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Peirce, Russell and Abductive Regression

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Abduction in Cognition and Action

Part of the book series: Studies in Applied Philosophy, Epistemology and Rational Ethics ((SAPERE,volume 59))

Abstract

Below are reflections on Peirce’s conception of abductive methods and Russell’s conception of regressive methods. Along the way, it will be necessary to examine the marked differences between Russell and Frege on the ins and outs of logicism, from which latter the regressivist ideas first emerged. Russell was aware of Peirce’s contributions to the algebraization of logic and Peirce was aware of Russell’s writings on logicism. However, in framing his thoughts about regressive methods, Russell showed no familiarity with Peirce’s treatment of abductive methods. In 1907, Russell read to the Cambridge Mathematics Club an essay entitled “The regressive method of discovering the premises of mathematics.” Since that paper didn’t see the published light of day until three years after Russell’s death in 1970, Peirce couldn’t have taken notice of it in developing his ideas about abduction. Even so, it has been suggested that there exists a noteworthy similarity between Russell’s regressivism and Peirce’s abductivism. The principal purpose of this essay is to show the resemblance to have been misjudged, in which case, my title would have to be corrected.

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Notes

  1. 1.

    See Peirce [25,26,27]. Putnam [32, p. 297] and Quine [34, p. 259]. See oppositely (and earlier) Goldfarb [12]. We needn’t settle the matter here.

  2. 2.

    Peirce [28, p. 143], Hereafter RLT.

  3. 3.

    Peirce (CP 5.189), in [29] Citations are structured as follows: “CP 5.189” denotes Volume V of Collected Papers, p. 189. Line numbers are for referential convenience, and I have changed the original schematic letters to more intuitive ones and removed the italics.

  4. 4.

    For a recent more detailed exposition, see Woods [45]. See also Gabbay and Woods [11], Magnani [22] and Park [23]. All these works adopt naturalistic assumptions for the logic of inference. A still unsettled disagreement is about whether all abductions are inferences to the best explanation. The authors cited in this note think that it is not that intrinsically. But here, too, we needn’t settle the question for what matters here.

  5. 5.

    For expositionary ease, I use “F” ambiguously. In Peirce’s Schema it names some given fact or state of affairs. When it occurs as the conclusion of a piece of reasoning, it names a proposition that states that fact. I leave it to context to disambiguate.

  6. 6.

    Fruitful conjecture is nicely discussed by philosophically trained historians of science. See, for example, Tappenden [42] and Ferreirós and Gray [7].

  7. 7.

    More on this can be found in Chap. 9, “Putting inconsistency in its place”, of Woods [46].

  8. 8.

    A causal-response epistemology sees the beliefs that qualify as knowledge as causal responses to information-processing under specified conditions. (Woods [44], Sect. 3.5). In contrast, a causal-contact epistemology, requires a believer’s causal contact with the object of belief [13].

  9. 9.

    For more enriched versions see Chiffi and Pietarinen [3, 4].

  10. 10.

    Poincaré’s Conjecture says that every simply connected closed 3-manifold is homeographic to the 3-sphere. Riemann’s Hypothesis is that all non-trivial zeros of the Riemann zeta function have a real part equal to 0.5. Hodge’s Conjecture is that certain de Rham cohomology classes are algebraic.

  11. 11.

    Since most epistemologies require that truth be a condition on knowledge, henceforth I’ll frame the worry as epistemic.

  12. 12.

    Notwithstanding some occasional slippage. For example, he endorsed the idea that the functions of which the True and the False were their respective values could be left to arbitrary stipulation.

  13. 13.

    Frege [9].

  14. 14.

    Frege [8].

  15. 15.

    Gray [15].

  16. 16.

    Poincaré [30].

  17. 17.

    Dedekind [5]. Reference here to the Foreword of the first edition.

  18. 18.

    Dedekind [6] and Peano [24].

  19. 19.

    Grattan-Guinness [14].

  20. 20.

    Whitehead and Russell [43].

  21. 21.

    In about these same words, Frege characterizes the à priori, thus collapsing the Kantian distinction between the alethic property of analyticity and the epistemic property of apriority.

  22. 22.

    Blanchette [2, p. 31].

  23. 23.

    For a fuller discussion of this difficulty, readers could consult Woods [47].

  24. 24.

    Russell [38].

  25. 25.

    In “On the axioms of geometry” of 1899, Russell lists seven simple and indefinable concepts: addition, number, order, equality, less, greater and manifold. See Griffin and Lewis [17].

  26. 26.

    Russell took a somewhat rigourist approach even to mathematical stipulation. He dismisses definition by abstraction, which “… suffers from a wholly fatal formal effect: it does not show that only one object satisfies the definition.” (p. 114).

  27. 27.

    See, for example, Putnam [31], Griffin [16] and Krall [21].

  28. 28.

    For reservations, see Griffin [16].

  29. 29.

    Principles, xviii.

  30. 30.

    Irvine [20].

  31. 31.

    Russell [36, 29–44]. Reprinted in the first edition of Russell (1910).

  32. 32.

    Bertrand Russell, Letter to Frege, in van Heijenoort [39, 40]. Frege’s letter in reply follows at pages 127–128.

  33. 33.

    Russell appears to have been unaware of Zermelo’s derivation of it the year before. See Hallett [19].

  34. 34.

    Russell [35]. Reprinted with revisions and a new title in Russell (1918).

  35. 35.

    This view is developed in Aristotle’s Posterior Analytics and Metaphysics [1]. Details can be found in Woods [47].

  36. 36.

    Irvine [20] reports that suggestion in ft. 26, p. 322. Kleiner is a philosopher of science at the University of Georgia.

  37. 37.

    Of course, volume one of Principia has yet to appear. Shouldn’t we instead take Russell to be thinking of the logic of the Principles? I think not. On May 13, 1903, a few days after its publication, Russell had lost confidence in Principles, writing that “it seems to me a foolish book, and I am ashamed to think that I have spent the best part of six years upon it. Now that it is done, I can allow myself to believe that it was not worth doing—an odd luxury!” See Griffin [18]. Even allowing for Russell’s habit of self-effacement, it is better to locate his logical thinking in 1907 in Russell [37] in van Heijenoort [10], pages 152–182, which would appear a year later and would be absorbed into Principia, whose first appearance was two years after that.

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  1. University of British Columbia, Vancouver, BC, V6T 1Z1, Canada

    John Woods

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  1. Philosophy and Science Education, University at Buffalo, Amherst, NY, USA

    John R. Shook

  2. Faculty of Educational Sciences, University of Helsinki, Helsinki, Finland

    Sami Paavola

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Woods, J. (2021). Peirce, Russell and Abductive Regression. In: Shook, J.R., Paavola, S. (eds) Abduction in Cognition and Action. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-030-61773-8_6

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