A Lesniewskian language for the nominalistic theory of substance and accident (original) (raw)

1983, Topoi an International Review of Philosophy

Le~niewski's contribution to scientific metaphysics took the form of two formalised theories, Ontology and Mereology. Both are couched in Legniewski's own distinctive formal language, which differs from more familiar formal languages in numerous ways, but principally in the fact that the nominal terms occurring within it may be semantically either empty, singular or plural. That is to say, a Legniewskian name may designate nothing at all, or just one thing, or several things. In this it differs from names in a Frege-Russell type of language, which may be singular only, and also from the unbound individual variables or parameters of free logic, which may be singular or empty, but not plural. 1 The provision of empty and plural terms in addition to singulars enables Legniewskian names to do work comparable to that done by monadic predicates, common nouns or terms for sets of individuals in other theories, since the Legniewskian names may be bound by quantifiers. However, because of Le~niewski's way of understanding the quantifiers 2 his theory avoids ontological commitment to abstract entities such as properties, species or sets. That we may in a certain fashion still regard Legniewski's names as class names does not mean that we recognise abstract sets, but only what Russell happily called 'classes as many'. 3 Whoever believes in the existence of at least two individuals is ipso facto committed to the existence of a class as many, since a class as many simply is the many individuals in question, and not some new abstract individual over and above these.