43 ideas
| 18543 | Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton] |
| Full Idea: The judgement of beauty makes a claim about its object, and can be supported by reasons. But the reasons do not compel the judgement and can be rejected without contradiction. So are they reasons or aren't they? | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: I suspect that what he is really referring to is evidence rather than reasons. |
| 18542 | Defining truth presupposes that there can be a true definition [Scruton] |
| Full Idea: How can you define truth, without already assuming the distinction between a true definition and a false one? | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: Don't say we have to accept truth as yet another primitive! Philosophers are out of business if all the basic concepts are primitive. The axiomatic approach to truth is an alternative - by specifying how the primitive should be used. |
| 22317 | Truth does not admit of more and less [Frege] |
| Full Idea: What is only half true is untrue. Truth does not admit of more and less. | |
| From: Gottlob Frege (works [1890], CP 353), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 48 'Truth' | |
| A reaction: What about a measurement which is accurate to three decimal places? Maybe being 'close to' the truth is not the same as being 'more' true. The truth about a distance between two points is unknowable? |
| 13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
| Full Idea: Frege did not think of himself as working with sets. | |
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: One can hardly blame him, given that set theory was only just being invented. |
| 16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
| Full Idea: Frege regarded the null set as an indefensible entity from the point of view of iterative set theory. It collects nothing. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 | |
| A reaction: The null set defines the possibility that something could be collected. At the very least, it introduces curly brackets into the language. |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
| Full Idea: Contrary to Dedekind's anti-realism, Frege proposed a realist definition of a set as the extension of a predicate (or concept, or function). | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.13 |
| 9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
| Full Idea: Frege frequently expressed a contempt for language. | |
| From: report of Gottlob Frege (works [1890], p.228) by Michael Dummett - Frege's Distinction of Sense and Reference p.228 | |
| A reaction: This strikes me as exactly the right attitude for a logician to have. Russell seems to have agreed. Attitudes to vagueness are the test case. Over-ambitious modern logicians dream of dealing with vagueness. Forget it. Stick to your last. |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
| Full Idea: Frege thinks there is a single right deductive order of the truths. This is not an epistemic order, but a logical order, and it is our job to arrange our beliefs in this order if we can make it out. | |
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Frege's dream rests on the belief that there exists a huge set of logical truths. Pluralism, conventionalism, constructivism etc. about logic would challenge this dream. I think the defence of Frege must rest on Russellian rooting of logic in nature. |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
| Full Idea: For Frege, a predicate does not refer to the objects of which it is true, but to the function that maps these objects onto the True and False; ..a predicate is a name for this function. | |
| From: report of Gottlob Frege (works [1890]) by Colin McGinn - Logical Properties Ch.3 | |
| A reaction: McGinn says this is close to the intuitive sense of a property. Perhaps 'predicates are what make objects the things they are?' |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
| Full Idea: The whole point of Frege's functional account of predication lies in its allowing us to dispense with all properties across the board. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
| Full Idea: Frege persistently neglected the question of the domain of quantification, which proved in the end to be fatal. | |
| From: comment on Gottlob Frege (works [1890]) by Michael Dummett - Frege philosophy of mathematics Ch.16 | |
| A reaction: The 'fatality' refers to Russell's paradox, and the fact that not all concepts have extensions. Common sense now says that this is catastrophic. A domain of quantification is a topic of conversation, which is basic to all language. Cf. Idea 9874. |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| Full Idea: In Frege's view axioms are basic truth, and basic truths do not need proof. Basic truths can be (justifiably) recognised as true by understanding their content. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: This is the underpinning of the rationalism in Frege's philosophy. |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
| Full Idea: There is a suspicion that Frege's definition of 5 (as the set of all sets with 5 members) may be infected with circularity, …and how can we be sure on a priori grounds that 4 and 5 are not both empty sets, and hence identical? | |
| From: comment on Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.14 |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge] |
| Full Idea: Frege saw arithmetical judgements as resting on a foundation of logical principles, and the discovery of this foundation as a discovery of the nature and structure of the justification of arithmetical truths and judgments. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations Intro | |
| A reaction: Burge's point is that the logic justifies the arithmetic, as well as underpinning it. |
