Abstract
This chapter discusses Wittgenstein’s early account of the epistemology of logic in relation to Frege, Russell, and Carnap. It explains how Wittgenstein’s early key insight that ‘logic takes care of itself’ enables him to solve several problems that arise for Frege’s and Russell’s philosophies and epistemologies of logic. These include problems relating to the justification of logical accounts and logical consequence, as well as to the status of logic as an a priori investigation distinct from empirical psychology. More specifically, Wittgenstein’s key insight eliminates the need to appeal in logic to any allegedly self-evident truths, intuitions, or substantial metaphysical knowledge regarding abstract objects. Further, his associated conception that the right way to articulate an account of logic isn’t theses, but a logical language whose design mirrors the logical structure of thought and language, puts him in a position to address what Sheffer later called ‘the logocentric predicament’. I conclude by explaining why the Tractatus doesn’t suffer from a paradox of nonsensical theses, and by outlining how Wittgenstein’s use of colloquial language to introduce his logical language foreshadows Carnap’s method of logical syntax. This explains why Carnap’s criticisms of Wittgenstein fail.
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Notes
- 1.
In the following I will use either the term ‘proposition’ or ‘thesis’ depending on context. Both stand for true/false representations of facts concerning thought, language or reality, and are substantial in this sense.
- 2.
For discussions of the problem of the justification of logic, see also Quine (1976) (originally 1935). Quine addresses the issue in relation to conventionalism, arguing that logical truth cannot be explained with reference to conventions, since logical justification would have to already rely on relevant conventions.
- 3.
Anssi Korhonen draws a similar distinction with reference to Frege and Russell between logic as science, that is ‘logic as principles of correct reasoning’, and logic as theory, that is a ‘particular formulation of logical principles’. Logic as science here refers to a science whose subject matter consist ‘very roughly, in truths about correct inferential transitions between non-linguistic entities of a certain kind (thoughts, propositions)’ that the logicians then try to model or represent and reconstruct in logical systems and explicit theories of logic (Korhonen 2012, 603). A related distinction between logic as science and logic as calculus is drawn by Gregory Landini (1998, Chap. 1). With Wittgenstein’s rejection of theses about logic in mind, I propose a different but related distinction between logic as the rules/norms/principles that govern thought and language use that are the target of logicians’ clarifications, and a logical language governed by relevant kind of rules/norms/principles put forward by a logician as an account of logic (see below, cf. Kuusela 2019a, 2019b, 49–51).
- 4.
In the case of such propositions the truth-tables laid out in the Tractatus don’t correctly reflect what Wittgenstein calls the ‘truth-possibilities’ of propositions (TLP 4.3-4.44). For example, the complex proposition ‘a is green and a is red all over’ is false, even though both conjuncts are true, contrary to standard truth-tables. Thus, as Wittgenstein realized, all sensible propositions can’t be expressed in his logical language. The logical behaviour of language is more complicated than he thought, and Tractarian’ truth-tables only account for part of the behaviour of the logical connectives. See Kuusela (2023) for Wittgenstein’s attempt to address this problem by introducing the notion of discreet propositional systems governed by different logical rules.
- 5.
- 6.
Russell maintained that we have immediate non-judgmental knowledge of abstract logical objects that ‘must underlie our knowledge of logic’ (Russell 1984, 97). But he never made much progress in clarifying this notion of immediate non-judgmental knowledge whose nature hardly becomes clearer by labelling it ‘intuition’. See also Russell (2001), Chap. 10.
- 7.
By dissolution I mean a way of dealing with philosophical problems by introducing an alternative way of thinking about an issue in the context of which a problem that arises in the context of another way of thinking no longer arises. Rather than answered in the previously presupposed terms the problem is thus made to disappear by introducing a better alternative view. See Kuusela (Forthcoming) for discussion of Wittgenstein’s notion of the dissolution of philosophical problems.
- 8.
This criticism, which relates more specifically to Frege’s and Russell’s failure to clearly distinguish rules of inference from axioms as true propositions, is spelt out at more length in Wittgenstein’s intended update on the Tractatus co-authored with Friedrich Waismann, but which was eventually abandoned (Wittgenstein & Weismann 2003, 179–183). It’s noteworthy that the Tractatus’ criticism of Frege’s and Russell’s axiomatic accounts of logic doesn’t imply any general objection to axiomatic accounts of logic. Insofar as logical axioms are understood as rules for the employment of the signs of a logical system, not true propositions, there’s no objection. Wittgenstein’s objection is directed specifically against Frege’s and Russell’s accounts of logic as a body of substantial truths, and the conception of axioms as a set of independently justified self-evident truths that constitute the foundation for logic in the style of metaphysical foundations.
- 9.
Wittgenstein further explicates the nature of this logical knowledge by means of his distinction between saying and showing. For an account of Wittgenstein’s distinction that is consistent with the proposed interpretation, see Kuusela (2021a).
- 10.
See Kuusela (2021b) for discussion of examples of traditional paradox-generating interpretations (G.E.M. Anscombe and Peter Hacker) and responses to them by so-called therapeutic and non-therapeutic resolute readers (including James Conant and Cora Diamond), and how the paradox is dissolved. For a critique of therapeutic interpretations of Wittgenstein, see Kuusela (2019a).
- 11.
For the notion of formality in the Tractatus, see Kuusela (2019b), 60–61, 80.
- 12.
See Kuusela (2019b), Chap. 3 for a detailed discussion and justification of this comparison between Wittgenstein and Carnap.
- 13.
I would like to thank the participants at the Heyting Day in Amsterdam in June 2022 for their questions and comments, in particular Maria van der Schaar and Göran Sundholm, as well as the editors of this collection.
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Kuusela, O. (2023). Wittgenstein’s Tractatus and the Epistemology of Logic. In: Stokhof, M., Tang, H. (eds) Wittgenstein's Tractatus at 100. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-29863-9_3
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