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16949 | Klein summarised geometry as grouped together by transformations [Quine] |
Full Idea: Felix Klein's so-called 'Erlangerprogramm' in geometry involved characterizing the various branches of geometry by what transformations were irrelevant to each. | |
From: Willard Quine (Natural Kinds [1969], p.137) |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |