Validity and Interpretation

Abstract

This paper claims that there is a plausible sense in which validity is a matter of truth preservation relative to interpretations of the sentences that occur in an argument, although it is not the sense one might have in mind. §1 outlines three independent problems: the first is the paradox of the sorites, the second concerns the fallacy of equivocation, and the third arises in connection with the standard treatment of indexicals. §2 elucidates the claim about validity, while §§3–5 show how the three problems outlined can be handled in accordance with it. §6 explains how the claim squares with the traditional idea that validity is related to formality, and in particular with a broadly accepted definition based on that idea, the model-theoretic definition of logical consequence. Unlike other works on the subject, this paper does not focus on necessity. It is not its intention to provide a characterization of necessity that conforms to some ideal of rigour or to some pre-theoretical understanding of validity. What follows can be taken as conditional on the assumption that such a characterization can be provided.

Notes

¹Logic textbooks don't help much in this sense. For example, Copi 1986: 113] can hardly be regarded as an explanation. The fallacy of equivocation is no isolated case. Usually logic textbooks introduce fallacies by drawing on a corpus of traditional examples accompanied by standard comments. But in many cases it is not clear from those examples or comments what is wrong with the argument.

²Fogelin and Sinnott-Armstrong 2001: 367] provide an account of this kind. Note that it is not essential to the account that the alleged real argument is defined in terms of propositions. Any set of entities—such as syntactic constructs—that ensures disambiguation will do.

³The same trouble arises if the fallacy is described in terms of a plurality of arguments disguised as a single one, as in Kirwan 1979 or in Woods and Walton 1979.

⁴The standard definition goes back to Kaplan 1977. There, ‘context’ is used instead of ‘index’. To avoid ambiguity, here ‘context’ is used only as a non-technical term, to refer to a possibly concrete situation in which a sentence or a set of sentences can be used. Predelli 2005: 83] and Braun 2001: §3.3] regard the standard definition as ‘intuitive’.

⁵Here ‘non-univocal’ is not to be read as synonymous with ‘equivocal’. Equivocality entails non-univocality, but is not entailed by it. The two cases considered involve a non-univocal use of a word, yet it seems incorrect to call that use equivocal. The problem surfaces in Kaplan 1989: 586–7]. Takashi Yagisawa is among the few who recognize its force, see Yagisawa 1993: 471–4].

⁶As far as vague predicates are concerned, admissibility is understood along the lines suggested in Fine 1975.

⁷Valuations differ from structures in the same way. The only respect in which valuations, unlike interpretations, resemble structures is that they are defined for the whole language rather than for single sentences.

⁸That is done in Iacona [forthcoming] (a)].

⁹See Williamson 1994: 147–8], Keefe 2000: §3], and Varzi 2007.

¹⁰According to Church 1942, this is part of the very definition of the fallacy.

¹¹Yagisawa 1993: 483] treats UC as a pragmatic principle that does not belong to logic.

¹²The material of this section is drawn from Iacona [forthcoming (b)], which focuses on arguments affected by context-sensitivity.

¹³As noted by Timothy Smiley 1982/3.

¹⁴The expression ‘adequate formalization’ is used in Sainsbury 1991.

¹⁵This is essentially the point made by Sainsbury 1991: 63], when he says that an adequate formalization must preserve what the sentences in the argument say.

¹⁶LC goes back to Tarski 1936.

¹⁷As it emerges from the debate generated by Etchemendy 1990. To use Etchemendy's terminology, LC is ‘interpretational’, while V_I and FV_I are ‘representational’ (at least if it is assumed that invariance of linguistic meaning suffices for representationality).

¹⁸An argument along these lines was first provided in Kreisel 1967. See also Hanson 1997 and Gómez-Torrente 2006.

¹⁹I should like to thank Mario Gómez-Torrente, Diego Marconi and three anonymous referees for some valuable remarks that helped me to improve the paper.