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Statistical Method and the Peircean Account of Truth
Published online by Cambridge University Press: 01 January 2020
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Peirce is often credited with having formulated a pragmatic theory of truth. This can be misleading, if it is assumed that Peirce was chiefly interested in providing a metaphysical analysis of the immediate conditions under which a belief or proposition is true, or the conditions under which a proposition or belief is said to be madetrue. Cheryl Misak has exposed the subtleties in Peirce's discussion of truth, especially showing the difficulties faced by any ascription to him of an analytic definition of truth. In this paper I follow Misak in urging that Peirce's contribution to the philosophical discussion about the nature of truth was not of that kind. What makes his pragmatic approach distinctive is that rather than attempting to state the nature of truth per se, it attempts to uncover the beliefs and expectations we commit ourselves to when we make specific claims that such and such is true or is the case.
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References
1 Misak, C. Truth and the End of Inquiry: A Peircean Account of Truth (Oxford: Clarendon 1991)Google Scholar
2 Misak, C. Truth and the End of Inquiry, and Verificationism: Its History and Prospects (London: Routledge 1995)Google Scholar
3 Cf. Truth and the End of Inquiry, especially 122-3. Quine's criticism is that the idea of a theory converging to a limit requires a precise notion of ‘nearer than’ which is definable for numbers, but not theories. Cf. Quine, W.V.O. Word and Object (Cambridge, MA: The MIT Press 1960), 23Google Scholar.
4 Peirce, C.S. Collected Papers. Vols. 1-6, Hartshorne, C. and Weiss, P. eds.; vols. 7-8, Burks, A. ed. (Cambridge, MA: Harvard University Press 1931)Google Scholar. Citations given by volume and paragraph number. They will take this form: 5.400.
5 In a paper of 1907 Peirce wrote that pragmatism ‘is merely a method of ascertaining the meanings of hard words and of abstract concepts.’ Cf. Peirce, C.S. Essential Peirce, Volume 2, Peirce Edition Project, ed. (Indianapolis: Indiana University Press 1998), 400Google Scholar.
6 Essential Peirce Vol.2 contains the following passage: ‘Now there are three grades of clearness in our apprehensions of the meanings of words. The first consists in the connection of the word with familiar experience …. The second grade consists in the abstract definition, depending upon an analysis of just what it is that makes the word applicable …. The third grade of clearness consists in such a representation of the idea that fruitful reasoning can be made to turn upon it, and that it can be applied to the resolution of difficult practical problems’ (556 n.5).
7 This is an attempt to render more explicit and clear Peirce's own formulation that ‘on the one hand, reality is independent, not necessarily of thought in general. but only of what you or I or any finite number of men may think about it; and that, on the other hand, though the object of the final opinion depends on what that opinion is, yet what that opinion is does not depend on what you or I or any man thinks’ (Peirce, 5.408).
8 See Putnam, Hilary Reason, Truth, and History (Cambridge: Cambridge University Press 1981 )CrossRefGoogle Scholar, for instance.
9 There is an added condition required here, though, for the sake of accurately capturing the objective of scientific inquiry. It is not just stability of belief that we are after, but informative content too. These two desiderata must be balanced against one another. James's dictum ‘Believe truth, shun error’ captures this tension nicely. If stability is all we want, then we should believe only tautologies; while the further we stretch our necks out in pursuit of informative content the more we risk having our beliefs upset at the earliest possible opportunity. Peirce did write that what we want from our beliefs is a ‘maximum of expectation and a minimum of surprise.’
10 Although I would like to suggest that the clarification offered here on behalf of Peirce should also extend to James, for as Putnam, in Pragmatism: An Open Question (Oxford: Blackwell 1995)Google Scholar, has recently pointed out, James's remarks on truth have been discussed very uncharitably.
11 As a most recent example, Kirkham's, Richard article ‘Truth, Pragmatic theory of’ in Vol. 9 of the Routledge Encyclopedia of Philosophy (London: Routledge 1998)Google Scholar contains a discussion of Peirce's treatment of truth that I have difficulty recognizing as Peirce's at all.
12 As Peirce writes, ‘It is mathematically certain that the general character of a limited experience will, as that experience is prolonged, approximate to the character of what will be true in the long run, if anything is true in the long run’ (Peirce, 6.200).
13 Witness the following remarks from Peirce: ‘The writer of this article has been led by much experience to believe that every physicist, and every chemist, and, in short, every master in any department of experimental science, has had his mind molded by his life in the laboratory to a degree that is little suspected … his disposition is to think of everything just as everything is thought of in the laboratory, that is, as a question of experimentation’ (Essential Peirce Vol.2, 331-2). Consider, for instance, that when Peirce applies the pragmatic maxim to the idea of reality in ‘How to Make Our Ideas Clear’ the sole example he considers involves attempts to measure the velocity of light by a number of different methods, all of which converge in their results. Cf. Peirce, C.S. Essential Peirce, Volume 1, Houser, N. and Kloesel, C. eds. (Indianapolis: Indiana University Press 1992), 138Google Scholar.
