is, on present evidence, an irrational one. If Sarkar is to establish that ‘there is ample reason nol to discard the notion of truth” from among the aims of science, then he must deal directly with that argument rather than with my model. Indeed, on my present understanding of the force of that argument, the only thing that would follow from Sarkar’s successfully showing that my model required a truth-oriented axiology would be the fact that my model - like most other extant ones - entails the irrationality of science. Such a consequence would, in my view, be sufficient to discredit my model as an account of scientific rationality; but it would not justify the claim ‘Sarkar,
op. cif.. p. 73.
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that science really does seek true theories after all. The object of this short essay is to suggest that Sarkar’s specific arguments about the necessity of a presumption of truth among the aims of science in the model of PIP are, by and large, wide of the mark. In brief, Sarkar makes three chief arguments in this regard. He insists, first, that my notion of a problem solution inevitably requires reference to truth. Secondly, he claims that my opposition to inconsistent theories only makes sense on the assumption that the scientist aspires to the truth. Thirdly, he alleges that my model runs into all the same difficulties that have confronted truth-oriented models of verisimilitude and that there is thus nothing to be gained by treating science as if it were other than a truth-seeking activity. Because I believe that all three arguments rest on serious conceptual confusions, I want to deal with them briefly.
I. Truth and Problem Solutions In PIP, I suggested that a theory can be credited with solving a problem just so long as that theory entails, or figures non-trivially in a complex of assumptions which entail, a statement of the problem in question. In response to this characterization of the nature of a solution, Sarkar makes the semantic point that entailment obtains only between statements which are either true or false. As he puts it, ‘the only viable analysis of entailment is in terms of logical consequence which in turn rests essentially on the notion of truth’.’ Because the notion of a solution involves entailments and because entailments involve statements possessing truth values, Sarkar concludes that I have prematurely and (given my account of problem solution) inconsistentlv written truth out of meta-methodology. The fact of the matter is that Sarkar is here confounding semantic and epistemic issues which need to be carefully distinguished. I have nowhere denied (indeed I have frequently stressed) that the statements making up the theories and problems of science have truth values. But it is one thing to make that semantic point and quite another to make the epistemic claim that there are circumstances under which we are warranted in ascribing truth to a scientific theory. Insofar as I have a quarrel with scientific realists, it is at the epistemic rather than the semantic level. The fact that theories have truth values manifestly does not justify our including the quest for true theories among the aims of science. That axiological thesis could only be justified by epistemic arguments. Sarkar evidently fails to see that semantic tools will not accomplish epistemic chores. ‘Sarkar,
op. cit., p. 66.
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What makes his use of this argument more than a little ironic is that I sketched out precisely these distinctions at some length in a paper to which he himself refers. Thus, in ‘The Philosophy of Progress’,5 I went to some pains to stress that ‘scientific theories have truth values’. I called this the thesis of semantic realism and endorsed it without qualifications. But I said then, and find it necessary to repeat here, that semantic realism entails nothing whatever about the appropriate goals of scientific inquiry. It is entirely consistent to say, on the one hand, that theories have truth values, and to insist, on the other hand, that we do not know of epistemic circumstances which would warrant the attribution of a positive truth value to the sorts of things that we customarily regard as scientific theories. Sarkar’s reiteration of my point that theories have truth values will not motivate the claim that it is legitimate to include the quest for true theories among the central aims of science.
II. Comparative
Assessments
of Problem-Solving
Efficacy
It is well known that the theories of progress of Popper and Lakatos have run into acute difficulties stemming from their efforts to articulate a measure for comparing rival scientific theories. To put the matter simply, both authors subscribe to the view that one theory can be better than a rival only if it explains everything explained by its rival plus some other things besides. Now there are a variety of paradoxes confronting this way of comparing theories which have been explored by Miller, Tiechy and Gruenbaum infer afia. Sarkar seems to believe that comparable paradoxes confront the machinery for comparing theories which I sketched out in PIP; it is just this belief which prompts his remark that ‘Laudan’s methodology is at least as inadequate as Popper’s’.B I want to discuss the one case he cites in some detail which, he believes, poses challenges to a problem-solving methodology as grave as those confronting measures of content and verisimilitude. I can do no better than quote Sarkar’s text: Now consider two consistent but incomplete theories, 7 and T’ , such that T entails the solution of a solved problem, P (Why is the sky blue?) and T’ entails the corresponding statement of the problem not-P (Why is the sky not blue?). Let K be some solvable-problem, not solved by T. Then (not-p or K) is a statement of a solvable-problem entailed by T’ , but not by T. In brief, any claim about the possibility of comparing the problem-content of two theories, which together are logically incompatible, remains unsupported.’
