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The Leibniz Review

Volume 21, December 2011

Richard T. W. Arthur
Pages 91-115

Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances

This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this depends on a generalized notion of aggregation, according to which a thing may be an aggregate of its constituents if every one of its actual parts presupposes such constituents, but is not composed from them. One of the premises of this argument is the reality of bodies. If this premise is denied, Leibniz’s argument for the infinitude of substances, and even of their plurality, cannot go through.

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