- 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.
- For the full text, follow this link (Local website only): PDF File1.
- Downloaded from Cambridge Core.
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2022
- Mauve: Text by correspondent(s) or other author(s); © the author(s)