A note on Leibniz' argument against infinite wholes
Résumé
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'.
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