Abstract
Abstract This chapter is concerned with the dispute in the philosophy of mathematics between mathematical realists (or Platonists) and mathematical nominalists, which has been simmering in the Anglo-American world of philosophy these past fifty or so years. A close approximation to what the terms ‘mathematical realist’ and ‘mathematical nominalist’ mean can be given as follows: a mathematical realist is one who maintains that mathematical objects exist, whereas a mathematical nominalist is one who opposes the realist’s position.1 Thus, there are two types of nominalists: those who deny that there are mathematical objects, and those who adopt the weaker thesis that we lack compelling grounds for believing in the existence of mathematical objects.
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