Abstract
“The Justification of Deduction” was written more than forty years ago; so probably I should begin by saying that it wasn’t I who wrote this, but my younger sister—the same young lady who wrote Deviant Logic. Now, however, since this younger sister is no longer around, it falls to me to say a few words on her behalf.
Neither my little sister nor I ever for a moment imagined that modus morons was a good rule of inference—of course it isn’t; that’s why it’s called modus morons! But Bloch et al. have done a nice job of articulating some ways in which it is, in their phrase, a “rogue” rule. They call primarily on the notion of “harmony,” a term they attribute to Michael Dummett, and describe as going back to an idea of Gerhard Gentzen’s: that the elimination rule for a connective is (or should be) a mere “consequence” of the introduction rule for the same connective. Using Dag Prawitz’s concept of reducibility, Neil Tennant’s “inferential truth-theory,” and considerations about the truth-table for “→,” Bloch et al. show that the introduction rule and the elimination rule for modus morons are, to put it mildly, not in harmony. No wonder, then that (like Arthur Prior’s rogue connective, “tonk”) modus morons would wreak havoc in any logical system. My sister and I thank Bloch and Co. for this careful work.
[Given my] rather heretical principles of philosophical research, one of which is [that] nothing can be admitted to be absolutely inexplicable, it behooves me to show how upon my principles the validity of the laws of logic can be other than inexplicable. —C. S. Peirce
C. S. Peirce, “Grounds of Validity of the Laws of Logic” (1868), in Peirce, Collected Papers, eds. Charles Hartshorne, Paul Weiss, and (vols. 7 and 8) Arthur Burks (Cambridge, MA: Harvard University Press, 1931–58), 5. 318–47.
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Notes
- 1.
Susan Haack, “The Justification of Deduction” Mind 85 (1976): 112–19. The paper was actually written in 1972, but spent several years awaiting publication—years during which, to my chagrin, Dummett published his paper of the same title.
- 2.
Susan Haack, Deviant Logic (Cambridge: Cambridge University Press, 1974).
- 3.
The quotation marks around “consequence” aren’t mine, but Bloch et al.’s; I assume they indicate that Bloch et al. realize that something remains to be said about what exactly this extra-systematic concept amounts to.
- 4.
I was, by the way, struck by the fact that Tennant reportedly refers to his rule for eliminating “T” (“true”) as “disquotation.” If (as I gather) the theory is meant to be Tarskian, this seems a most unfortunate choice of word for what might better be called “semantic descent.”
- 5.
There is a brief discussion of axiomatic vs. natural-deduction approaches in my Philosophy of Logics (Cambridge: Cambridge University Press, 1978), pp, 1921; but this discussion is (deliberately) entirely neutral.
- 6.
This is the last of Peirce’s series of three articles critical of the Cartesian philosophy, published in 1868. In this paper Peirce writes largely about syllogistic logic; later, however (a few years after, and quite independently, of Frege), he developed a unified propositional and predicate calculus. For those who aren’t familiar with this part of the history of logic, I recommend Hilary Putnam, “Peirce the Logician” (1982), reprinted in Putnam, Realism with a Human Face, (Cambridge, MA: Harvard University Press, 1990), 252–60.
- 7.
Peirce, Collected Papers (note 1 above), 5.31 (1868).
- 8.
The “Gefühl theory,” which Peirce attributes specifically to Christopher Sigwart, but describes as common among German logicians at the time. Id., 2.19, 2.152 ff. (1902).
- 9.
Id., 2.20, 160 ff. (1902). “To some degree” because, unlike Frege’s, Peirce’s conception of logic includes the inductive and the abductive as well as the deductive.
- 10.
Id., 2.188 ff. (1902).
- 11.
Id., 2.197 (1902). As this reveals (even though he was aware of the possibility of reducing mathematics to logic) Peirce did not, like Frege, take mathematics to be epistemologically secondary to logic—quite the contrary. See Susan Haack, “Peirce and Logicism: Notes Towards an Exposition,” Transactions of the Charles S. Peirce Society, 29.1 (1992): 33–56.
- 12.
Peirce, Collected Papers (note 1 above), 2.216 (1902).
- 13.
Id., 1.54 (c.1896); 2.216 (1902). Bynum reports that by 1924 Frege had reached a similar conclusion, abandoning logicism and seeking the foundations of arithmetic in geometry. Terrell Ward Bynum, ed., Conceptual Notation and Related Articles (Oxford: Clarendon Press, 1972), p. 54.
- 14.
Peirce, Collected Papers (note 1 above), 4.429 (c.1903).
- 15.
Id., 4.394 ff. (1903). Peirce described the existential graphs as his “chef d’oeuvre.”
- 16.
Susan Haack, Deviant Logic, Fuzzy Logic: Beyond the Formalism (Chicago: University of Chicago Press, 1996).
- 17.
See Susan Haack, “The Fragmentation of Philosophy, the Road to Reintegration,” pp. 000–000 in this volume.
- 18.
Susan Haack, “Reflections on Relativism: From Momentous Tautology to Seductive Contradiction” (1996), reprinted in Haack, Manifesto of a Passionate Moderate: Unfashionable Essays (Chicago: University of Chicago Press, 1998), 149–66. As I recall, I sent Prof. Boghossian a copy of this paper around the time it appeared; I always assumed that the reason he never cited it was that I’m not a member of his (or indeed of any) citation cartel!
- 19.
Many of the papers in Manifesto of a Passionate Moderate do precisely this, for one or more of the myriad relevant confusions involved. See also “”Staying for an answer” (1999), in Susan Haack, Putting Philosophy to Work” Inquiry and its Place in Culture (2008: expanded ed. Amherst, NY: Prometheus Books, 2013), 35–45 and 269–70; “The Unity of Truth and the Plurality of Truths” (2005), in the same volume, 53–67 and 271–73.
- 20.
Susan Haack, Evidence and Inquiry (1993; second ed., Amherst, NY: Prometheus Books, 2009).
- 21.
Susan Haack, Evidence Matters: Science, Proof, and Truth in the Law (New York: Cambridge University Press, forthcoming 2014).
- 22.
Susan Haack, Defending Science—Within Reason: Between Scientism and Cynicism (Amherst, NY: Prometheus Books, 2003).
- 23.
See e.g., Susan Haack, “Realisms and their Rivals,” Facta Philosophica 4.1 (2002): 67–88; The World of Innocent Realism” (first published in German in 2014), in this volume, pp. 33–55); “The Real, the Fictional, and the Fake,” Spazio Filosofico 8 (2013): 209–17; and my response to Göhner et al. in this volume, pp. 167–73.
- 24.
Markus Gabriel, ed., Der Neue Realismus (Berlin: Suhrkamp, 2014).
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Haack, S. (2016). The Grounds of Logic: Response to Sascha Bloch, Martin Pleitz, Markus Pohlman, and Jakob Wrobel. In: Göhner, J., Jung, EM. (eds) Susan Haack: Reintegrating Philosophy. Münster Lectures in Philosophy, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-24969-8_12
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