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. |
| 19513 | A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose] |
| Full Idea: If you are a coherentist and a contextualist, you'll probably want to hold that how strongly beliefs must cohere with one another in order to count as knowledge (if they are true), or to count as justified, is a contextually variable matter. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1.09) | |
| A reaction: How exciting! He's talking about ME! Context might not only dictate the strength of the coherence, but also the range of beliefs involved. In fact all of Thagard's criteria of coherence may be subject to contextual variation. |
| 19514 | Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose] |
| Full Idea: The great rival to contextualism is classical 'invariantism' - invariantism about the truth-conditions [for knowing], combined with variable standards for warranted assertability. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1.12) | |
| A reaction: That is, I take it, that we might want to assert that someone 'knows' something, when the truth is that they don't. That is, either you know or you don't, but we can bend the rules as to whether we say you know. I take this view to be false. |
| 19515 | We can make contextualism more precise, by specifying the discrimination needed each time [DeRose] |
| Full Idea: We might make the basic contextualist schema more precise ...by saying the change in content will consist in a change in the range of relevant alternatives. Higher standards would discriminate from a broader range of alternatives. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1.14) | |
| A reaction: This would handle the 'fake barn' and 'disguised zebra' examples, by saying lower standards do not expect such discriminations. The zebra case has a lower standard than the barn case (because fake barns are the norm here). |
| 19510 | In some contexts there is little more to knowledge than true belief. [DeRose] |
| Full Idea: I'm inclined to accept that in certain contexts the standards for knowledge are so low that little more than true belief is required. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1.6) | |
| A reaction: DeRose emphasises that 'a little more' is needed, rather than none. The example given is where 'he knew that p' means little more than 'the information that p was available to him' (in a political scandal). |
| 19516 | Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose] |
| Full Idea: While skepticism has drawn much of the attention of contextualists, support for contextualism should also - and perhaps primarily - be looked for in how 'knows' is utilised in non-philosophical conversation. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1016) | |
| A reaction: Contextualists say scepticism is just raising the standards absurdly high. I take it that the ordinary use of the word 'know' is obviously highly contextual, and so varied that I don't see how philosophers could 'regiment' it into invariant form. |
| 19511 | If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose] |
| Full Idea: Maybe contextualism isn't a theory about knowledge at all, but about knowledge attributions. As such, it is not a piece of epistemology at all, but of philosophy of language. | |
| From: Keith DeRose (The Case for Contextualism [2009], 1.7) | |
| A reaction: DeRose takes this view to be wrong. At the very least this will have to include self-attributions, by the supposed knower, because I might say 'I know that p', meaning 'but only in this rather low-standard context'. |
| 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? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |