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SYNTHESE
2008

Categories for the working mathematician: making the impossible possible

13 years 3 months ago
Categories for the working mathematician: making the impossible possible
This paper discusses the notion of necessity in the light of results from contemporary mathematical practice. Two descriptions of necessity are considered. According to the first, necessarily true statements are true because they describe `unchangeable properties of unchangeable objects'. The result that I present is argued to provide a counterexample to this description, as it concerns a case where objects are moved from one category to another in order to change the properties of these objects. The second description concerns necessary `structural properties'. Although I grant that mathematical statements could be considered as necessarily true in this sense, I question whether this justifies the claim that mathematics as a whole is necessary. Keywords Philosophy of mathematical practice
Jessica Carter
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where SYNTHESE
Authors Jessica Carter
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