23 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? |
| 13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
| Full Idea: On the now dominant Quinean view, metaphysics is about what there is (such as properties, meanings and numbers). I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. | |
| From: Jonathan Schaffer (On What Grounds What [2009], Intro) | |
| A reaction: I find that an enormously helpful distinction, and support the Aristotelian view. Schaffer's general line is that what exists is fairly uncontroversial and dull, but the interesting truths about the world emerge when we grasp its structure. |
| 13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
| Full Idea: Traditional metaphysics is so tightly woven into the fabric of philosophy that it cannot be torn out without the whole tapestry unravelling. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) | |
| A reaction: I often wonder why the opponents of metaphysics still continue to do philosophy. I don't see how you address questions of ethics, or philosophy of mathematics (etc) without coming up against highly general and abstract over-questions. |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| Full Idea: Occam's Razor should only be understood to concern substances: do not multiply basic entities without necessity. There is no problem with the multiplication of derivative entities - they are an 'ontological free lunch'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The phrase 'ontological free lunch' comes from Armstrong. This is probably what Occam meant. A few extra specks of dust, or even a few more numbers (thank you, Cantor!) don't seem to challenge the principle. |
| 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. |
| 13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
| Full Idea: We can automatically infer 'there are roses' from 'there are red roses' (with no shift in the meaning of 'roses'). Likewise one can automatically infer 'there are numbers' from 'there are prime numbers'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: He similarly observes that the atheist's 'God is a fictional character' implies 'there are fictional characters'. Schaffer is not committing to a strong platonism with his claim - merely that the existence of numbers is hardly worth disputing. |
| 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. |
| 13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
| Full Idea: Grounding should be taken as primitive, as per the neo-Aristotelian approach. Grounding is an unanalyzable but needed notion - it is the primitive structuring conception of metaphysics. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) | |
| A reaction: [he cites K.Fine 1991] I find that this simple claim clarifies the discussions of Kit Fine, where you are not always quite sure what the game is. I agree fully with it. It makes metaphysics interesting, where cataloguing entities is boring. |
| 13747 | Supervenience is just modal correlation [Schaffer,J] |
| Full Idea: Supervenience is mere modal correlation. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| Full Idea: My preferred view is that there is only one fundamental entity - the whole concrete cosmos - from which all else exists by abstraction. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: This looks to me like weak anti-realism - that there are no natural 'joints' in nature - but I don't think Schaffer intends that. I take the joints to be fundamentals, which necessitates that the cosmos has parts. His 'abstraction' is clearly a process. |
| 13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
| Full Idea: Maybe the categories are determined by the different grounding relations, ..so that categories just are the ways things depend on substances. ...Categories are places in the dependence ordering. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 1.3) |
| 16065 | Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman] |
| Full Idea: Some insist that constitution is identity, on the grounds that distinct material objects cannot occupy the same place at the same time. Others argue that constitution is not identity, since the statue and its material differ in important respects. | |
| From: Ryan Wasserman (Material Constitution [2009], Intro) | |
| A reaction: The 'important respects' seem to concern possibilities rather than actualities, which is suspicious. It is misleading to think we are dealing with two things and their relation here. Objects must have constitutions; constitutions make objects. |
| 16067 | Constitution is not identity, because it is an asymmetric dependence relation [Wasserman] |
| Full Idea: For those for whom 'constitution is not identity' (the 'constitution view'), constitution is said to be an asymmetric relation, and also a dependence relation (unlike identity). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: It seems obvious that constitution is not identity, because there is more to a thing's identity than its mere constitution. But this idea makes it sound as if constitution has nothing to do with identity (chalk and cheese), and that can't be right. |
| 16069 | There are three main objections to seeing constitution as different from identity [Wasserman] |
| Full Idea: The three most common objections to the constitution view are the Impenetrability Objection (two things in one place?), the Extensionality Objection (mereology says wholes are just their parts), and the Grounding Objection (their ground is the same). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: [summary] He adds a fourth, that if two things can be in one place, why stop at two? [Among defenders of the Constitution View he lists Baker, Fine, Forbes, Koslicki, Kripke, Lowe, Oderberg, N.Salmon, Shoemaker, Simons and Yablo.] |
| 16068 | The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman] |
| Full Idea: We do not calculate the weight of something by summing the weights of all its parts - weigh bricks and the molecules of a wall and you will get the wrong result, since you have weighed some parts more than once. | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: In fact the complete inventory of the parts of a thing is irrelevant to almost anything we would like to know about the thing. The parts must be counted at some 'level' of division into parts. An element can belong to many different sets. |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| Full Idea: I am happy to accept universal composition, on the grounds that there are heaps, piles etc with no integral unity, and that arbitrary composites are no less unified than heaps. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1 n11) | |
| A reaction: The metaphysical focus is then placed on what constitutes 'integral unity', which is precisely the question which most interested Aristotle. Clearly if there is nothing more to an entity than its components, scattering them isn't destruction. |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| Full Idea: The notion of grounding my capture a crucial mereological distinction (missing from classical mereology) between an integrated whole with genuine unity, and a mere aggregate. x is an integrated whole if it grounds its proper parts. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 3.1) | |
| A reaction: That gives a nice theoretical notion, but if you remove each of the proper parts, does x remain? Is it a bare particular? I take it that it will have to be an abstract principle, the one Aristotle was aiming at with his notion of 'form'. Schaffer agrees. |
| 16074 | Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman] |
| Full Idea: If the relative identity theorist denies transitivity (to deal with the Ship of Theseus, for example), this would make us suspect that relativised identity relations are not identity relations, since transitivity seems central to identity. | |
| From: Ryan Wasserman (Material Constitution [2009], 6) | |
| A reaction: The problem here, I think, focuses on the meaning of the word 'same'. One change of plank leaves you with the same ship, but that is not transitive. If 'identical' is too pure to give the meaning of 'the same' it's not much use in discussing the world. |
| 13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
| Full Idea: One motivation for dialetheism is the view that there are impossible worlds. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) |
| 13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
| Full Idea: A 'Moorean certainty' is when something is more credible than any philosopher's argument to the contrary. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The reference is to G.E. Moore's famous claim that the existence of his hand is more certain than standard sceptical arguments. It sounds empiricist, but they might be parallel rational truths, of basic logic or arithmetic. |
| 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? |