42 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? |
13736 | Quinean metaphysics just lists the beings, which is a domain with no internal structure [Schaffer,J on Quine] |
Full Idea: The Quinean task in metaphysics is to say what exists. What exists forms the domain of quantification. The domain is a set (or class, or plurality) - it has no internal structure. In other words, the Quinean task is to list the beings. | |
From: comment on Willard Quine (works [1961]) by Jonathan Schaffer - On What Grounds What 1.1 | |
A reaction: I really warm to this thesis. The Quinean version is what you get when you think that logic is the best tool for explicating metaphysics. Schaffer goes on to say that the only real aim for Quine is the cardinality of what exists! |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA] |
Full Idea: Quine has showed us how set theory - now recognised to be positively awash in Platonistic metaphysics - can and should be prevented from infecting logic proper. | |
From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Intro |
10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
Full Idea: Quine suggests that V = L be accepted in set theory because it makes for a cleaner theory, even though most set theorists are skeptical of V = L. | |
From: report of Willard Quine (works [1961]) by Stewart Shapiro - Philosophy of Mathematics Ch.1 | |
A reaction: Shapiro cites it as a case of a philosopher trying to make recommendations to mathematicians. Maddy supports Quine. |
3336 | Two things can never entail three things [Quine, by Benardete,JA] |
Full Idea: Two things can never entail three things. | |
From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.17 |
8453 | If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine] |
Full Idea: Since one wants to say that real numbers exist and yet one cannot name each of them, it is not unreasonable to relinquish the connection between naming an object and making an existence claim about it. | |
From: Willard Quine (works [1961]), quoted by Alex Orenstein - W.V. Quine Ch.2 | |
A reaction: One could say that same about people, such as 'the most recent citizen of Brazil'. Some sort of successful reference seems to be needed, such as 'the next prime beyond the biggest so far found'. Depends what your predicate is going to be. |
10311 | No sense can be made of quantification into opaque contexts [Quine, by Hale] |
Full Idea: Quine says that no good sense can be made of quantification into opaque contexts. | |
From: report of Willard Quine (works [1961]) by Bob Hale - Abstract Objects Ch.2 | |
A reaction: This is because poor old Quine was trapped in a world of language, and had lost touch with reality. I can quantify over the things you are thinking about, as long as you are thinking about things that can be quantified over. |
10538 | Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett] |
Full Idea: Quine even asserts that where we have no infinite domains, quantification can be eliminated in favour of finite disjunction and conjunction. | |
From: report of Willard Quine (works [1961]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
A reaction: Thus ∃x is expressed as 'this or this or this...', and ∀ is expressed as 'this and this and this...' Dummett raises an eyebrow, but it sounds OK to me. |
10793 | Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)] |
Full Idea: Quine at first regarded substitutional quantification as incoherent, behind which there lurked use-mention confusions, but has over the years, given his nominalist dispositions, come to notice its appeal. | |
From: report of Willard Quine (works [1961]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.166 |
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. |
8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
Full Idea: Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics. | |
From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
A reaction: Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism. |
8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
Full Idea: Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit | |
From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
A reaction: (See Idea 8454 for the categories of numbers). This is a problem for Dummett. |
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. |
10667 | A logically perfect language could express all truths, so all truths must be logically expressible [Quine, by Hossack] |
Full Idea: Quine's test of ontological commitment says that anything that can be said truly at all must be capable of being said in a logically perfect language, so there must be a paraphrase of every truth into the language of logic. | |
From: report of Willard Quine (works [1961]) by Keith Hossack - Plurals and Complexes 2 | |
