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4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
Full Idea: A weaker form of relativism holds that developments in logic, in maths and in geometry have shown how a relativised notion of the a priori is possible. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: This is non-Euclidean geometry, and multiple formalisations of logic. Personally I don't believe it. You can expand these subjects, and pursue whimsical speculations, but I have faith in their stable natural core. Neo-Platonism. |
2301 | We know by thought that what is done cannot be undone [Descartes] |
Full Idea: Some ideas belong exclusively to the mind, such as perceiving that what has been done cannot be undone, and everything else that is known by the light of nature. | |
From: René Descartes (Meditations [1641], §6.82) |
3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
Full Idea: You can't reason 'I know the triangle is right-angled, but I doubt Pythagoras' Theorem, therefore it does not belong to the essence of right-angled triangles that the square on the hypotenuse is equal to the sum of the squares on the other two sides'. | |
From: comment on René Descartes (Meditations [1641], §6.78) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 202 |