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I find the notion of fictionalism in mathematics utterly perplexing. From what I understand of it, it seems that fictionalism is the thesis that mathematics is a created fiction, and that there is no mathematical truth separate from the relevant fiction. On this view, it seems, mathematical statements -- such as 2 + 2 = 4 -- are analogous to statements like “Humbert Humbert is infatuated by Dolores Haze.” But how can this be right? Does this mean I can construct a mathematical fiction in which, e.g., 2 + 2 = 5? On the fictionalist account, I can’t see why we ought to prefer, say, a mathematics in which 2 + 2 = 4 over one where 2 + 2 = 5 unless the former captures some inherent truth that the latter misses.

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