Multicategorial Ontology and Logicism

Abstract

This paper discusses the philosophical background to the paper by lejewski in this issue. lejewski offers an ontologically neutral logic for the first two types (individuals and classes thereof). some peculiarities of the logic used are noted, in particular the distinction between empty individual terms, empty class terms, and non-empty class terms designating the empty class. lejewski ends by denying the truth of the formula meaning "there are classes," but we argue that the way in which truth-conditions for formulae containing class terms are introduced absolves us from taking this as seriously committing us to the existence of classes. the main (inclining but not necessitating) reason for being a platonist lies in the sheer mass of mathematical results for which a non-platonist account has yet to be given. the theory of classes as fictions suggested by our modification of lejewski's view is insufficient to support frege-russell style logicism, but for a non-platonist the upper reaches of cantor's paradise must be regarded as fictitious anyway.