‘Laudan, ‘The Philosophy ‘Sarkar. ‘Ibid.
op. cit., p. 70.
of Progress’,
PSA 1978.
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It is quite clear why examples of this sort are worrying to Popperians, for what they show is that incomplete theories can never explain everything explained by their (false) rivals and thus can never be said to include the content of their rivals. Under such circumstances, Popperian assessments of progress seem out of the question. But examples such as these cut no ice against the appraisal measures I have proposed, as I shall show below. Is Sarkar right in saying that the comparison of the problem-solving effectiveness of two rival theories, as I have defined it, has not been shown to be possible? The answer is surely no, because I do not require one theory to be able to solve all the problems of its rivals before it can be judged progressive over its rivals. The example which Sarkar cites is decisive against any measure of progress which, like Popper’s and Lakatos’, requires a superior theory to have all the successes of its rivals. But I have argued that progressive theories should solve more problems than their rivals have solved, not that they should solve all the problems credited to their rivals. The fact that, in Sarkar’s example, T’ can solve a problem (the ‘problem’ formed by disjoining the statements ‘R and ‘not-P’) not solved by T does not preclude the possibility that T may nonetheless have solved more problems than T’ and thus may still emerge, as our intuitions about the case would suggest, as superior to T. Indeed, what can be shown in the specific case Sarkar cites is that, provided T initially had a better problem-solving record than T’ prior to the consideration of Sarkar’s example, then Twill emerge from Sarkar’s example with a better problem-solving record than T' . But before I prove that result, it should be noted how bizarre Sarkar’s example is in the first place. Typically, scientific ‘problems’ are not generated by applying the logical operation of disjunction introduction between statements referring to nomologically-independent events. I take it that no scientist would hold this to be a well-defined ‘problem’: ‘either light does not bend near the sun or saccharin induces cancer’. Nor would any scientist regard Newton’s theory as ‘solving’ this bizarre problem just because Newton’s theory entails the first (false) disjunct. Yet such is the character of Sarkar’s example. But for the sake of argument, let us grant that such problems are legitimate and that a theory solves such a problem so long as it entails at least one of the disjuncts (even if it is the false disjunct). The admission of such problems and solutions will not upset the problem-solving bookkeeping. Consider: we have two rival theories, T and T’ , such that T entails P and T’ entails not-P (where P is presumed to be true). In these circumstances, T will be credited with solving P and T’ will get no credit. But now enters Sarkar with the insistence that T’ can solve the problem ‘not-P or K’, which T cannot solve because it entails neither ‘not-P’ nor ‘K’. Score one, as it were, for T’ . But, of course, we need not stop here, because Twill be able to ‘solve’ the ‘problem’, ‘P or K’ -
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a problem which T’ cannot solve. Now we have a situation where Tsolves two problems (‘P’ and ‘P or K’) while T’ solves only one (‘not-P or K’), thus preserving the initial problem-solving superiority of T over T’. More generally, one can see that corresponding to every solved problem of T’ generated by disjoining a false entailment of T’ with a statement independent of T, there will be a corresponding solved problem credited to T, formed by disjoining a true entailment of T with a statement independent of T. In short, such problem solutions credited to Tand T’ will ‘cancel out’ and it will remain true that T (because it solves P while T’ does not) has solved more problems than T' . So long as T solves more problems than T’ prior to the assessment of Sarkar-like disjunctive problems, then T will continue to beat T’ once problems of Sarkar’s sort are reckoned with. Under the circumstances, Sarkar’s charge that comparison of relative problem-solving effectiveness is impossible in such cases is without merit. By showing that Sarkar’s specific counter-example fails to be compelling, I do not mean to suggest that similar sorts of counter-examples can be met by the same response. On the contrary, it seems to me that there clearly are cases, parallel to Sarkar’s, where the problem-solving ‘success’ of an intuitively less successful theory can be jacked up so as to exceed the successes of its (intuitively superior) rival.8 But all the examples of this sort which I can conceive of depend upon accepting