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Full Idea
If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation.
Gist of Idea
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying
Source
Penelope Maddy (Defending the Axioms [2011], 3.3)
Book Ref
Maddy,Penelope: 'Defending the Axioms' [OUP 2013], p.99
A Reaction
I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics.
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| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
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| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
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