| 8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend] |
| Full Idea: After the problem with Russell's paradox, Frege did not publish for fourteen years, and he then tried to re-found arithmetic in Euclidean geometry, rather than in logic. | |
| From: report of Gottlob Frege (works [1890], 3.4) by Michčle Friend - Introducing the Philosophy of Mathematics 3.4 | |
| A reaction: I take it that his new road would have led him to modern Structuralism, so I think he was probably on the right lines. Unfortunately Frege had already done enough for one good lifetime. |
| 5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
| Full Idea: Frege's quantificational logic vindicates Kant's insight that existence is not a predicate and leads to fallacies when treated as one; and we might also say, despite Hegel, that there is no concept of being. | |
| From: report of Gottlob Frege (works [1890]) by Roger Scruton - Short History of Modern Philosophy Ch.17 | |
| A reaction: I notice that Colin McGinn has questioned the value of quantificational logic. It is difficult to assert that 'there is no concept of x', if several people have written large books about it. |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
| Full Idea: It was Frege who first made identity a logical notion, enshrining it above all in the formula (x) x=x. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 16885 | To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge] |
| Full Idea: Frege famously realised that understanding a thought requires understanding its inferential connections to other thoughts. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: If true, this is probably our greatest advance in grasping the concept of 'understanding' since Aristotle - but is it true? It is a striking and interesting idea, and central to the importance of Frege in modern analytic philosophy. |
| 16887 | Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge] |
| Full Idea: Frege's terms that translate 'self-evident' usually make no explicit reference to actual minds. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: This follows the distinction in Aquinas, between things that are intrinsically self-evident, and things that are self-evident to particular people. God, presumably, knows all of the former. |
| 16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
| Full Idea: Generality for Frege is simply universal quantification; what makes a truth apriori is that its ultimate grounds are universally quantified. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 |
| 16882 | The building blocks contain the whole contents of a discipline [Frege] |
| Full Idea: The ultimate building blocks of a discipline contain, as it were in a nutshell, its whole contents. | |
| From: Gottlob Frege (works [1890]), quoted by Tyler Burge - Frege on Knowing the Foundations 1 | |
| A reaction: [Burge gives a reference] I would describe this nutshell as the 'essence' of the subject, and it fits Aristotle's concept of an essence perfectly. Does it fit biology or sociology, in the way it might fit maths or logic? Think of DNA or cells in biology. |
| 5816 | Frege said concepts were abstract entities, not mental entities [Frege, by Putnam] |
| Full Idea: Frege, rebelling against 'psychologism', identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |
| From: report of Gottlob Frege (works [1890]) by Hilary Putnam - Meaning and Reference p.119 | |
| A reaction: This, of course, assumes that 'abstract' entities and 'mental' entities are quite distinct things. A concept is presumably a mental item which has content, and the word 'concept' is simply ambiguous, between the container and the contents. |
| 7307 | A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A] |
| Full Idea: For Frege, a thought is not something psychological or subjective; rather, it is objective in the sense that it specifies some condition in the world the obtaining of which is necessary and sufficient for the truth of the sentence that expresses it. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.2 | |
| A reaction: It is worth emphasising Russell's anti-Berkeley point about 'ideas', that the idea is in the mind, but its contents are in the world. Since the contents are what matter, this endorses Frege, and also points towards modern externalism. |
| 7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A] |
| Full Idea: Frege held that "and" and "but" have the same 'sense' but different 'tones' (note: they have the same truth tables); the sense of an expression is what a sentence strictly and literally means, stripped of its tone. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.6 | |
| A reaction: It seems important when studying Frege to remember what has been stripped out. In "he is a genius and he plays football", if you substitute 'but' for 'and', the new version says (literally?) something very distinctive about football. |
| 7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A] |
| Full Idea: Frege's introduction of 'sense' was motivated by the desire to solve three problems: the problem of bearerless names, the problem of substitution in belief contexts, and the problem of informativeness. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.9 | |
| A reaction: A proposal which solves three problems sounds pretty good! These three problems can be used to test the counter-proposals of Russell and Kripke. |
| 7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner] |
| Full Idea: 'It is raining or it is not raining' appears to true because of the general principle 'p or not-p', so it is analytic; but this does not fit Kant's idea of an analytic truth, because it is not obvious that it has a subject concept or a predicate concept. | |
| From: report of Gottlob Frege (works [1890]) by Joan Weiner - Frege Ch.2 | |
