Aleksandar Kellenberg

Part One of the paper presents a structural analysis of a restricted version of Frege's puzzle regarding the cognitive value of sentences of the kind "a = b". It attempts to clarify the puzzle's nature and to distinguish strategies for a solution. Part Two argues that only one of four possible strategies may lead to an acceptable solution. It submits that the puzzle concerns essentially, not knowledge, but identity; that the underlying problem lies in an inadequate conception of entities; and that a reasonable solution is to regard all identity sentences of the kind "the F is the same entity as the G", in which "F" and "G" are non-synonymous predicates, as being necessarily, analytically and a priori false.

I discuss E. J. Lowe's conception of criteria of identity and sketch a different and, I think, more adequate conception. On my view, criteria of identity are some of the things we can do. They are what we do when distinguishing between single entities of the kind in question and pairs of entities of the relevant domain. And they enable us to make such distinctions because they are applicable to all single and to all pairs of entities of the relevant domain but fulfilled only by all single entities of the kind in question. This feature of criteria of identity allows us to define these criteria, to explain how to identify a particular criterion of identity and to determine the logical form in which to express such identifications.

There is a solution to the antinomy of the variable that does not call for semantic relationism. I argue that if we carefully distinguish between variable types and variable tokens or occurrences, and if we take the number of variable types involved properly into account, then coordination among variable tokens or occurrences is reducible to an intrinsic semantic feature of those tokens or occurrences. The fact that two tokens or occurrences of the same variable type contained in the same sentence or context assume the same value at a time derives from an intrinsic semantic feature of a token or occurrence, namely from being a token or occurrence of a type whose tokens or occurrences must assume the same value at a time if contained in the same sentence or context.