a view of what constitutes a problem and a solution which I reject. Specifically, these examples require one to maintain both that every disjunctive statement is a problem and that a theory solves every statement it entails. I deny both claims. It is true that I have said that a theory solves a problem when it entails a statement of the problem. But that is a far cry from the claim - crucial for the generation of Sarkar-like examples - that every statement so entailed by a theory describes a problem which the theory can be credited with solving. Problems arise in a certain context of inquiry; given a particular context, and the expectations about natural processes which constitute that context, only certain problems can conceivably arise as problems. To show the inadequacy of the bookkeeping mechanisms I have proposed for assessing comparative problem solving effectiveness, one must deal with a theory’s problems rather than with the broader set of its logical entailments. ‘Here is one example of how one might proceed: imagine two incomplete and contrary theories, T, and K, such that T, solves P, and S, while T, solves P, but not P,. Thus far, T, is a better problem-solver than 71. Now, imagine that G entails S,, S, and S, and that all three are false. 7,. by contrast, entails nothing about S,, S,, or .S, and nothing about their negations. Under these circumstances, we can disjoin any of these false entailments with a statement K independent of 27. In such a situation, K will have a host of true entailments which cannot be ‘paired’ with entailments of T,. More generally, one can say that the more refutations a theory has (provided those refutations are logically independent of its rivals), the higher its problem-solving success will appear to be. Assuming, of course, that any genuine entailment of a theory counts among its solved problems.
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III. Problem-Solving and Inconsistency Like Mellor and Gutting before him, Sarkar takes the view that, if we abandon the aim of true theories, we will no long be able to object to a theory that is inconsistent since, as he sees it, ‘only if truth is our aim can we have any objection to theories that are logically inconsistent’.g His strategy here, as above, is decidedly ad hominem. He seeks to show that, in terms of the model of PIP, inconsistent theories solve more problems than consistent ones. Since, on his construal of my position, I have no way of discrediting inconsistent theories, he concludes that only models of change which give pride of place to the quest for truth are viable. Before dealing specifically with the role of inconsistent theories in my model, it is important to stress that Sarkar’s general thesis is a non sequitur. The fact, if it were a fact, that my model gives high marks to inconsistent theories, would in no way establish that inconsistency can only emerge as a cognitive liability in those philosophies of science which portray science as a truth-seeking activity. That much said, let me proceed to Sarkar’s more specific claim to the effect that my model, far from preserving our intuition that inconsistent theories are otiose, makes inconsistent theories highly desirable. His argument, in brief, is this: because an inconsistent theory arguably entails every statement (and its negation), inconsistent theories will always be able to take credit for solving (i.e. entailing) every problem. It follows that every inconsistent theory will solve more problems than any consistent (but incomplete) theory, whether true or false. There are several points to be made in reply to Sarkar’s claim that a problem-solving approach such as mine must accord high positive status to inconsistent theories. (1) Sarkar’s analysis chronically ignores the fact that the problem-solving effectiveness of a theory is related to both the empirical and the conceptual problems which it solves.‘o As I pointed out at length in PIP, internal inconsistency constitutes an acute conceptual difficulty for a theory which exhibits it. Once the conceptual appraisal of a theory is factored into our assessment of that theory’s adequacy, it does not follow that a theory which solves the largest number of empirical problems will necessarily be the theory of choice. Only by completely ignoring the central role of conceptual problems in theory assessment can Sarkar reach the conclusion that, on my analysis, progress necessarily occurs when a consistent theory is replaced by an inconsistent one. (2) But there are other grounds, independent of the issue of conceptual OSarkar,op. cir.. p. 70. ‘This particular response duplicates an argument made by M. Finocchiaro in his ‘Remarks on
Truth, Problem-Solvingand Methodology’,Studies in Hisrory und Phitosophy of Science 12 (1981). 261- 268.
