Abstract
On the standard interpretation of Lewis’s criticism of Russell, Lewis takes his own account of strict implication to be more intuitive than the paradoxes to which Russell’s material implication leads. This chapter argues against the standard interpretation by showing that Russell’s views are not counterintuitive, but that appeals to “intuition” are not the substance of Lewis’s criticism of Russell. Lewis’s debate with Russell undergoes two main phases. In the first phase, Lewis argues both that the logic of material implication fails to represent correctly the distinction between correct and incorrect inferences and that the logic of material implication is not useful. In the second phase, Lewis argues that Russell’s explication of implication neither coheres fully with Russell’s deductive practices nor can Russell avoid appealing to strict implications. A better understanding of the Russell-Lewis dispute points to a conception of the nature of logic: it must be possible for logical principles to play a practical role in reasoning, else logic becomes disconnected from rational thought and discourse.
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Notes
- 1.
See also Russell’s glosses on *2.21, “ \( {\sim}p \supset \left( {p \supset q} \right)\)” and *2.02, “ \(p \supset \left( {q \supset p} \right)\)” of Principia Mathematica.
- 2.
- 3.
- 4.
I defend this interpretation in Shieh (forthcoming-a).
- 5.
Some of these complexities are explored in the fine discussion of Lewis on strict implication in Curley (1975).
- 6.
I set out the full account of Lewis’s view of logic in Shieh (forthcoming-a), from which the discussion in this essay is derived.
- 7.
- 8.
For more on this metaphysics of propositions, see Griffin (1980), Hylton (1990), and Cartwright (2003).
Russell does not explicitly provide an account truth in virtue of logical structure in Principles, but I provide a sketch in Shieh (forthcoming-a). See Almog (1989) for a similar idea.
- 9.
This attempt to understand Russell through Gödel is partly justified by Gödel’s extensive interest in Russell, as evidenced by the Max-Phil Notebooks; see in particular Floyd and Kanamori (2015).
- 10.
I omit Russell’s conditionalization on \(p,q,r\) being propositions.
- 11.
Arguments by reductio are strictly speaking not proofs; but all such arguments can be converted into genuine proofs.
- 12.
We’ll see later that Lewis says, “Pragmatically,…material implication is an obviously false logic” (Lewis 1914, p. 246; emphasis mine).
- 13.
This passage suggests that Lewis takes all of Russell’s axioms and theorems to have a double use, but it is plausible that Russell supposes only some of them to have that double use. In Principles this is shown, for example, by the fact that an axiom of the calculus of relations is “implication is a relation,” which surely has no use as a rule of inference. In Principia it’s unclear how the axiom of reducibility could have such a double use. Of course what is important for Lewis is that the axioms and theorems of the propositional calculus have this double use.
- 14.
I’m indebted to Curley (1975) for my formulation of this problem for material implication.
- 15.
So practical apriority is not the same thing as Lewis’s pragmatic conception of the a priori, as articulated in the (1923) paper of that title and in Mind and the World-Order (1929). Practically a priori knowledge of implications and disjunctions is not claimed to be independent of the given, or attained in virtue of being postulated by the mind and so not constrained by the given.
- 16.
Russell and Lewis were not alone among philosopher-logicians of the turn of the twentieth century in holding that logical principles must be useful actual reasoning; two other prominent examples are C. S. Peirce and F. P. Ramsey. For discussion of Peirce’s views, see Cheryl Misak (1988, 2013). In forthcoming work she also discusses Ramsey’s views and their connection to Peirce.
- 17.
- 18.
- 19.
- 20.
I’m grateful to Cheryl Misak for urging me to clarify my view of Lewis’s conception of truth. I tell much of the long story in Shieh (forthcoming-b).
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Acknowledgements
Thanks are due to members of the audiences to which earlier versions of this essay were presented: Ian Proops’s seminar at the University of Michigan, a seminar at Auburn University, the Orange Beach Epistemology Workshop, the Relativization of the A Priori Symposium at l’Université de Bordeaux Montaigne, and the Beijing International Conference on Analytic Philosophy at Beijing Normal University. In particular, I’m grateful to the comments and suggestions of Ian Proops, Arata Hamawaki, Kelly Jolley, Richard Fumerton, Juliet Floyd, Jim O’Shea, and Tom Stoneham. I would like to thank Cheryl Misak for comments on an earlier version of this chapter, as well as letting me see her forthcoming work on the influence of American pragmatism on early twentieth-century philosophy in Cambridge, England. Special thanks are due to Jean-Philippe Narboux, Timur Uçan, and Henri Wagner for creating such a splendid symposium at Bordeaux.
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Shieh, S. (2017). Pragmatism, Apriority, and Modality: C.I. Lewis Against Russell’s Material Implication. In: Olen, P., Sachs, C. (eds) Pragmatism in Transition . Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-52863-2_6
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