A reaction: A very nice statement of the Quinean view, much more persuasive than other statements I have encountered. I am suddenly almost converted to a doctrine I have hitherto despised. Isn't philosophy wonderful? |
16021 | Quine says we can expand predicates easily (ideology), but not names (ontology) [Quine, by Noonan] |
Full Idea: The highly intuitive methodological programme enunciated by Quine says that as our knowledge expands we should unhesitatingly expand our ideology, our stock of predicables, but should be much more wary about ontology, the name variables. | |
From: report of Willard Quine (works [1961]) by Harold Noonan - Identity §3 | |
A reaction: I suddenly embrace this as a crucial truth. This distinction allows you to expand on truths without expanding on reality. I would add that it is also crucial to distinguish properties from predicates. A new predicate isn't a new property. |
3325 | For Quine everything exists theoretically, as reference, predication and quantification [Quine, by Benardete,JA] |
Full Idea: Theoretical entities (which is everything, according to Quine) are postulated by us in a threefold fashion as an object (1) to which we refer, (2) of which we predicate, and (3) over which we quantify. | |
From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.12 |
8534 | Quine says the predicate of a true statement has no ontological implications [Quine, by Armstrong] |
Full Idea: Quine's doctrine is that the predicate of a true statement carries no ontological implications. | |
From: report of Willard Quine (works [1961]) by David M. Armstrong - Properties §1 | |
A reaction: Quine is ontologically committed to the subject of the statement (an object). The predicate seems to be an inseparable part of that object. Quine is, of course, a holist, so ontological commitment isn't judged in single statements. |
10295 | Quine suggests that properties can be replaced with extensional entities like sets [Quine, by Shapiro] |
Full Idea: Quine doubts the existence of properties, and, trying to be helpful, suggests that variables ranging over properties be replaced with variables ranging over respectable extensional entities like sets, so we can 'identify' a property with a singleton set. | |
From: report of Willard Quine (works [1961]) by Stewart Shapiro - Higher-Order Logic 2.1 | |
A reaction: This strikes me as a classic modern heresy, a slippery slope that loses all grip on what a property is, replacing it with entities that mean nothing, but make the logic work. |
3322 | Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic [Quine, by Benardete,JA] |
Full Idea: Quine assures us that if the specific mission of second-order logic is quantifying over properties, the task can readily be performed by first-order predicate logic, as in (Ex) x is a property, and (y) y has x. | |
From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
6078 | Quine brought classes into semantics to get rid of properties [Quine, by McGinn] |
Full Idea: Quine brought classes into semantics in order to oust properties. | |
From: report of Willard Quine (works [1961]) by Colin McGinn - Logical Properties Ch.3 | |
A reaction: Quine's view has always struck me as odd, as I don't see how you can decide what set something belongs to if you haven't already decided its properties. But then I take it that nature informs you of most properties, and set membership is not arbitrary. |
8479 | Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things' [Quine, by Orenstein] |
Full Idea: Quine proposes that 'red is a colour' does not require analysis, such as 'there is an x which is the property of being red and it is a colour' which needs an ontology of properties. We can just say that all red things are coloured things. | |
From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.6 | |
A reaction: The question of the ontology of properties is here approached, in twentieth century style, as the question 'what is the logical form of property attribution sentences?' Quine's version deals in sets of prior objects, rather than abstract entities. |
3751 | Universals are acceptable if they are needed to make an accepted theory true [Quine, by Jacquette] |
Full Idea: Abstract entities (universals) are admitted to an ontology by Quine's criterion if they must be supposed to exist (or subsist) in order to make the propositions of an accepted theory true. | |
From: report of Willard Quine (works [1961]) by Dale Jacquette - Abstract Entity p.3 |
7970 | Quine is committed to sets, but is more a Class Nominalist than a Platonist [Quine, by Macdonald,C] |
Full Idea: Armstrong dubs Quine an 'Ostrich Nominalist' (what problem??), but Quine calls himself a Platonist, because he is committed to classes or sets as well as particulars. He is not an extreme nominalist, and might best be called a Class Nominalist. | |
From: report of Willard Quine (works [1961], Ch.6 n15) by Cynthia Macdonald - Varieties of Things | |
