8 ideas
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
Full Idea: Philosophy's role consists in informing mathematics of its own speculative grandeur. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.11) | |
A reaction: Revealing the grandeur of something sounds more like a rhetorical than a rational exercise. How would you reveal the grandeur of a sunset to someone? |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
Full Idea: Only in mathematics can one unequivocally maintain that if thought can formulate a problem, it can and will solve it, regardless of how long it takes. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.17) | |
A reaction: I hope this includes proving the Continuum Hypothesis, and Goldbach's Conjecture. It doesn't seem quite true, but it shows why philosophers of a rationalist persuasion are drawn to mathematics. |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
Full Idea: Mathematics teaches us that there is no reason whatsoever to confne thinking within the ambit of finitude. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.19) | |
A reaction: This would perhaps make Cantor the greatest thinker who ever lived. It is an exhilarating idea, but we should ward the reader against romping of into unrestrained philosophical thought about infinities. You may be jumping without your Cantorian parachute. |
9809 | Mathematics inscribes being as such [Badiou] |
Full Idea: Mathematics inscribes being as such. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.12) | |
A reaction: I don't pretend to understand that, but there is something about the purity and certainty of mathematics that makes us feel we are grappling with the core of existence. Perhaps. The same might be said of stubbing your toe on a bedpost. |
9811 | It is of the essence of being to appear [Badiou] |
Full Idea: It is of the essence of being to appear. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.16) | |
A reaction: Nice slogan. In my humble opinion 'continental' philosophy is well worth reading because, despite the fluffy rhetoric and the shameless egotism and the desire to shock the bourgeoisie, they occasionally make wonderfully thought-provoking remarks. |
10650 | In the military, persons are parts of parts of large units, but not parts of those large units [Rescher] |
Full Idea: In military usage, persons can be parts of small units, and small units parts of large ones; but persons are never parts of large units. | |
From: Nicholas Rescher (Axioms for the Part Relation [1955]), quoted by Achille Varzi - Mereology 2.1 | |
A reaction: This much-cited objection to the transitivity of the 'part' relation seems very odd. There could hardly be an army or a regiment if there weren't soldiers to make up parts of it. |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
Full Idea: Like every great poet, Mallarmé was engaged in a tacit rivalry with mathematics. | |
From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.20) | |
A reaction: I love these French pronouncements! Would Mallarmé have agreed? If poetry and mathematics are the poles, where is philosophy to be found? |