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

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.

Music and Metaphor

Peter Kivy’s contour theory provides a promising explanation of the way we describe instrumental music as expressive of emotions. I argue that if, unlike Kivy, we emphasise the metaphorical character of such descriptions, the contour theory, as a strategy for unpacking such metaphors, can be defended convincingly against common objections. This approach is more satisfactory than those of Scruton and Peacocke, who make much of metaphorical experiences, but leave the underlying metaphors unexplained. Moreover, it gives the contour theory a wider scope than Kivy intended, for even very specific narrative descriptions of music in non-musical terms are perfectly legitimate as long as they are presented, and justified, as metaphors, that is, as mere comparisons, rather than as interpretative claims about the music’s actual contents.

Art, value and function

Is the concept of a work of art an evaluative concept: does its application imply a positive evaluation? I shall discuss this question by considering two opposing attempts at defining art, namely the Institutional Theory and the view that art is a functional concept. I shall argue that the concept of art does not imply an unconditionally positive evaluation, but that art is a prestige concept. Moreover, it will be shown that functional definitions of art are flawed.