Abstract: Radical conventionalism treats every necessary truth as a linguistic convention, akin to the statement ’There are seven days in a week’. Wittgenstein's endorsement of this view was a result of his belief that nothing can explain the fact of the acceptance of necessary truths. There could not be necessary truths being a consequence of human nature, which have not yet been recognized, or those which would never be recognized as such. This view stands in contrast to moderate conventionalism, which is powerless to explain the necessity of logical consequence.

Keywords: conventionalism intuitionism, mathematical proof, Necessity, Putnam, Wittgenstein,