I consider different versions of a structuralist view of mathematical objects, according to which characteristic mathematical objects have no more of a 'nature' than is given by the basic relations of a structure in which they reside. My own version of such a view is non-eliminative in the sense that it does not lead to a programme for eliminating reference to mathematical objects. I reply to criticisms of non-eliminative structuralism recently advanced by Keränen and Hellman. In replying to the former, (...) I rely on a distinction between 'basic' and 'constructed' structures. A conclusion is that ideas from the metaphysical tradition can be misleading when applied to the objects of modern mathematics. (shrink)

This paper argues that Dummett’s interpretation of the relationship between Frege’s anti-psychologism and Wittgenstein’s doctrine that meaning is use results in a misreading of Frege. It points out that anti-mentalism is a form of anti-psychologism, but that mentalism is not the only version of psycholgism. Thus, while Frege and Wittgenstein are united in their opposition to mentalism, they are not equally opposed to psychologism, and from Frege’s point of view, the doctrine that meaning is use could also imply a version (...) of psychologism. It then offers a realist and externalist reading of Frege’s understanding of concepts, which is more in line with what Frege intended by anti-psychologism. (shrink)