A NOTE ON LOGICAL TRUTH

Abstract

Classical logic counts sentences such as ‘Alice is identical with Alice’ as logically true. A standard objection to classical logic is that Alice’s self-identity, for instance, is not a matter of logic because the identity of particular objects is not a matter of logic. For this reason, many philosophers argue that classical logic is not the right logic, and that it should be abandoned in favour of free logic — logic free of existential commitments with respect to singular terms. In most standard free logics, sentences such as ‘Alice is identical with Alice’ are not logically true. This paper argues that this objection from existential commitments is somewhat superficial and that there is a deeper reason why ‘Alice is identical with Alice’ should not be considered a logical truth. Indeed, a key fundamental thought about the nature of logic is that a logical truth is true in virtue of its logical form. The fundamental problem I raise is that a sentence such as ‘Alice is identical with Alice’ appears to not even be true in virtue of its logical form. Thus this paper argues that given that such a sentence is not true in virtue of its logical form, it should not be counted as logically true. It moreover argues, on the same grounds, that even the sentences which free logicians regard as logically true shouldn’t be regarded as logically true. So in this sense free logic is no repair to classical logic. I. Introduction The paper is organised as follows. In sections II and III, I outline the standard problem of existential commitments for classical logic, as well as its standard solution in terms of free logic. Doing this will be useful to set up the key issue of the paper. Section IV then moves to considerations about logical form and outlines a new problem for sentences such as ‘Alice is identical with Alice’ being considered logical truths. Sections IV-XI put forward considerations meant to cast doubt on the idea that sentences such as ‘Alice is identical with Alice’ are logical truths in the formal sense. Section XII elaborates on these considerations and offers a way of thinking of the relationship of sentences such as ‘Alice is identical with Alice’ to logical truths proper.