Infinitesimals, nations, and persons: In memoriam D.A.P. 11 December 1942 − 1 January 2017

Journal article

I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Excluded Middle for statements of identity. Adherents of Smooth Infinitesimal Analysis deny that Excluded Middle holds for statements saying that an infinitesimal is identical with zero. Derek Parfit contended that, in certain sci-fi scenarios, the Law does not hold for some statements of personal identity. He also claimed that it fails for the statement ‘England in 1065 was the same nation as England in 1067’. I argue that none of these cases poses a serious threat to Excluded Middle. My analysis of the last example casts doubt on the principle of the Determinacy of Distinctness. While David Wiggins’s ‘conceptualist realism’ provides a metaphysics which can dispense with that principle, it leaves no house-room for infinitesimals.

Authors: Rumfitt, I

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Philosophy
• Volume: 94
• Issue: 4
• Pages: 513-528
• Publication date: 2019-10-09
• Acceptance date: 2019-01-11
• DOI: 10.1017/S003181911900010X
• EISSN: 1469-817X
• ISSN: 0031-8191