Single Idea 13673

[catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another.

Gist of Idea

The notion of finitude is actually built into first-order languages


Stewart Shapiro (Foundations without Foundationalism [1991], 9.1)

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.238

A Reaction

Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic.