Neo-Logicism An Ontological Reduction of Mathematics to Metaphysics 2 citations ? 1 self

Abstract:  individuals are said to be identical whenever they necessarily encode the same properties, but to show that x and y are the same abstract individual, it suffices to show that x and y encode the same properties, since the logic of encoding is rigid (i.e., 3xF ! 2xF ). The canonical formulation of the theory of abstract individuals also includes two kinds of complex term. There is a complex way of denoting individuals, namely, rigid definite descriptions of the form --x' (for any formula '). These definite descriptions are axiomatized in the usual way, namely, by a principle which asserts that Russell's analysis of descriptions applies to any atomic formula that contains a description. 5 There is also a complex way of denoting relations, namely, -expressions of the form [y 1 : : : yn '] (where ' has no free F s, no encoding subformulas and no descriptions). These -expressions are axiomatized by the usual principle -Conversion (i.e., -abstraction), and by a principle which ensures that...