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(2015) Essays on Gödel's reception of Leibniz, Husserl and Brouwer, Dordrecht, Springer.
Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of Cantorian set theory; (3) This refutation does not cast doubt on the part-whole axiom. Hence, should there be an obstacle to Gödel's wish to integrate Cantorian set theory within Leibniz' philosophy, it will not be this famous argument of Leibniz'.
Publication details
DOI: 10.1007/978-3-319-10031-9_2
Full citation:
Van Atten, M. (2015). A note on Leibniz's argument against infinite wholes, in Essays on Gödel's reception of Leibniz, Husserl and Brouwer, Dordrecht, Springer, pp. 23-32.
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