Composition as identity and plural Cantor's theorem

Composition occurs when one or more objects are parts of another object. The metaphysics of composition concerns the nature of composition – i.e. what it is, and how it works. Some of the more important questions philosophers have regarding the metaphysics of composition are the following: (1) When does composition occur? This is van Inwagen’s ‘Special Composition Question’. Four prominent answers to this question include: (i) objects compose another object when those former objects are in contact; (ii) any two or more objects compose another object; (iii) objects never compose another object; (iv) objects compose another object when the activities of the former objects constitute a life. (2) Are composite objects identical with their parts? Proponents of ‘composition as identity’ answer ‘yes’ to this question. There are two primary variants of composition as identity, ‘strong’ composition as identity and ‘weak’ composition as identity. The most prominent objection to strong composition as identity is an objection from Leibniz’s Law: composite objects cannot be identical with their parts, since they seem to have properties which their parts do not have. (3) Is it possible for one object to constitute another object? Here ‘constitution’ is the relation which is alleged to obtain between, for example, a clay statue and the lump of clay from which it is formed. We can distinguish between the thesis that constitution is identity, and the thesis that constitution is not identity. The chief motivation which leads some philosophers to reject the thesis that constitution is not identity is the ‘grounding problem’ for that thesis. (4) Are there, in addition to composite objects, the ‘forms’ of those objects, and if so, what is the relationship between composite objects and their forms? We can distinguish between (at least) two variants of hylomorphism (the thesis that objects have forms), with the main distinction between the two views being whether or not they regard forms as being among the parts of composite objects.

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