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problems, for faulting inconsistent theories. One of them is that further progress in science would be impossible if we were prepared to allow a sequence of inconsistent theories. In a passage of mine which Sarkar quotes but proceeds to ignore, I pointed out that the ‘replacement of one inconsistent theory by another could never count as progress with respect to problemsolving effectiveness’.” If one can show that the adoption of a certain research strategy would permanently foreclose the possibility of further progress in science, I believe that constitutes grounds for rejecting the strategy. Because the strategy of countenancing inconsistent theories would preclude the possibility of further empirical progress (since no inconsistent theory can solve more problems than any other), it should be rejected. And that rejection has nothing whatever to do with the inclusion of truth among the aims of science. (3) I take it that on virtually any analysis of science, one of the tasks that we chiefly expect our theories to perform is that of putting us in a position to anticipate nature. We do not expect, and certainly do not require, that a theory will always lead to correct anticipations of nature; but we do expect it to shape our expectations in various ways. That is indeed the raison d’gtre of science. Now, the central trouble with inconsistent theories, as I see it, is that they dismally fail to fulfil this central function. If a theory is inconsistent, it does nothing whatever to shape our expectations about how the world might behave. It is true in an abstract sense that an inconsistent theory will have among its entailments statements which truly describe the world. But that is of no heuristic use to us at all, so far as the shaping of expectations is concerned. Theory plays a vital heuristic role in directing our attention to certain dimensions of a situation; and this is as true of false theories as it is of true ones. But inconsistent theories cannot play this heuristic role, because we do not know what to do with them. If someone offers me the ‘theory’ T (which says ‘snow is white and snow is not white’), he has given me no clues about how to proceed in interacting with nature. By contrast, if he offers me a consistent (but non-tautologous) theory - whether true or false - he will have begun to indicate features of the situation which I might explore. The point is this: there are a host of heuristic, conceptual and pragmatic considerations which provide a rationale for objecting to inconsistent theories. One need not believe that the aim of science is the discovery of true theories in order to find inconsistency undesirable. What we see in Sarkar’s essay is an example of the increasingly frequent phenomenon of extravagant claims being made concerning the explanatory riches of realism, linked to largely undocumented assertions about the explanatory poverty of non-realist epistemologies. (I have examined some more familiar instances of this syndrome elsewhere.“) “Cf. Laudan, ‘The Philosophy of Progress’, note 7, and Sarkar, op. cit., p. 71 “See Laudan, ‘A Confutation of Convergent Realism’.
Husain Sarkar posed some fundamental challenges to my version of a problem-solving methodology of science. Sarkar’s essay consists both of criticisms of some of my formulations of that model and of constructive recommendations about ways in which that model might be fruitfully amended. Some of his criticisms are cogent and some of the recommendations are highly useful; but in certain respects, he has mistaken my ambitions and in several cases his criticisms will not sustain detailed analysis. Above all, Sarkar is concerned to get truth back into an account of the scientific enterprise. As I understand his position, he is generally sympathetic to a pragmatic and problem-solving approach to scientific inquiry, but believes that such an approach, to be coherent, must assign a central role to the quest for truth in the scientific enterprise. He finds my analysis wanting chiefly (but not exclusively) because I do not represent science as the search for true theories. Indeed, virtually all of his criticisms, and most of his counterexamples, are designed to show how central a role considerations of truth play in an account of science. In Progress and Its Problems (hereafter: PIP), and several more recent publications,* I have been puzzling with one of the paradoxes that confounds contemporary philosophy of science. In a nutshell, it amounts to this: the possibility of exhibiting science as a rational activity seems to depend (given our understanding of rationality in general) on our showing: (a) that there are certain aims or goals of scientific inquiry and (b) that the methods of theory assessment and appraisal used in science can be shown to conduce to the achievement, at least partially, of those goals and aims. Unless an appropriate ends/means relation can be established between the aims of science and its *University of Pittsburgh. Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A. ‘H. Sarkar, ‘Truth, Problem-Solving and Methodology’, Studies in Hisrory and Philosophy of Science 12 (1981). 61-73. ‘See especially ‘A Confutation
of Convergent Realism’, Phibsophy of Science 48 (1981), 19 - 49; ‘A Problem-Solving Approach to Scientific Progress’, in 1. Hacking (ed.), Scientific Revolutions (Oxford, 1981); and ‘The Philosophy of Progress’, in I. Hacking (ed.), PSA 1978, Vol. 2. Stud. Hist. Phil. Sci., Vol. 13, No. 1 pp. 13 - 80, 1982.
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methods, we will be in no position warrantedly to assert that science is a rational activity. This much is uncontroversial: goal-directed activity which chronically fails to further the relevant goals is a paradigmatic instance of irrationality. Almost as uncontroversial is the claim that the methods presently used in the sciences do not, so far as anyone has been able to show, lead to the formulation of theories which are true, verisimilar or approximately true. We would like it to be otherwise, of course; but few if any philosophers of science would claim themselves to be in a position to show that the methodological repertoire of contemporary science includes methods which can be shown to lead us closer and closer to true theoretical accounts of the physical world. It takes little ingenuity to put these two points together and to realize that they lead to this staggering conclusion: insofar as, and to the extent that, the aim of science is the formulation of true (or ever more nearly true) theories, then we have no grounds for viewing science as a rational activity. Because we have not documented the appropriate sort of ends/means linkage necessary to justify an attribution of rationality to science - conceived as the search for true theories - I have suggested that it might be as well to leave questions of truth outside of our account of the aims of science. My project in PIP was to explore whether, with respects to goals or aims other than securing true theories, science might turn out to be a paradigmatically rational activity. The strategy of Sarkar’s essay is to exhibit that, despite my efforts to read truth out of the axiology of science, my own problem-solving model requires me to fall back on truth as a goal of science. Virtually all of his specific arguments, including the three which I shall examine below, involve efforts to show that my account is incoherent unless we imagine that the scientist aspires to the truth. The first point to note is that Sarkar’s strategy is itself fundamentally ad hominem. Even if it were the case that the model I have articulated required the inclusion of truth among the aims of science, that would in no way count against the argument briefly summarized above which seeks to show that the search for true theories is, on present evidence, an irrational one. If Sarkar is to establish that ‘there is ample reason nol to discard the notion of truth” from among the aims of science, then he must deal directly with that argument rather than with my model. Indeed, on my present understanding of the force of that argument, the only thing that would follow from Sarkar’s successfully showing that my model required a truth-oriented axiology would be the fact that my model - like most other extant ones - entails the irrationality of science. Such a consequence would, in my view, be sufficient to discredit my model as an account of scientific rationality; but it would not justify the claim ‘Sarkar,
op. cif.. p. 73.
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that science really does seek true theories after all. The object of this short essay is to suggest that Sarkar’s specific arguments about the necessity of a presumption of truth among the aims of science in the model of PIP are, by and large, wide of the mark. In brief, Sarkar makes three chief arguments in this regard. He insists, first, that my notion of a problem solution inevitably requires reference to truth. Secondly, he claims that my opposition to inconsistent theories only makes sense on the assumption that the scientist aspires to the truth. Thirdly, he alleges that my model runs into all the same difficulties that have confronted truth-oriented models of verisimilitude and that there is thus nothing to be gained by treating science as if it were other than a truth-seeking activity. Because I believe that all three arguments rest on serious conceptual confusions, I want to deal with them briefly.
I. Truth and Problem Solutions In PIP, I suggested that a theory can be credited with solving a problem just so long as that theory entails, or figures non-trivially in a complex of assumptions which entail, a statement of the problem in question. In response to this characterization of the nature of a solution, Sarkar makes the semantic point that entailment obtains only between statements which are either true or false. As he puts it, ‘the only viable analysis of entailment is in terms of logical consequence which in turn rests essentially on the notion of truth’.’ Because the notion of a solution involves entailments and because entailments involve statements possessing truth values, Sarkar concludes that I have prematurely and (given my account of problem solution) inconsistentlv written truth out of meta-methodology. The fact of the matter is that Sarkar is here confounding semantic and epistemic issues which need to be carefully distinguished. I have nowhere denied (indeed I have frequently stressed) that the statements making up the theories and problems of science have truth values. But it is one thing to make that semantic point and quite another to make the epistemic claim that there are circumstances under which we are warranted in ascribing truth to a scientific theory. Insofar as I have a quarrel with scientific realists, it is at the epistemic rather than the semantic level. The fact that theories have truth values manifestly does not justify our including the quest for true theories among the aims of science. That axiological thesis could only be justified by epistemic arguments. Sarkar evidently fails to see that semantic tools will not accomplish epistemic chores. ‘Sarkar,
op. cit., p. 66.
