Single Idea 10257

[catalogued under 5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens]

Full Idea

In some intuitionist semantics modus ponens is not sanctioned. At any given time there is likely to be a conditional such that it and its antecedent have been proved, but nobody has bothered to prove the consequent.

Gist of Idea

Intuitionism only sanctions modus ponens if all three components are proved

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 6.7)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.207


A Reaction

[He cites Heyting] This is a bit baffling. In what sense can 'it' (i.e. the conditional implication) have been 'proved' if the consequent doesn't immediately follow? Proving both propositions seems to make the conditional redundant.