A reaction: For someone as ontologically austere as Quine to show 'commitment' to sets deserves some recognition. If he wants to be a Platonist, I say that's fine. What on earth is a set, apart from its members? |
15783 | Definite descriptions can't unambiguously pick out an object which doesn't exist [Lycan on Quine] |
Full Idea: Meinong characteristically refers to his Objects using definite descriptions, such as 'the golden mountain'. But on his view there are many golden mountains, with different features. How can 'the golden mountain' then succeed in denoting a single Object? | |
From: comment on Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01 | |
A reaction: Use of definite descriptions doesn't seem obligatory in this situation. 'Think of a golden mountain' - 'which one?' - 'never mind which one!'. |
15782 | Quine wants identity and individuation-conditions for possibilia [Quine, by Lycan] |
Full Idea: Quine notoriously demands identity and individuation-conditions for mere possibilia. | |
From: report of Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01 | |
A reaction: Demanding individuation before speaking of anything strikes me as dubious. 'Whoever did this should own up'. 'There must be something we can do'. Obviously you need some idea of what you are talking about - but not much. |
2796 | For Quine the only way to know a necessity is empirically [Quine, by Dancy,J] |
Full Idea: Quine argues that no necessity can be known other than empirically. | |
From: report of Willard Quine (works [1961]) by Jonathan Dancy - Intro to Contemporary Epistemology 14.6 |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
9342 | Understanding needs a priori commitment [Horwich] |
Full Idea: Understanding is itself based on a priori commitment. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |
8450 | Quine's empiricism is based on whole theoretical systems, not on single mental events [Quine, by Orenstein] |
Full Idea: Traditional empiricism takes impressions, ideas or sense data as the basic unit of empirical thought, but Quine takes account of the theoretical as well as the observational; the unit of empirical significance is whole systems of belief. | |
From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.1 | |
A reaction: This invites either the question of what components make up the whole systems, or (alternatively) what sort of mental events decide to accept a system as a whole. Should Quine revert either to traditional empiricism, or to rationalism? |
3868 | To proclaim cultural relativism is to thereby rise above it [Quine, by Newton-Smith] |
Full Idea: Truth, says the cultural relativist, is culture-bound. But if it were, then he, within his own culture, ought to see his own culture-bound truth as absolute. He cannot proclaim cultural relativism without rising above it. | |
From: report of Willard Quine (works [1961]) by W.H. Newton-Smith - The Rationality of Science VII.10 |
4713 | For Quine, theories are instruments used to make predictions about observations [Quine, by O'Grady] |
Full Idea: Quine's epistemological position is instrumentalist. Our theories are instruments we use to make predictions about observations. | |
From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3 | |
A reaction: This is the pragmatist in Quine. It fits the evolutionary view to think that the bottom line is prediction. My theory about the Pelopponesian War seems an exception. |
4712 | Quine says there is no matter of fact about reference - it is 'inscrutable' [Quine, by O'Grady] |
Full Idea: Quine holds the doctrine of the 'inscrutability of reference', which means there is no fact of the matter about reference. | |
From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3 | |
A reaction: Presumably reference depends on conventions like pointing, or the functioning of words like "that", or the ambiguities of descriptions. If you can't define it, it doesn't exist? I don't believe him. |
7330 | The principle of charity only applies to the logical constants [Quine, by Miller,A] |
Full Idea: Quine takes to the principle of charity to apply only to the translation of the logical constants. | |
From: report of Willard Quine (works [1961]) by Alexander Miller - Philosophy of Language 8.7 | |
A reaction: Given how weird some people's view of the world seems to be, this very cautious approach has an interesting rival appeal to Davidson't much more charitable view, that people mostly speak truth. It depends whether you are discussing lunch or the gods. |
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? |
17862 | Essence gives an illusion of understanding [Quine, by Almog] |
Full Idea: Essence engenders a mere illusion of understanding | |
From: report of Willard Quine (works [1961]) by Joseph Almog - Nature Without Essence Intro | |
A reaction: [Almog quotes Quine, but doesn't give a reference] This is roughly the same as Popper's criticism of essentialism. |