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What makes his use of this argument more than a little ironic is that I sketched out precisely these distinctions at some length in a paper to which he himself refers. Thus, in ‘The Philosophy of Progress’,5 I went to some pains to stress that ‘scientific theories have truth values’. I called this the thesis of semantic realism and endorsed it without qualifications. But I said then, and find it necessary to repeat here, that semantic realism entails nothing whatever about the appropriate goals of scientific inquiry. It is entirely consistent to say, on the one hand, that theories have truth values, and to insist, on the other hand, that we do not know of epistemic circumstances which would warrant the attribution of a positive truth value to the sorts of things that we customarily regard as scientific theories. Sarkar’s reiteration of my point that theories have truth values will not motivate the claim that it is legitimate to include the quest for true theories among the central aims of science.
II. Comparative
Assessments
of Problem-Solving
Efficacy
It is well known that the theories of progress of Popper and Lakatos have run into acute difficulties stemming from their efforts to articulate a measure for comparing rival scientific theories. To put the matter simply, both authors subscribe to the view that one theory can be better than a rival only if it explains everything explained by its rival plus some other things besides. Now there are a variety of paradoxes confronting this way of comparing theories which have been explored by Miller, Tiechy and Gruenbaum infer afia. Sarkar seems to believe that comparable paradoxes confront the machinery for comparing theories which I sketched out in PIP; it is just this belief which prompts his remark that ‘Laudan’s methodology is at least as inadequate as Popper’s’.B I want to discuss the one case he cites in some detail which, he believes, poses challenges to a problem-solving methodology as grave as those confronting measures of content and verisimilitude. I can do no better than quote Sarkar’s text: Now consider two consistent but incomplete theories, 7 and T’ , such that T entails the solution of a solved problem, P (Why is the sky blue?) and T’ entails the corresponding statement of the problem not-P (Why is the sky not blue?). Let K be some solvable-problem, not solved by T. Then (not-p or K) is a statement of a solvable-problem entailed by T’ , but not by T. In brief, any claim about the possibility of comparing the problem-content of two theories, which together are logically incompatible, remains unsupported.’
‘Laudan, ‘The Philosophy ‘Sarkar. ‘Ibid.
op. cit., p. 70.
of Progress’,
PSA 1978.
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It is quite clear why examples of this sort are worrying to Popperians, for what they show is that incomplete theories can never explain everything explained by their (false) rivals and thus can never be said to include the content of their rivals. Under such circumstances, Popperian assessments of progress seem out of the question. But examples such as these cut no ice against the appraisal measures I have proposed, as I shall show below. Is Sarkar right in saying that the comparison of the problem-solving effectiveness of two rival theories, as I have defined it, has not been shown to be possible? The answer is surely no, because I do not require one theory to be able to solve all the problems of its rivals before it can be judged progressive over its rivals. The example which Sarkar cites is decisive against any measure of progress which, like Popper’s and Lakatos’, requires a superior theory to have all the successes of its rivals. But I have argued that progressive theories should solve more problems than their rivals have solved, not that they should solve all the problems credited to their rivals. The fact that, in Sarkar’s example, T’ can solve a problem (the ‘problem’ formed by disjoining the statements ‘R and ‘not-P’) not solved by T does not preclude the possibility that T may nonetheless have solved more problems than T’ and thus may still emerge, as our intuitions about the case would suggest, as superior to T. Indeed, what can be shown in the specific case Sarkar cites is that, provided T initially had a better problem-solving record than T’ prior to the consideration of Sarkar’s example, then Twill emerge from Sarkar’s example with a better problem-solving record than T' . But before I prove that result, it should be noted how bizarre Sarkar’s example is in the first place. Typically, scientific ‘problems’ are not generated by applying the logical operation of disjunction introduction between statements referring to nomologically-independent events. I take it that no scientist would hold this to be a well-defined ‘problem’: ‘either light does not bend near the sun or saccharin induces cancer’. Nor would any scientist regard Newton’s theory as ‘solving’ this bizarre problem just because Newton’s theory entails the first (false) disjunct. Yet such is the character of Sarkar’s example. But for the sake of argument, let us grant that such problems are legitimate and that a theory solves such a problem so long as it entails at least one of the disjuncts (even if it is the false disjunct). The admission of such problems and solutions will not upset the problem-solving bookkeeping. Consider: we have two rival theories, T and T’ , such that T entails P and T’ entails not-P (where P is presumed to be true). In these circumstances, T will be credited with solving P and T’ will get no credit. But now enters Sarkar with the insistence that T’ can solve the problem ‘not-P or K’, which T cannot solve because it entails neither ‘not-P’ nor ‘K’. Score one, as it were, for T’ . But, of course, we need not stop here, because Twill be able to ‘solve’ the ‘problem’, ‘P or K’ -
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a problem which T’ cannot solve. Now we have a situation where Tsolves two problems (‘P’ and ‘P or K’) while T’ solves only one (‘not-P or K’), thus preserving the initial problem-solving superiority of T over T’. More generally, one can see that corresponding to every solved problem of T’ generated by disjoining a false entailment of T’ with a statement independent of T, there will be a corresponding solved problem credited to T, formed by disjoining a true entailment of T with a statement independent of T. In short, such problem solutions credited to Tand T’ will ‘cancel out’ and it will remain true that T (because it solves P while T’ does not) has solved more problems than T' . So long as T solves more problems than T’ prior to the assessment of Sarkar-like disjunctive problems, then T will continue to beat T’ once problems of Sarkar’s sort are reckoned with. Under the circumstances, Sarkar’s charge that comparison of relative problem-solving effectiveness is impossible in such cases is without merit. By showing that Sarkar’s specific counter-example fails to be compelling, I do not mean to suggest that similar sorts of counter-examples can be met by the same response. On the contrary, it seems to me that there clearly are cases, parallel to Sarkar’s, where the problem-solving ‘success’ of an intuitively less successful theory can be jacked up so as to exceed the successes of its (intuitively superior) rival.8 But all the examples of this sort which I can conceive of depend upon accepting a view of what constitutes a problem and a solution which I reject. Specifically, these examples require one to maintain both that every disjunctive statement is a problem and that a theory solves every statement it entails. I deny both claims. It is true that I have said that a theory solves a problem when it entails a statement of the problem. But that is a far cry from the claim - crucial for the generation of Sarkar-like examples - that every statement so entailed by a theory describes a problem which the theory can be credited with solving. Problems arise in a certain context of inquiry; given a particular context, and the expectations about natural processes which constitute that context, only certain problems can conceivably arise as problems. To show the inadequacy of the bookkeeping mechanisms I have proposed for assessing comparative problem solving effectiveness, one must deal with a theory’s problems rather than with the broader set of its logical entailments. ‘Here is one example of how one might proceed: imagine two incomplete and contrary theories, T, and K, such that T, solves P, and S, while T, solves P, but not P,. Thus far, T, is a better problem-solver than 71. Now, imagine that G entails S,, S, and S, and that all three are false. 7,. by contrast, entails nothing about S,, S,, or .S, and nothing about their negations. Under these circumstances, we can disjoin any of these false entailments with a statement K independent of 27. In such a situation, K will have a host of true entailments which cannot be ‘paired’ with entailments of T,. More generally, one can say that the more refutations a theory has (provided those refutations are logically independent of its rivals), the higher its problem-solving success will appear to be. Assuming, of course, that any genuine entailment of a theory counts among its solved problems.
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III. Problem-Solving and Inconsistency Like Mellor and Gutting before him, Sarkar takes the view that, if we abandon the aim of true theories, we will no long be able to object to a theory that is inconsistent since, as he sees it, ‘only if truth is our aim can we have any objection to theories that are logically inconsistent’.g His strategy here, as above, is decidedly ad hominem. He seeks to show that, in terms of the model of PIP, inconsistent theories solve more problems than consistent ones. Since, on his construal of my position, I have no way of discrediting inconsistent theories, he concludes that only models of change which give pride of place to the quest for truth are viable. Before dealing specifically with the role of inconsistent theories in my model, it is important to stress that Sarkar’s general thesis is a non sequitur. The fact, if it were a fact, that my model gives high marks to inconsistent theories, would in no way establish that inconsistency can only emerge as a cognitive liability in those philosophies of science which portray science as a truth-seeking activity. That much said, let me proceed to Sarkar’s more specific claim to the effect that my model, far from preserving our intuition that inconsistent theories are otiose, makes inconsistent theories highly desirable. His argument, in brief, is this: because an inconsistent theory arguably entails every statement (and its negation), inconsistent theories will always be able to take credit for solving (i.e. entailing) every problem. It follows that every inconsistent theory will solve more problems than any consistent (but incomplete) theory, whether true or false. There are several points to be made in reply to Sarkar’s claim that a problem-solving approach such as mine must accord high positive status to inconsistent theories. (1) Sarkar’s analysis chronically ignores the fact that the problem-solving effectiveness of a theory is related to both the empirical and the conceptual problems which it solves.‘o As I pointed out at length in PIP, internal inconsistency constitutes an acute conceptual difficulty for a theory which exhibits it. Once the conceptual appraisal of a theory is factored into our assessment of that theory’s adequacy, it does not follow that a theory which solves the largest number of empirical problems will necessarily be the theory of choice. Only by completely ignoring the central role of conceptual problems in theory assessment can Sarkar reach the conclusion that, on my analysis, progress necessarily occurs when a consistent theory is replaced by an inconsistent one. (2) But there are other grounds, independent of the issue of conceptual OSarkar,op. cir.. p. 70. ‘This particular response duplicates an argument made by M. Finocchiaro in his ‘Remarks on
Truth, Problem-Solvingand Methodology’,Studies in Hisrory und Phitosophy of Science 12 (1981). 261- 268.
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problems, for faulting inconsistent theories. One of them is that further progress in science would be impossible if we were prepared to allow a sequence of inconsistent theories. In a passage of mine which Sarkar quotes but proceeds to ignore, I pointed out that the ‘replacement of one inconsistent theory by another could never count as progress with respect to problemsolving effectiveness’.” If one can show that the adoption of a certain research strategy would permanently foreclose the possibility of further progress in science, I believe that constitutes grounds for rejecting the strategy. Because the strategy of countenancing inconsistent theories would preclude the possibility of further empirical progress (since no inconsistent theory can solve more problems than any other), it should be rejected. And that rejection has nothing whatever to do with the inclusion of truth among the aims of science. (3) I take it that on virtually any analysis of science, one of the tasks that we chiefly expect our theories to perform is that of putting us in a position to anticipate nature. We do not expect, and certainly do not require, that a theory will always lead to correct anticipations of nature; but we do expect it to shape our expectations in various ways. That is indeed the raison d’gtre of science. Now, the central trouble with inconsistent theories, as I see it, is that they dismally fail to fulfil this central function. If a theory is inconsistent, it does nothing whatever to shape our expectations about how the world might behave. It is true in an abstract sense that an inconsistent theory will have among its entailments statements which truly describe the world. But that is of no heuristic use to us at all, so far as the shaping of expectations is concerned. Theory plays a vital heuristic role in directing our attention to certain dimensions of a situation; and this is as true of false theories as it is of true ones. But inconsistent theories cannot play this heuristic role, because we do not know what to do with them. If someone offers me the ‘theory’ T (which says ‘snow is white and snow is not white’), he has given me no clues about how to proceed in interacting with nature. By contrast, if he offers me a consistent (but non-tautologous) theory - whether true or false - he will have begun to indicate features of the situation which I might explore. The point is this: there are a host of heuristic, conceptual and pragmatic considerations which provide a rationale for objecting to inconsistent theories. One need not believe that the aim of science is the discovery of true theories in order to find inconsistency undesirable. What we see in Sarkar’s essay is an example of the increasingly frequent phenomenon of extravagant claims being made concerning the explanatory riches of realism, linked to largely undocumented assertions about the explanatory poverty of non-realist epistemologies. (I have examined some more familiar instances of this syndrome elsewhere.“) “Cf. Laudan, ‘The Philosophy of Progress’, note 7, and Sarkar, op. cit., p. 71 “See Laudan, ‘A Confutation of Convergent Realism’.