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. |
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. |
9545 | Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara] |
Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'. | |
From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3 | |
A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject. |
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. |
13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
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? |