Single Idea 18832

[catalogued under 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic]

Full Idea

On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result.

Gist of Idea

Mathematical statements and entities that result from an infinite process must lack a truth-value

Source

Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3

Book Reference

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.199


A Reaction

This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent.