Cechy, zbiory i możliwe światy

Abstrakt

The paper is devoted to the problem of the reduction of properties into sets of objects. It consists of three major parts. The first part deals with the conceptual framework where the notions of ‘property’ and ‘set’ are discussed. While the sets are taken straight from the mathematical set theory, properties and their relation to objects require much more complex description. The author adopts the Aristotelian approach based on an ontological relation of inherence.

In the second part, the existing views on the reduction in question are presented and reviewed. The central issue here is the one of the extensional equality of properties and sets. Most of the contemporary ideas on that matter point out that said equality between those two is impossible, thus the reduction cannot happen. Some of them try to omit the axiom of extensionality, but the author argues that those attempts are futile.

Finally, in the third part, an alternative way of dealing with the problem is presented, the one that leaves the principle of the extensional equality intact: the modal realism of David Lewis. While all other approaches are based on the idea of the single world, modal realism offers us a theory of possible worlds. The significance of Lewis’ approach and his idea of reduction of properties into sets of objects are briefly discussed. Although the reduction within the possible worlds seems very plausible, the author of the paper points out certain difficulties, like its inability to explain necessarily coextensive properties. Despite the fact that modal realism offers us the way of reducing properties into sets in most cases, it still does not enable us to make the complete reduction. Though Lewis’ theory seems fruitful, it is, in fact, futile with respect to the problem in question. Hence, the author argues that the answer to the question of reduction of properties into sets