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Epistemology Without History is Blind

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Abstract

In the spirit of James and Dewey, I ask what one might want from a theory of knowledge. Much Anglophone epistemology is centered on questions that were once highly pertinent, but are no longer central to broader human and scientific concerns. The first sense in which epistemology without history is blind lies in the tendency of philosophers to ignore the history of philosophical problems. A second sense consists in the perennial attraction of approaches to knowledge that divorce knowing subjects from their societies and from the tradition of socially assembling a body of transmitted knowledge. When epistemology fails to use the history of inquiry as a laboratory in which methodological claims can be tested, there is a third way in which it becomes blind. Finally, lack of attention to the growth of knowledge in various domains leaves us with puzzles about the character of the knowledge we have. I illustrate this last theme by showing how reflections on the history of mathematics can expand our options for understanding mathematical knowledge.

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Notes

  1. For a sustained defense of this reading, see (Kitcher 2011a).

  2. Dewey articulates this perspective in three major works: Dewey (1920/1988), (1925/1981), and (1930/1988).

  3. My formulation indicates both agreement and disagreement with Richard Rorty. Rorty sees correctly that the classical pragmatists wanted to change the way philosophy is done, but he is more concerned with their judgments about old ways of proceeding than with their thoughts about the way in which the subject might continue. For further discussion of these themes, see (Kitcher 2011b, c).

  4. Although see the work of Clark Glymour and his associates on the generation of statistical hypotheses in the social sciences (Spirtes et al. 2001).

  5. Here I am indebted to the thoughtful essay by Barry Stroud, and to conversations with him.

  6. As rightly emphasized in the essays of Barry Stroud and Wolfgang Carl.

  7. Including, most notably, Bayesian approaches, as well as the belief-revision theories of Isaac Levi and Peter Gardenfors (Levi 1982; Gärdenfors 1988).

  8. For a pioneering exception, see (Goldman 1999).

  9. I scrutinize conceptions of this sort in (Kitcher 1980, 2006).

  10. The famous proposal about texts and footnotes comes from (Lakatos 1976).

  11. In (Kitcher 1993) Chapter 7, I have examined some facets of both these episodes in a way that achieves both goals. That is not to say, however, that the accounts I offer there would not benefit from extension and deepening.

  12. A lucid twentieth-century formulation of the problem is provided by Paul Benacerraf in “Mathematical Truth” (Benacerraf 1973). Benacerraf is more specific than I have been, posing the question as that of combining an adequate theory of mathematical truth with an adequate account of mathematical knowledge. This leads him to pose the important, and seminal, dilemma, which I discuss in the text.

  13. Or, more exactly, truth is that kind of correspondence delineated by Tarski in his celebrated reconstruction of the concept of truth. Benacerraf (1973) presents this idea very clearly.

  14. It is striking how frequently labels are adopted as a substitute for any theory of knowledge in the twentieth-century Anglo-Saxon tradition of discussing mathematics. Many eminent philosophers have been entirely satisfied to declare that basic truths of mathematics are “certain”, “a priori”, “evident”, “analytic”, “logical truths” and so forth, without feeling any need to say how they have this status or how they are known. Despite the forceful challenge in Benacerraf (1973), and despite the influence of that essay, the strategy of evasion continues happily into the present.

  15. See, for example, the history of basic claims about the existence of different types of numbers—zero, negative numbers, “imaginary” numbers, and so on. I discuss cases from the history of analysis—principles about continuity and infinite sums—in Chapter 10 of (Kitcher 1983).

  16. Here I offer only the briefest sketch of a way of endowing elementary—historically primary—parts of mathematics with content, that is of relating them to our interactions with physical nature. In Chapter 6 of (Kitcher 1983), I tried to provide a systematic reconstruction of mathematics along these lines; but, although there are some points of kinship with the approach I adopt here, that systematic reconstruction was insufficiently attuned to the historical processes through which mathematics has evolved. My present views are elaborated in (Kitcher, ms.) where I develop the connection with the ideas of the later Wittgenstein (1953, §1), which is already implicit in the sketch offered in the text.

