4 - Some issues in logic and semantics

Summary

I … beg the reader not to make up his mind against the view – as he might be tempted to do, on account of its apparently excessive complication – until he has attempted to construct a theory of his own on the subject. … This attempt, I believe, will convince him that, whatever the true theory may be, it cannot have such a simplicity as one might have expected beforehand.

Bertrand Russell, “On Denoting”

Chapter 3 set out the rudiments of a view of the semantics of attitude ascriptions. It suppressed discussion of complications and subsidiary issues. In this chapter, I address a few of the issues ignored in Chapter 3.

I begin by discussing quantification. The account of quantification into attitude ascriptions I have given violates Leibniz's law, the principle that universal closures of

If x = y, then if … x …, then … y …

are invariably true. This principle has been said to be fundamental to objectual quantification; thus, the fact that my account violates it might be thought to be a defect. I argue that violating the principle is no defect, since Leibniz's law is no law of quantification theory: A language's quantifiers may one and all be objectual without the law being true of it.