14 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. |
| 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. |
| 19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
| Full Idea: I will define 'quus' by x-quus-y = x + y, if x, y < 57, and otherwise it equals 5. Who is to say that this is not the function I previously meant by '+'? | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Kripke's famous example, to illustrate the big new scepticism introduced by Wittgenstein's questions about the rationality of following a rule. I suspect that you have to delve into psychology to understand rule-following, rather than logic. |
| 19271 | No rule can be fully explained [Kripke] |
| Full Idea: Every explanation of a rule could conceivably be misunderstood. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 3) | |
| A reaction: This is Kripke's summary of what he takes to be Wittgenstein's scepticism about rules. |
| 7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
| Full Idea: Quine and Kripke's Wittgenstein attempt to argue that there are no facts about meaning, that the notion of meaning, as Kripke puts it, 'vanishes into thin air'. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Alexander Miller - Philosophy of Language Pref | |
| A reaction: A tempting solution to the problem. If, though, it is possible for someone to say something that is self-evidently meaningless, or to accuse someone of speaking (deep down) without meaning, then that needs explaining. |
| 19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
| Full Idea: What can there be in my mind that I make use of when I follow a general rule to add in the future? It seems that the entire idea of meaning vanishes into thin air. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Introspection probably isn't the best way to investigate the phenomenon of meaning. Indeed it seems rather old-fashioned and Cartesian. Kripke says, though, that seeking 'tacit' rules is even worse [end of note 22]. |
| 11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
| Full Idea: If we take account of the fact that a speaker is in a community, then we must adopt an assertability-conditions semantics (based on what is legitimately assertible), and reject truth-conditional semantics (based on correspondence to the facts). | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: [Part of Hanna's full summary of Kripke's argument] This sounds wrong to me. There are conditions where it is agreed that a lie should be told. Two people can be guilty of the same malapropism. |
| 11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
| Full Idea: Kripke argues that the 'rule-following paradox' is essential to the more controversial private language argument, and introduces a radically new form of scepticism. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: It certainly seems that Kripke is right to emphasise the separateness of the two, as the paradox is quite persuasive, but the private language argument seems less so. |
| 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? |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |