An 'i' for an i, a Truth for a Truth. Issue 3 (11th April 2018)

• Record Type: Journal Article
• Authors: Leng, Mary
• Is Part Of: Philosophia Mathematica. Volume 28:Issue 3(2020)
• Page Start: 347
• Page End: 359
• Publication Date: 2018-04-11
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nky005
• Languages: English
• ISSNs: 0031-8019

Abstract

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.