Structural Isomorphism of Meaning and Synonymy

Abstract

In this paper I am going to deal with the
phenomenon of synonymy from the logical point of
view. In Transparent Intensional Logic (TIL), which is
my background theory, the sense of an expression is
an algorithmically structured procedure detailing what
operations to apply to what procedural constituents to
arrive at the object (if any) denoted by the expression.
Such procedures are rigorously defined as TIL
constructions. In this new orthodoxy of structured
meanings and procedural semantics we encounter the
problem of the granularity of procedure individuation.
Though the identity of TIL constructions is rigorously
defined, they are a bit too fine-grained from the
procedural point of view. In an effort to solve the
problem we introduced the notion of procedural
isomorphism. Any two terms or expressions whose
respective meanings are procedurally isomorphic are
deemed semantically indistinguishable, hence
synonymous and thus substitutable in any context,
whether extensional, intensional or hyperintensional.
The novel contribution of this paper is a formally
worked-out, philosophically motivated criterion of
hyperintensional individuation, which is defined in terms
of a slightly more carefully formulated version of -
conversion and -conversion by value, which amounts
to a modification of Church’s Alternative (A1).