An 'i' for an i, a Truth for a Truth. Issue 3 (11th April 2018) - Leng, Mary
Abstract: Stewart Shapiro's ante rem structuralism recognizes the structural or 'algebraic' aspects of mathematical practice while still offering a face-value semantics. Fictionalism, as a purely 'algebraic' approach, is held to be at a disadvantage, as compared with Shapiro's structuralism, in not interpreting mathematics at face value. However, the face-value reading of mathematical singular terms has difficulty explaining how we can use such terms to pick out a unique referent in cases where the relevant mathematical structures admit non-trivial automorphisms. Shapiro offers a solution to this difficulty, but his solution, I argue, evens the score between Shapiro's structuralism and fictionalism.