Talk:Structuralism (philosophy of mathematics)

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Ante rem

I have added the "Editorializing" tag to the ante rem paragraph of the article's introduction. This may not be the right tag, only I could not find a better. I do not suspect that the writer's actual intent was to editorialize, but still: maybe the article would benefit by a clearer explanation of why Platonism should be a form of structuralism at all, for it is not clear to me that it is.

Would a Thomist agree that Platonism faced "usual problems of explaining the interaction between abstract ... structures and flesh-and-blood" people? Would not a Thomist prefer the word "form" to the word "structure"? Since Thomism is and has long been a major school of philosophy, can the words the article presently uses comport with a neutral point of view?

I do not have the answers to these questions, but am a little uneasy of the article's current approach. I am not sure that either Platonism or its sister, Thomism, is in fact structuralist. I suspect that the article's writer is himself a structuralist, which understandably is what would motivate him to write the article in the first place. Not a professional philosopher, I do not know how to improve the article, but maybe someone who does know how will do it. Tbtkorg (talk) 00:41, 24 August 2012 (UTC)[reply]

Varieties

The attribution of thinkers and labels to the ante-rem, in-re and post-rem categories seems confusing or mistaken at some points. The Ante-rem description seems to agree with the literature, but the other two don't.

Shapiro says ^[1] on p.271 that "Benacerraf (1965) adopts an eliminative, in re version of structuralism...". So Benacerraf can't be purely allocated to the Post-rem category. If his position shifted, this should be acknowledged.</li?
Concerning Hellman's position, Shapiro (op. cit.) says (p274) "Call this modal eliminative structuralism. Hellman (1989) carries out a programme like this...". Then Hellman ^[2] says about his own modal structuralism (MS): "with regard to the in re/ante rem distinction, literally it doesn't apply to MS". So Hellman can't be purely allocated to the In-re category, especially when the article applies the label "eliminative" to the Post-rem category.

RMGunton (talk) 23:14, 23 November 2020 (UTC)[reply]

References

^ Shapiro, S. (2000) Thinking About Mathematics. Oxford
^ Hellman, G. (2001) Three varieties of mathematical structuralism. Philosophia Mathematica 9, 184-211

[1] Shapiro, S. (2000) Thinking About Mathematics. Oxford

[2] Hellman, G. (2001) Three varieties of mathematical structuralism. Philosophia Mathematica 9, 184-211

[1]

[2]