David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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British Journal for the History of Philosophy 19 (5):935-961 (2011)
The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved
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References found in this work BETA
Richard Arthur (2001). Leibniz on Infinite Number, Infinite Wholes, and the Whole World. The Leibniz Review 11:103-116.
O. Bradley Bassler (1998). Leibniz on the Indefinite as Infinite. Review of Metaphysics 51 (4):849 - 874.
Gregory Brown (2005). Leibniz's Mathematical Argument Against a Soul of the World. British Journal for the History of Philosophy 13 (3):449 – 488.
Gregory Brown (2000). Leibniz on Wholes, Unities, and Infinite Number. The Leibniz Review 10:21-51.
Hidé Ishiguro (1990). Leibniz's Philosophy of Logic and Language. Cambridge University Press.
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