  17. Without algebraic notation, the procedure for solving quadratic equations is extremely hard to formulate, and the recognition of it a great intellectual achievement. Similarly, problems in multiplying large numbers are difficult to solve without a good notation (Roman numerals do not work well in this regard!). It is a mistake to dismiss particular historical developments (the contributions of the Arabic scholars who gave us a workable numerical system, for example) as “merely” matters of introducing new language.

  18. Niccoló Tartaglia and Girolamo Cardano both made their living through public displays of mathematical prowess. Hence Tartaglia’s fury when Cardano published the method for solving cubic equations that he had elaborated (and had been independently found by Scipione del Ferro).

  19. The language stems from the Italian of Rafaello Bombelli, who recognized a purely mathematical point in introducing terms for square roots of negative numbers. That language only became firmly established significantly later, when Euler showed how mathematically valuable it was, specifically by forging a connection between the exponential and trigonometric functions. (Nagel 1935/1979 provides a valuable account of these developments).

  20. Interestingly, the great mathematicians of the seventeenth and eighteenth centuries typically worked both on the articulation of language to solve mathematical puzzles and on the application of those languages in the study of nature. Even as late as the nineteenth century, apparently “pure” mathematical researches are bound up with “applied” concerns—witness the work of Cauchy and Hamilton—as if the legitimacy of the proposed extensions must still be established by revealing pragmatic benefits. Gradually, however, confidence develops that at least some of the linguistic novelties will prove beneficial in broader inquiry, and pure mathematics obtains its full license.

  21. The connections between mathematical language and nature become increasingly complex through the centuries, but one can see the beginnings in the simple practices of collecting, matching, and tallying, as well as in land measurement. Later modifications are often interwoven with the development of scales of measurement.

  22. Here I am indebted to a referee.

  23. There are other, more technical worries, for example the concern that identifying truth with derivability founders on Gödel’s first Incompleteness Theorem. On my view, the sequence of worthwhile systems (the languages of mathematical interest) proceeds indefinitely. One of the directions in which it can extend consists in the addition to any formal system adequate for arithmetic of the pertinent Gödel sentence, to yield a new formal system for which the same extension can again be carried out. Once one has seen this, and understood why this is the preferred way of going on, these further articulations are of no particular further interest. We learn from Gödel that there will be no first-order theory adequate for the whole of mathematics. That lesson is perfectly compatible with the thesis I espouse, to wit that, for any mathematical truth, there is a worthwhile system within which that truth can be reached by licensed transitions.

  24. This paragraph owes an obvious debt to Wittgenstein’s Philosophical Investigations, in particular to the opening sections. For more detail about the Wittgensteinian connections, see (Kitcher, ms.).

  25. Here, the conception of truth recapitulates ideas of classical pragmatism, specifically the proposals of Peirce and James.

  26. Since, as my discussion of natural science emphasized, the goals of inquiry evolve, so too the legitimacy of extensions of mathematical language will be partly shaped by contingent ideas about what scientific issues are worth pursuing. Even if mathematicians justifiably extend their languages in response to previously-posed mathematical questions, similar points about evolving interests apply. This means that there may be no ideally complete system that is the inevitable result of inquiry, even though any justifiable development of mathematics must contain certain mathematical languages at its core.

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Correspondence to Philip Kitcher.

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Many thanks to Uljana Feest and Thomas Sturm for conceiving the conference at which this essay was originally presented, and for inviting me to take part in it. I learned much from the reactions of the audience to an earlier (and more strident) version of this essay. I am particularly indebted to Wolfgang Carl, Hannah Ginsborg, and especially Barry Stroud (who deserves commendation for his extraordinary patience). Two anonymous referees for Erkenntnis offered further constructive suggestions.

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Kitcher, P. Epistemology Without History is Blind. Erkenn 75, 505–524 (2011). https://doi.org/10.1007/s10670-011-9334-7

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