Abstract
The aims of this chapter are two-fold: first and primarily, to identify and to summarize the development of an important but hitherto unnoticed tradition in 19th-century methodological thought, and secondly, to suggest that certain aspects of the history of this tradition give us a new perspective from which to assess certain strains in contemporary philosophy of science. In Part I below, I attempt to define this tradition, to document its existence, and to note some features of its evolution. In Part II, I briefly indicate the manner in which this history may shed new light on some recent trends in inductive logic.
If science lead us astray, more science will set us straight.— E. V. DAVIS (1914)
Since this chapter first appeared, it has been discussed at length by Nicholas Rescher and Iikka Niiniluoto. It shoulg be evaluated in the light of the constructive criticisms they have made of its central thesis.
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Notes
Mid-West Quarterly 2 (1914), 49.
There is a vast body of exegetical and critical literature dealing with Peirce’s philosophy. The following are concerned explicitly with Peirce’s treatment of self-correction: A. W. Burks, ‘Peirce’s Theory of Abduction’, Philosophy of Science 13 (1946), 3016. C. W. Cheng, Peirce’s and Lewis’s Theories of Induction (The Hague, 1969), H. G. Frankfurt, ‘Peirce’s Notion of Abduction’, Journal of Philosophy 55 (1958), 5937; J. Lenz, ‘Induction as Self-Corrective’, in Moore and Robin (eds.), Studies in the Philosophy of Charles Sanders Peirce (Amherst, Mass., 1964 ); E. Madden, ‘Peirce on Probability’, in ibid.; F. E. Reilly, The Method of the Sciences According to C. S. Peirce, Doctoral dissertation, St Louis University, 1959. While acknowledging a debt to all of these works, I believe it is fair to say that none of these authors treats Peirce’s approach to SCT within the historical framework in which I have tried to place it.
See, for instance, Burks, ‘Peirce’s Theory’. Even Peirce himself tries to give the impression that he was the first to enunciate the view that scientific reasoning is self-corrective. For instance, he wrote in 1893 that “you will search in vain for any mention in any book I can think of” of the view “that reasoning tends to correct itself”. C. S. Peirce, Collected Papers, ed. Hartshorne, Weiss et al., 8 vols. (Cambridge: Harvard University Press, 1931–58) Vol. 5, p. 579. Without questioning Peirce’s integrity, we do have some grounds for doubting his memory. Peirce makes numerous references to the works of may of the writers whom I cite below as Peirce’s predecessors in this matter. (See, for example, ibid., Vol. 5, p. 276 n., where he writes knowledgeably of the philosophies of science of both LeSage and Hartley, who had stressed the self-correcting aspects of scientific reasoning.)
This point requires some qualification. As is well known, passages can be adduced from all these authors where they seem to abandon the infallibilism of TICT and to replace it by a more modest “probabilism”. (Many of the relevant texts are discussed in Chapter 4.) However, it would be a serious error of judgment to let these concessions to fallibilism obscure the fact that all of these figures shared the classical view that science at its best is demonstrated knowledge from true principles. Bacon, Descartes, Locke, and Boyle all see it as a goal that science become infallible; until that goal is realized they are willing to settle — but only temporarily — for merely probable belief. Their long-term aim, however, is to replace such mere opinion by genuine knowledge.
See Robert Hooke’s posthumously published account of “inductive logic” in The Posthumous Works of Robert Hooke, ed. R. Waller (London, 1705), pp. 3 ff.
See Chapter 4.
A century and a half later Max Planck gave eloquent expression to this quintessentially 18th-century viewpoint: “Nicht der Besitz der Wahrheit, sondern dass erfolgreiche Suchen nach ihr befruchtet and beglüchte den Froscher”. (Wege zur physikalischen Erkenntnis, 4th ed. [Leipzig, 19441, p. 208.)
Some, but by no means all. As late as the 1790s, philosophers such as Thomas Reid were still arguing for a strictly inductive methodology. (Cf. Chapter 7.)
To be faithful to the historical situation, it is important to point out that some 18th-and early 19th-century methodologists, while accepting SCT as a general thesis, were not altogether happy with the idea expressed in (2) above. As formulated there, SCT is committed to the view that there is a mechanical process for fmding alternatives. Some methodologists denied this. What they did insist on, however, was that: (2’) Science possess techniques for determining unambiguously whether an alternative T’ is closer to the truth than a refuted T.William Whewell, for instance, denied the claim implicit in (2) that the scientist possessed any algorithm for automatically correcting an hypothesis. Nonetheless, he was convinced that it was generally possible, given a (refuted) theory and an alternative to it, to determine which of the two was (in Whewell’s language) “nearer to the truth”. Hereafter, I shall refer to the pair (1) and (2) as the strong self-correction thesis (or SSCT) and to the pair (1) and (2’) as the weak thesis of self-correction (WSCT).There is another important qualification to make here. Although all the figures I discuss talk about “getting closer to the truth”, “moving nearer to the truth”, etc., it is not altogether clear that there is a shared, conception of what truth consists in. With some writers, for instance, the notion of truth seems to be an instrumental one (viz., that is true which adequately “saves the phenomena”); with others, the concept of truth is a correspondence one. Nonetheless, most discussions of self-correction and proximity to the truth seem to be conducted independently of various conceptions of, and criteria for, the truth.
