- The notion of an individual object or thing is an indispensable primitive for theories of meaning grounded in standard model theoretic semantics. One begins with a domain of individuals, and there are no prima facie constraints as to what counts as an individual except those of a most general and seemingly redundant kind. Each individual must be distinct from every other and identical to itself. Individuals can be assembled into sets, ordered into n'tuples, which in turn can be assembled into sets. There are vaguer restrictions: individuals must have a certain definiteness, a closure, the seeming lack of which in concepts prompted Frege to deny that a concept was an object. It is redundant to say that individuals are individuated, but that does not suppose that there is always available to us a way of deciding that a given identity statement is true.
- On the standard semantics individuals are basic to a logical structure, but nothing prescribes that they be in turn unconstructed. They need not be logical atoms in a reductionist sense unless of course one appends a theory of logical atomism. Nor are there any preferred categories of individuals whether irreducible or not. Disagreements about the choice of an object domain in an interpreted theory, whether the theory be metaphysical, mathematical, or empirical, are thrashed out elsewhere. Nor must one apply Occam's razor. There are no requisite restrictions on the number of individuals or how many sorts or categories.
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