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9226
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If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
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Full Idea:
Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects.
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From:
Hartry Field (Recent Debates on the A Priori [2005], 7)
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A reaction:
For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect.
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22200
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If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
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Full Idea:
When you have eliminated the impossible, whatever remains, however improbable, must be the truth.
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From:
Arthur Conan Doyle (The Sign of Four [1890], Ch. 6)
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A reaction:
A beautiful statement, by Sherlock Holmes, of Eliminative Induction. It is obviously not true, of course. Many options may still face you after you have eliminated what is actually impossible.
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