See note 9 above.
This claim for the priority of LeSage and Hartley is, like all claims for historical priority, necessarily tentative. R. V. Sampson, in his Progress in the Age of Reason (London, 1956 ), asserts that Blaise Pascal conceived of science as “cumulative, self-corrective” and progressive. I have been unable to find such an argument in Pascal and (unfortunately) Sampson offers no evidence for his interpretation. Similarly, Charles Frankel (The Faith of Reason, [New York, 1948]) argues likewise without evidence, that “For Pascal... scientific method was progressive because it was public, cumulative, and self-corrective” (p. 35 ). Until more substantive evidence is produced, I believe the available historical evidence supports my priority claims for Hartley and LeSage. However, the argument in the body of the essay does not depend on the priority issue.
David Hartley, Observations on Man (London, 1749 ), 1: 341–2.
Ibid., 1: 345–6. Basically, the rule of false position worked as follows: If one sought the solution to an equation of the form ax + b = 0, one made a conjecture, m, as to the value of x. The result, n, of substituting m for x in the left-hand side of the equation is given by am + b. The correct value of x was then determined by the formula x = mb/(b-n) The rule of false position was one of the earliest known rules for the solution of simple equations. It should be added that during the 18th century, the term “rule of false position” normally referred, not specifically to the rule given above, but rather to what we call the rule of double position, which involves two conjectures rather than one. An interesting discussion of this latter rule may be found in Robert Hooke’s Philosophical Experiments and Observations, ed. Durham (London, 1726 ), pp. 84–6.
R. Recorde, Ground of Artes (London, 1558), fol. Z4.
Observations on Man, n12, 1: 349.
Ibid., 1: 349. It is perhaps worth observing that Hartley adhered to a theory of moral progress and self-improvement which paralleled the progress and self-correction of science. “We have”, he writes, “a Power of suiting our Frame of Mind to our Circumstances, of correcting what is amiss, and improving what is right” (Ibid., 1: 463).
Ibid., 1: 349. There is, we should observe, a very great difference in the results which these various “approximative methods” yield. Some of these methods — such as the Newtonian method of approximation to the roots of a general equation — do not necessarily ever yield a true result. We can, by their use, constantly improve our estimate, but there is no guarantee that we will ever determine precisely the correct answer. However, other methods Hartley mentions, especially the rule of false position, not only correct a false guess, but immediately replace it by the correct solution. These differences become very significant when applied to a scientific context. If our model for scientific method is the rule of false position, then one can imagine science rapidly reaching a stage where all the false theories have been replaced by true ones, and where scientific knowledge would be both static and non-conjectural. If, on the other hand, our model for inquiry is the search by approximation for the roots of an equation, then science would seem to be perhaps perennially in a state of change and flux, with no guarantee whatever that it could ever reach the fmal truth. Hartley, as well as most of his 19th-century successors, seems to vacillate between these two very different models.
Talk of a ‘self-correcting method’ is, of course, slightly misleading since the method does not correct itself, but rather it allegedly corrects those statements which an earlier application of the method produced. However, since linguistic traditions sanctify all manner of confusions, and since it is de rigueur to speak of methods with these properties as self-corrective methods, I will do so, hoping the reader will bear this caveat in mind.
A method will be weakly self-corrective (WSCM) if (a) above and if (b) without itself specifying a ‘truer’ alternative, it can determine for certain whether a given alternative is truer. (See also Note 6 above).
Precisely this criticism was raised by Condillac in 1749 against the view that science can borrow the approximative methods of the mathematician. (Cf. his Traité des Systèmes [Paris, 749], pp. 329–31.) It was also raised by J. Senebier a generation later. (Cf. his Essai sur l’Art d’Observer et de Faire des Expériences [Génève, 1802], 2: 215–6.)
