### Single Idea 10703

#### [catalogued under 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions]

Full Idea

A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism.

Gist of Idea

Supposing axioms (rather than accepting them) give truths, but they are conditional

Source

Michael Potter (Set Theory and Its Philosophy [2004], 01.1)

Book Reference

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.8

A Reaction

Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth).