Combining Texts

All the ideas for 'works', 'Recent Debates on the A Priori' and 'Mathematics and Indispensibility'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

9226	If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
	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.
	From: Hartry Field (Recent Debates on the A Priori [2005], 7)
	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.

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

9558	All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
	Full Idea: If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.
	From: Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
	A reaction: This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.

29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy

16713	Philosophers are the forefathers of heretics [Tertullian]
	Full Idea: Philosophers are the forefathers of heretics.
	From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2

29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism

6610	I believe because it is absurd [Tertullian]
	Full Idea: I believe because it is absurd ('Credo quia absurdum est').
	From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
	A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.