As LeSage puts it: “The corrections made of these particular suppositions, resulting from the small multiplications which serve to test their validity, have as their sole aim to bring closer together these suppositions and the [true] number; with the exception of the last partial division, which must be performed rigorously because it is here that one fmally rejects the inaccuracies one has permitted oneself in the previous operations.” G. H. LeSage, ‘Quelques Opuscules rélatifs a la Méthode’, posthumously published by Pierre Prevost in his Essais de Philosophie (Paris, 1804), 2: 253–35. The passage in question dates from the 1750s, and appears on p. 261. (I discuss LeSage’s work at much greater length in Chapter 8.)
Ibid., 2: 261.
Joseph Priestley, The History and Present State of Electricity (London, 1767), p. 381.
Souvent on s’écarte du vrai, sans douter, et on le fuit en croyant le poursuivre“ (Essai, 2: 220).
Prevost, Essais de Philosophie (Paris, 1804), 2: 196. Prevost nevertheless believes that there are self-corrective methods which the scientist can use.
See, for instance, the several essays on progress in Whewell’s Philosophy of Discovery (London, 1860) and Auguste Comte’s preliminary discourse to the System of Positive Polity (4 vols. [London, 1875–7]). Similar, if more vague, sentiments are involved in John Herschel’s discussion (Preliminary Discourse on the Study of Natural Philosophy [London, 1831], para. 224 ff.).
E. Renan, ‘Claude Bernard’, in Renan (ed.), L ’Oeuvre de Claude Bernard (Paris, 1881), p. 33. My italics.
T. H. Huxley, Hume (London, 1894 ), p. 65.
My labels are, of course, anachronistic. The concepts they denote are not.
For Peirce’s application of SCT to the history of science, see his Lessons from the History of Science, (c. 1896), in Collected Papers, 1: 19–49, especially para. 108, p. 44.
Collected Papers, 5: 579.
Ibid., 5: 582.
Ibid., 6: 526; cf. also 2:
Ibid., 7: 110.
Ibid., 2: 775.
Ibid., 2: 729.
Ibid., 2: 769. 755.
Ibid., 1:67.
Ibid., 5: 576. Other relevant passages would include: 1868 (revised 1893): “we cannot say that the generality of inductions are true, but only that in the long run they approximate to the truth” (5: 350). 1898: “A properly conducted inductive research corrects its own premises” (5: 576). 1901: “[Induction] commences a proceeding which must in the long run approximate to the truth” (2: 780). `persistently applied to the problem [induction] must produce a convergence (through irregular) to the truth“ (2: 775). ”the method of induction must generally approximate to the truth“ (6: 100). 1903: ”The justification of [induction] is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error“ (5: 145). ”Suppose we define Inductive reasoning as that reasoning whose conclusion is justifiedchrw(133) by its being the result of a method which if steadfastly persisted in must bring the reasoner to the truth of the matter or must cause his conclusion in its changes to converge to the truth as its limit“ (7: 110). ”.. if this mode of reasoning [viz., induction] leads us away from the truth, yet steadily pursued, it will lead to the truth at last“ (7: 111). See also Collected Papers, 2: 709.
Ibid., 2: 756.
Ibid., 2: 758.
Ibid., 2: 77 ff.
Ibid., 2: 770.
Provided, of course, that there is some limit to the sequence in question; a qualification which Peirce realized to be essential.
Ibid., 5: 574. Peirce’s example, that of the extraction of roots, is identical to Hartley’s and LeSage’s. It is perhaps appropriate to add here that Peirce knew Hartley’s Observations on Man first-hand, and makes numerous references to it in his Collected Papers. Moreover, he knew of LeSage’s work, at least second-hand, citing it in volume 5 of his Collected Papers.I know too little about Peirce’s intellectual biography to assert with any confidence that it was definitely Hartley and LeSage who gave him the idea of a SCM; but, given Peirce’s knowledge of Hartley and the obvious similarities in the initial approaches to the problem, it seems a reasonable conjecture that Hartley may have stirred Peirce to consider the question of self-correction in detail.
For references to the vast body of technical literature on the straight rule, cf. the bibliography in Salmon’s The Foundations of Scientific Inference (Pittsburgh, 1967).
Whether that replacement is closer to the truth than that which it replaces, is, of course, another matter. But at least quantitative induction can specify a replacement, and is thus (potentially) a strong self-corrective method.
This point, viz., that qualitative induction is not (or, at least, has not been shown to be) self-corrective, has gone unnoticed by several of Peirce’s commentators. For instance, Cheng writes: “To say that a qualitative induction is self-correcting is either to say that a given hypothesis is replaceable by a new hypothesis or that the scope of the given hypothesis is modifiable or limitablechrw... ” (Peirce’s and Lewis’s Theories, p. 73).In arguing this point, Cheng has used an unfortunate sense of `self-correcting’. That an hypothesis is replaceable or ‘modifiable’ merely means that we have techniques for discarding or altering it. If qualitative induction is to be self-correcting then we need, at a minimum, the further assurance that its replacement or altered expression is an improvement. This assurance Peirce nowhere provides, and on occasion even denies that we can obtain it.
Collected Papers, 2: 771.
Ibid., 2: 759.
Ibid., 5: 578.
The titles of these 32 papers are listed in appendix I to Cheng’s Peirce’s and Lewis’s Theories of Induction. Ironically, Cheng himself discusses Peirce’s work as if it were designed explicitly as a reply to Hume.
Collected Papers, 7: 114–9.
J. W. Lenz, `Induction as Self-Corrective’, in E. Moore and R. Robin (eds.), Studies of Peirce, n. 2, p. 152. Cheng echoes Lenz when he observes that “Peirce does not make clear what the self-correcting process of induction meanschrw(133) ” (Peirce and Lewis’s Theories of Induction, p. 67).
One could schematically survey the major changes in SCT by looking at three formulations, the first, typically 18th-century, the second, 19th-century, and the third, Peirce’s:
SCTI: The methods of science are such that, given a refuted hypothesis H, a mechanical procedure exists for generating a `truer’ H’chrw(133). Science is progressive (i.e., getting closer to the truth).
SCT2: The methods of science are such that, given a refuted hypothesis H, we can always determine whether an alternative H’ is `truer’chrw.... Science is progressive.
SCT3: The method of enumerative induction is such that, given a refuted H (and the available evidence) we can mechanically produce an alternative H’ which is likely to be truer than Hchrw(133). Science is progressive.
The sequence SCTI —SCT2 —SCT3 is one in which the premises become increasingly preicse and defensible; but the price paid is that the premises seem to lend less and less inferential support to the conclusion.
Collected Papers, 5: 582.
Ibid., 1: 81. Peirce insists “that it is a primary hypothesischrw... that the human mind is akin to the truth in the sense that in a finite number of guesses it will light upon the correct hypothesis” (Ibid., 7: 220).
Ibid., 6: 531. Cf. also 1: 121.
Pierre Duhem, The Aim and Structure of Physical Theory, trans. Wiener (New York, 1962 ), pp. 26–7.
Ibid., p. 297. Duhem summarizes his position when he observes: “To the extent that physical theory makes progress, it becomes more and more similar to a natural classification which is its ideal end. Physical theory is powerless to prove this assertion is warranted, but if it were not, the tendency which directs the development of physics would remain incomprehensible. Thus, in order to fmd the title to establish its legitimacy [as an SCM], physical theory has to demand it of metaphysics” (Ibid., p. 298).
My suspicion is that this `cheap’ form of inductive self-correction has its origins in Laplace’s rule of succession, and the discussions that rule engendered in 19th-century probability theory.
Reichenbach writes: “The method of scientific inquiry may be considered as a concatenation of [enumerative] inductive inferencechrw(133) ” (Experience and Prediction, [Chicago, 1938], p. 364).
Cf. G. H. von Wright, The Logical Problem of Induction, 2nd ed. (Oxford, 1965), chap. viii. It is, however, to von Wright’s credit that he, almost alone among Peirce’s commentators, perceives the limited scope of Peirce’s treatment of self-correction. As he puts the point: “the Peircean idea of induction as a self-correcting approximation to the truth has no immediate significancechrw... for other types of inductive reasoning than statistical generalization” (Ibid., p. 226).
See, for instance, W. Salmon, ‘Vindication of Induction’, in H. Feigl and G. Maxwell (eds.), Current Issues in the Philosophy of Science (New York, 1961), p. 256; and W. Salmon, ’Inductive Inference’, in B. Brody (ed.), Readings in the Philosophy of Science ( Englewood Cliffs, N. J., 1970 ), p. 615.
A very different formulation of SCT has been developed by Karl Popper in his Conjectures and Refutations (London, 1963). Popper’s approach, unlike that of Peirce, Reichenbach and Salmon, does not attempt to make enumerative induction the cornerstone of scientific inference. It depends, rather, upon showing (unsuccessfully, I believe) that the method of hypothesis is weakly self-corrective in virtue of methodological conventions about increases in content. Popper is perhaps alone among contemporary philosophers of science in facing the issues raised by SCT in their full generality. As inadequate as his discussion of verisimilitude is, he has sensed the magnitude of the problem. In this, as in other ways, Popper is probably closer to the 19th-century methodological tradition than is any other living philosopher.
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Laudan, L. (1981). Peirce and the Trivialization of the Self-Corrective Thesis. In: Science and Hypothesis. The University of Western Ontario Series in Philosophy of Science, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7288-0_14
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