157 ideas
| 3879 | Philosophy aims to provide a theory of everything [Scruton] |
| 12170 | Amusement rests on superiority, or relief, or incongruity [Scruton] |
| 12173 | The central object of amusement is the human [Scruton] |
| 12169 | Since only men laugh, it seems to be an attribute of reason [Scruton] |
| 12172 | Objects of amusement do not have to be real [Scruton] |
| 3891 | If p entails q, then p is sufficient for q, and q is necessary for p [Scruton] |
| 8988 | Two marxist ideas have dominated in France: base and superstructure, and ideology [Scruton] |
| 8987 | On the surface of deconstructive writing, technicalities float and then drift away [Scruton] |
| 8992 | Deconstruction is the last spasm of romanticism, now become hopeless and destructive [Scruton] |
| 18543 | Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton] |
| 3894 | We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton] |
| 3883 | A true proposition is consistent with every other true proposition [Scruton] |
| 18542 | Defining truth presupposes that there can be a true definition [Scruton] |
| 3884 | The pragmatist does not really have a theory of truth [Scruton] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
| 3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
| 3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
| 3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
| 3897 | Epistemology is about the justification of belief, not the definition of knowledge [Scruton] |
| 4266 | Having beliefs involves recognition, expectation and surprise [Scruton] |
| 4265 | If an animal has beliefs, that implies not only that it can make mistakes, but that it can learn from them [Scruton] |
| 3881 | In the Cogito argument consciousness develops into self-consciousness [Scruton] |
| 3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
| 4264 | Perception (which involves an assessment) is a higher state than sensation [Scruton] |
| 3901 | Touch only seems to reveal primary qualities [Scruton] |
| 3885 | We only conceive of primary qualities as attached to secondary qualities [Scruton] |
| 3910 | If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton] |
| 3899 | The representational theory says perceptual states are intentional states [Scruton] |
| 3898 | My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton] |
| 3880 | Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton] |
| 3878 | Why should you believe someone who says there are no truths? [Scruton] |
| 4271 | There is consciousness whenever behaviour must be explained in terms of mental activity [Scruton] |
| 4272 | Our concept of a person is derived from Roman law [Scruton] |
| 3892 | Every event having a cause, and every event being determined by its cause, are not the same [Scruton] |
| 3911 | The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton] |
| 4267 | Conditioning may change behaviour without changing the mind [Scruton] |
| 4269 | An emotion is a motive which is also a feeling [Scruton] |
| 12174 | Only rational beings are attentive without motive or concern [Scruton] |
| 4270 | Do we use reason to distinguish people from animals, or use that difference to define reason? [Scruton] |
| 5636 | Cartesian 'ideas' confuse concepts and propositions [Scruton] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
| 3882 | Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton] |
| 12156 | Aesthetics has risen and fallen with Romanticism [Scruton] |
| 12158 | Aesthetic experience informs the world with the values of the observer [Scruton] |
| 18550 | Art gives us imaginary worlds which we can view impartially [Scruton] |
| 18546 | The pleasure taken in beauty also aims at understanding and valuing [Scruton] |
| 12163 | Literary meaning emerges in comparisons, and tradition shows which comparisons are relevant [Scruton] |
| 18544 | Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton] |
| 18553 | Beauty shows us what we should want in order to achieve human fulfilment [Scruton] |
| 18556 | Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton] |
| 18548 | Natural beauty reassures us that the world is where we belong [Scruton] |
| 12165 | Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton] |
| 18551 | Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton] |
| 12167 | Reference without predication is the characteristic of expression [Scruton] |
| 12162 | In literature, word replacement changes literary meaning [Scruton] |
| 12166 | If music refers to love, it contains no predication, so it is expression, not language [Scruton] |
| 12168 | Music is not representational, since thoughts about a subject are never essential to it [Scruton] |
| 12159 | Without intentions we can't perceive sculpture, but that is not the whole story [Scruton] |
| 12160 | In aesthetic interest, even what is true is treated as though it were not [Scruton] |
| 12164 | Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton] |
| 12161 | We can be objective about conventions, but love of art is needed to understand its traditions [Scruton] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 4284 | All moral life depends ultimately on piety, which is our recognition of our own dependence [Scruton] |
| 18541 | Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton] |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| 4273 | Kant's Moral Law is the rules rational beings would accept when trying to live by agreement [Scruton] |
| 3896 | Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton] |
| 4274 | The modern virtues are courage, prudence, wisdom, temperance, justice, charity and loyalty [Scruton] |
| 4286 | Only just people will drop their own self-interests when faced with an impartial verdict [Scruton] |
| 4283 | Sympathy can undermine the moral order just as much as crime does [Scruton] |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| 3886 | Membership is the greatest source of obligation [Scruton] |
| 4290 | That which can only be done by a callous person, ought not to be done [Scruton] |
| 4285 | As soon as we drop self-interest and judge impartially, we find ourselves agreeing about conflicts [Scruton] |
| 3895 | The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton] |
| 4280 | