11 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. |
| 18969 | How do you distinguish three beliefs from four beliefs or two beliefs? [Quine] |
| Full Idea: Suppose I say that I have given up precisely three beliefs since lunch. An over-coarse individuation could reduce the number to two, and an over-fine one could raise it to four. | |
| From: Willard Quine (Propositional Objects [1965], p.144) | |
| A reaction: Obviously if you ask how many beliefs I hold, it would be crazy to give a precise answer. But if I search for my cat, I give up my belief that it is in the kitchen, in the lounge and in the bathroom. That's precise enough to be three beliefs, I think. |
| 18967 | A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine] |
| Full Idea: A 'proposition' is the meaning of a sentence. More precisely, since propositions are supposed to be true or false once and for all, it is the meaning of an eternal sentence. More precisely still, it is the 'cognitive' meaning, involving truth, not poetry. | |
| From: Willard Quine (Propositional Objects [1965], p.139) | |
| A reaction: Quine defines this in order to attack it. I equate a proposition with a thought, and take a sentence to be an attempt to express a proposition. I have no idea why they are supposed to be 'timeless'. Philosophers have some very odd ideas. |
| 18968 | The problem with propositions is their individuation. When do two sentences express one proposition? [Quine] |
| Full Idea: The trouble with propositions, as cognitive meanings of eternal sentences, is individuation. Given two eternal sentences, themselves visibly different linguistically, it is not sufficiently clear under when to say that they mean the same proposition. | |
| From: Willard Quine (Propositional Objects [1965], p.140) | |
| A reaction: If a group of people agree that two sentences mean the same thing, which happens all the time, I don't see what gives Quine the right to have a philosophical moan about some dubious activity called 'individuation'. |
| 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? |
| 18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |
| Full Idea: Unless we are prepared to believe that absolute position makes sense, the very idea of a point as an entity in its own right must be rejected as not merely mysterious but absurd. | |
| From: Willard Quine (Propositional Objects [1965], p.149) | |
| A reaction: The fact that without absolute position we can only think of 'points' as relative to a conceptual grid doesn't stop the grid from picking out actual locations in space, as shown by latitude and longitude. |