On Identity Criteria

Consider this example. We bring a friend into a room. There is a table, a chair, a book, and a cat sleeping on the chair. Nothing else. We ask: “How many objects are there?”. Suppose that the friend’s answer is: “Four”. Again, we ask: “Which objects are there?”. Answer: “A table, a chair, a book, and a cat”. We insist: “Do you not count yourself?”. Answer: “Then, five”. “And what about the pages of the book? The chair legs? The cat’s tail?”. And so on (the example is taken from [Putnam 1988, cap. 7]). One way to stop this chain of queries is to argue that the first one does not hold a determinate meaning. It would be rightly raised if there was a specification of the kind or sort of objects to count (this solution is advanced, among the others, – with some differences – by [Dummett, 1981, p. 547]; [Geach, 1980, p. 63]; [Wright, 1983, p. 3]). Therefore, according to this solution, it is appropriate, where the use of “appropriate” is the common one, to ask how many tables are in the room, or how many chairs, or how many books, or how many cats, or how many human beings... because in all these cases there is a suitable specification of the query at issue. Doing 2 so, we associate to the term for a kind or sort — the sortal term — in some way, an identity criterion. So, a question concerning counting is determinate, or appropriate, if and only if it is specified by a sortal and there is a criterion of identity for the kind (or sort) of the term. The goal of this paper is to analyse the expression “criterion of identity” occurring in the above biconditional. We want to exclude that some standard meanings are the meaning of the expression discussed. If criteria of identity are used in that way, in order to specify a question concerning counting, and if the specification of the question is the solution proposed to stop the chain of queries produced by the first question: “How many objects are in the room?” then the solution is false.