14 I am going to leave aside questions about whether or not the concept of objective propensities is a legitimate one, or whether statements of probability are best understood as statements about propensities, etc. Peirce himself believed in them and that they were a legitimate way of construing probability statements about statistical facts, and that is good enough for my present purposes.
15 For small sample sizes the proper formula is slightly more complicated. Let p = the objective chance to be estimated, P = the proportion of heads observed, N = sample size or number of trials observed, and zc = the confidence coefficient (1.96 in this example). Then
which reduces to the simpler formula used since as 
It should also be noted that we are using the above formula to construct a range of dispersion or variance about the sample proportion. We must construct this term since in our example we are only making one trial of ten tosses. Were we making several trials of ten tosses each we would have an actual variation of sample proportions upon which to base our error term. I have used the one trial example merely for the sake of brevity and convenience.
16 In fact the law of large numbers does not warrant this belief. As Feller, W. in An Introduction to Probability Theory and Its Applications, 3rd ed. (New York: Wiley 1968)Google Scholar, explains, the theorem in question (and there is actually a whole family of related results) says that of an infinite number of similar series of infinitely many random trials, the probability is overwhelmingly large (equal to one) that for the vast majority of them the relative frequency of heads will converge to the true objective chance of heads (142). This technicality need not worry us here, however, since we are concerned only to show that Peirce's elucidation of what it means to say of a belief that it is true adequately captures what we do in fact take it to mean.
17 For a more detailed picture of Peirce's theory of statistical inference, see Levi, I. ‘Induction as Self-Correcting According to Peirce,’ in Mellor, H. ed., Science, Belief and Behavior: Essays in Honour of R.B. Braithwaite (Cambridge: Cambridge University Press 1984)Google Scholar or Mayo, D. Error and the Growth of Experimental Knowledge (Chicago: University of Chicago Press 1996)CrossRefGoogle Scholar, ch. 12.
18 At least this is what we should expect if we are all adjusting our beliefs via some rule of conditionalization such as Bayes's theorem, and no one of us has already fixed our belief at either extreme value of p = 1 or p = 0.
19 Technically we should keep the notions of convergence to a fixed limiting value and merger of opinion separate. The former is exhibited by a series of mathematical values, the latter by a group of epistemic agents; the former should be restricted to subjects of a quantitative nature, the latter may be applied to qualitative ones. That a series does converge to some limiting value may be sufficient reason for a community of inquirers to merge in their opinions, for instance about the true value of a coin's propensity to turn up heads. By contrast, a group of individuals could exhibit a merger of opinion on the value of a quantitative parameter without there having been any convergence exhibited by the evidence, or without any evidence at all for that matter. Any but the last of the four methods of fixing belief which Peirce considers in ‘The Fixation of Belief’ might permit such a merger of opinion without the proper evidential convergence. Peirce's argument was that only the scientific method will take convergence in the evidence as a necessary and sufficient condition for a merging of opinions.
20 This point about the order of the quantifiers has been made before by Glymour, C. and Kelley, K. ‘Convergence to the Truth and Nothing But the Truth,’ Philosophy of Science 56.2 (1989) 185–220Google Scholar.
21 An ideal community of inquirers would be one which devoted all its time and expenses to the investigation of hypotheses and beliefs. It would be limitless in its extension into the future, thereby allowing sense to be made of the final limit of inquiry.
22 Levi, I. The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance (Cambridge, MA: The MIT Press 1980)Google Scholar
23 Misak, C. ‘Discussion: Peirce, Levi, and the Aims of Inquiry,’ Philosophy of Science 54.2 (1987) 256–65CrossRefGoogle Scholar
24 See Russell, B. Wisdom of the West (London: Bloomsbury Books 1989), 276–7Google Scholar.
25 In Reason, Truth, and History, Putnam made a similar argument in defense of the notion (which he no longer defends) of ideally warranted assertibility. Okruhlik, K. in ‘Review of Putnam 1981,’ Philosophy of Science 51.4 (1984)Google Scholar, questioned whether the idealization involved there is analogous in the right way to the idealizations of physics.
26 Hacking, I. The Taming of Chance (Cambridge: Cambridge University Press 1990)CrossRefGoogle Scholar
27 Misak also covers this misreading briefly in Truth and the End of Inquiry.
28 I am grateful to Ian Hacking for asking me this very question.
29 There is a common tendency among some ‘postmodern’ thinkers to suppose that there is no difference between having shown a particular belief or practice to be contingent and having shown that it is arbitrary. It deserves notice, however, that one of the most visible defenders of postmodern attitudes, Richard Rorty, recognizes this move for the fallacy it is. See Rorty, Contingency, Irony, and Solidarity (Cambridge: Cambridge University Press 1989), 6.CrossRefGoogle Scholar
30 I take it that Derrida, Barnes and Bloor, Latour and Woolgar, and Rorty are examples of those who are skeptical of the claim that science is not only a process of creation or construction, but also one of genuine discovery.
31 Think of the coin's two faces (heads, tails) as its firstness, its ‘quality.’ The actual outcomes of the trials are seconds. The limit to which the ratio of heads to tails converges is the coin's thirdness. The law of large numbers then describes the emergence of a statistical law from random chance (independent) events; it is the emergence of secondness from firstness via thirdness. It is for this reason that what Peirce called the law of ‘high’ numbers is so important for understanding his evolutionary metaphysics. Cf. Reynolds, A. Irreversibility and Evolution in Peirce's Cosmology (PhD Dissertation, University of Western Ontario, 1997)Google Scholar.
32 Yet I do not intend to deny that in many cases, especially within the human sciences, our theorizing does create new realities. See, for instance, the discussion in Hacking, I. The Social Construction of What? (Cambridge, MA: Harvard University Press 1999).Google Scholar My objection is that reality not be wholly reduced to a human construct.
33 This interpretation is backed up I believe by the fact that, when in ‘How to Make Our Ideas Clear’ Peirce considers what the pragmatic maxim makes of the concept of reality, he uses as an example a problem of measurement (viz. the speed of light). Moreover, the rest of the papers in that series all deal with what might easily be called the principles of statistical inference and estimation. The following quote from ‘The Doctrine of Chances,’ which immediately follows ‘How to Make Our Ideas Clear,’ is of particular interest in this regard: ‘It is not … so much from counting as from measuring … that the advantage of mathematical treatment [to scientific topics] comes’ (Essential Peirce Vol.1, 143).
34 Witness his remarks in the concluding paragraphs of ‘How to Make Our Ideas Clear,’ where after explicitly considering the truth of historical facts, he says, ‘It seems to me, however, that we have, by the application of our rule [i.e. the pragmatic maxim], reached so clear an apprehension of what we mean by reality, and of the fact which the idea rests on, that we should not, perhaps, be making a pretension so presumptuous as it would be singular, if we were to offer a metaphysical theory of existence for universal acceptance among those who employ the scientific method of fixing belief.’ And a little further on he adds, ‘I will not trouble the reader with any more Ontology at this moment. I have already been led much further into that path than I should have desired’ (Essential Peirce Vol.1, 140).
35 See Rorty, R. Objectivity, Relativism, and Truth: Philosophical Papers Volume 1 (Cambridge: Cambridge University Press 1991)Google Scholar.
36 The term is borrowed from Jardine, Nicholas The Fortunes of Inquiry (Oxford: Clarendon 1986), 30Google Scholar.
37 In a personal communication, Misak has urged that the O.J. case involves only what she has called ‘mundane’ counterfactual bravado. Since there were potential observers in existence then (none of whom happened to be in the right place at the right time), this example need not invoke the fanciful mechanism of time travel. As I see it though it does not much matter whether the example involves mundane or extraordinary counterfactual bravado, since my point is that the Peircean account is best thought of as an explication of the concept of truth, not as a means of demarcating legitimate hypotheses from those which are inaccessible to actual practices of inquiry.
38 One might wonder whether this account precludes us from saying that some beliefs are true right now, not just that they will be shown true in the future. But what real content is there in saying—asks the Peircean—that some beliefs are true right now, but that they will continue to be vindicated in the future (of a duration appropriate to the situation in question)?
39 Witness his remark that ‘the will be's, the actually is's, and the have beens are not the sum of the reals. They only cover actuality. There are besides the would be's and can be's that are real’ (Peirce, 8.216). While this statement does not include any explicit mention of the ‘could have beens,’ I see no reason why they should be excluded from the spirit of the statement.
40 Misak has informed me that she now thinks it wrong to suggest that the pragmatist must stick to those methods that are actually available to inquiry. This change is to be reflected in her forthcoming book, Truth, Justice, Morality.
41 On the issue of verificationism we find Peirce making a related plea for the sake of statements about the past: ‘Whatever Comte himself meant by verifiable … it certainly ought not to be understood to mean verifiable by direct observation, since that would cut off all history as an inadmissible hypothesis’ (Essential Peirce Vol.2, 225).
42 Remark the quotation in full excerpted in note 2: ‘Suffice it to say once more that pragmatism is, in itself, no doctrine of metaphysics, no attempt to determine any truth of things. It is merely a method of ascertaining the meanings of hard words and of abstract concepts. All pragmatists of whatsoever stripe will cordially assent to that statement’ (Essential Peirce Vol.2, 400).
43 Thanks are due to William Harper and John Nicholas for drawing my attention to this.
44 See Rescher, N. The Limits of Science (Berkeley: University of California Press 1984)Google Scholar and Jardine, The Fortunes of Inquiry for extended discussions of this and related themes.
45 I would like to thank Cheryl Misak and two anonymous referees for this journal whose helpful comments led to improvements in this paper. Christopher Hookway provided comments on an earlier draft which was presented at the Twentieth World Congress of Philosophy held in August 1998 in Boston, MA, in a session organized by the C.S. Peirce Society. Financial assistance for this research was provided by a Social Sciences and Humanities Research Council of Canada Postdoctoral Fellowship. I would also like to thank Hilary Putnam for agreeing to act as supervisor for my postdoctoral research project at Harvard University.