Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

Schroeder, S. ORCID: https://orcid.org/0000-0002-4480-6458 (2011) Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics. In: 34th International Wittgenstein Symposium, 7 - 13 of August 2011, Kirchberg am Wechsel, pp. 459-471. doi: 10.1515/9783110329018.459

Abstract/Summary

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.