Would the identity be a logical constant? Between Logic and Metaphysics
Logical constants; identity; rules of inference.
What we call the problem of logical constants is a attempt to afford a non-arbitrary criteria for distinguish the realm of logical expressions from non-logical ones. Traditionally the expression of logical vocabulary were viewed as responsible for the validity of arguments. In this tradition negation (~), conjunction (∧), disjunction (∨), implication (→), the universal (∀) and existencial (∃) quantifiers were considered members of the privileged set of logical constants. But there is a large dispute about which others expressions should be introduced in this list. Our goal is to investigate one of these cases, namely, the disputes about the logicality of identity (=). We note that in disputes about identity the arguments are mainly couched in a representationalistic way. Then, we argue that if we give up this assumption is possible to defend the logicality of identity. To do that we approach the problem trough the so called inferential characterizations. In such a approach rules of inference are used to expose the logical behaviour of a logical constant. In particular, we will follow Popper (1946), and Dosen (1989). We use his ideas jointly with some of Humberstone e Townsend (1994) to expose in which conditions we could give a adequate answear to the problem of identity as a logical constant.