A note on Leibniz' argument against infinite wholes

Mark van Atten (1)

1 SND - Sciences, Normes, Décision

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'.

Mots clés: philosophy of mathematics; Leibniz Gottfried Wilhelm 1646-1716

Domaines: Histoire, Philosophie et Sociologie des sciences; Mathématiques générales [math.GM]

Mark van Atten. A note on Leibniz' argument against infinite wholes. British Journal for the History of Philosophy, 2011, 19 (1), pp.121-129. ⟨10.1080/09608788.2011.533015⟩. ⟨halshs-00775348⟩