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.

中文翻译：

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“ i”代表i，真理代表真理†

摘要

斯图尔特·夏皮罗（Stewart Shapiro）的事前结构主义认识到数学实践的结构或“代数”方面，同时仍提供了面值语义。与夏皮罗的结构主义相比，虚构主义作为一种纯粹的“代数”方法被认为处于劣势，因为它不能以表面价值来解释数学。但是，数学奇异术语的面值读取很难解释在相关数学结构允许非平凡自同构的情况下如何使用此类术语挑选唯一的对象。夏皮罗提供了解决这一难题的方法，但我认为，他的解决方案使夏皮罗的结构主义和虚构主义之间的得分持平。