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? |
17699 | Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel] |
Full Idea: A variable in a proposition of logic ....has the status of a mere auxiliary notion that is really inappropriate to the constant, 'eternal' essence of the propositions of logic. | |
From: Moses Schönfinkel (Building Blocks of Mathematical Logic [1924], §1) | |
A reaction: He presumably thinks that what the variables stand for (and he mentions 'argument places' and 'operators') will be included in the essence. My attention was caught by the thought that he takes logic to have an essence. |
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. |
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? |