| A reaction: The general progress of logic seems to be a widening out to embrace problem sentences. However, see Idea 7315 for the next problem that arises with analyticity. All this culminates in Quine's attack (e.g. Idea 1624). |
| 7316 | Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A] |
| Full Idea: Frege (according to Quine) characterises analytic truths as those that can be demonstrated or proved using only logical laws and definitions as premises. | |
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 4.2 | |
| A reaction: This is the big shift away from the Kantian version (predicate contained in the subject) towards a modern version, perhaps fixed by a truth table giving true for all values. |
| 18546 | The pleasure taken in beauty also aims at understanding and valuing [Scruton] |
| Full Idea: Like the pleasure in friendship, the pleasure in beauty is curious: it aims to understand its object, and to value what it finds. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: At least he is trying to pin down the way in which aesthetic pleasure is phenomenologically different from other kinds of pleasure. |
| 18550 | Art gives us imaginary worlds which we can view impartially [Scruton] |
| Full Idea: One aim of art is to present imaginary worlds, towards which we can adopt, as part of the integral aesthetic attitude, a posture of impartial concern. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 5) | |
| A reaction: It connects to the pleasure of watching people when they don't know they are being watched (such as watching the street from a restaurant window). Scruton's suggestion makes art resemble examples in philosophy. Cf the Frege-Geach problem in ethics. |
| 18544 | Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton] |
| Full Idea: Maybe we can understand the 'beauty' of a building better if we describe it in another and less loaded way, as a form of fittingness or harmony. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: Almost everyone accepts the word 'beauty' for some things, such as a beautiful face, or goal, or steak. I remember a female interviewer writing that, reluctantly, the only appropriate word she could find for Nureyev's face was 'beautiful'. |
| 18553 | Beauty shows us what we should want in order to achieve human fulfilment [Scruton] |
| Full Idea: Beauty speaks to us of human fulfilment: not of things that we want, but of things that we ought to want, because human nature requires them. Such, at least, is my belief. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 7) | |
| A reaction: I'm not sure how this works with a beautiful natural landscape. And what should I see that I ought to desire after viewing a great Rembrandt self-portrait? That I don't want to end up looking as bleak as that? Hm. Lofty words. |
| 18556 | Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton] |
| Full Idea: Beauty is rationally founded; it challenges us to find meaning in its object, to make critical comparisons, and to examine our own lives and emotions in the light of what we find. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 9) | |
| A reaction: This is the Kantian tradition, and I'm not finding it very persuasive. It seems to place the value of beauty in what we do with it afterwards, and he seems to make beauty a necessary stepping stone to virtue. I see beauty as more sui generis. |
| 18548 | Natural beauty reassures us that the world is where we belong [Scruton] |
| Full Idea: The experience of natural beauty is not a sense of 'how nice!' or 'how pleasant!' It contains a reassurance that this world is a right and fitting place to be - a home in which our human powers and prospects find confirmation. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 2) | |
| A reaction: To call it a 'reassurance' and 'confirmation' sounds like theism, anthropomorphism, or the pathetic fallacy. That said, this is certainly a heart-warming idea, and hence must contain a grain of truth. |
| 18551 | Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton] |
| Full Idea: The Croce model is of an inarticulate inner state (an 'intuition') becoming articulate and conscious through artistic expression. The rival model is fitting thing together so as to create links which resonate in the audience's feelings. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 5) | |
| A reaction: The first model tells you nothing about how the artist imagines the audience reacting. The second model tells you nothing about what matters personally to the artist. A good theory must do both! |
| 18541 | Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton] |
| Full Idea: The status of beauty as an ultimate value is questionable, in the way that the status of truth and goodness are not. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 1) | |
| A reaction: We suspect that a love of beauty may be a bit parochial, where it is hard to conceive of living creatures anywhere in the cosmos who don't value the other two. |
| 18554 | Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton] |
| Full Idea: The condemnation of prostitution was not just puritan bigotry; it was a recognition of a profound truth, that you and your body are not two things but one, and by selling the body you harden your soul. | |
| From: Roger Scruton (Beauty: a very short introduction [2011], 7) | |
| A reaction: No one, I imagine, who condones or even enthuses about prostitution would hope that their own daughter followed the profession, so there is something wrong with it. But must an enthusiastic and cheerful prostitute necessarily have a hard soul? |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |
| Full Idea: Frege put forward an ontological argument for the existence of numbers. | |
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.4 |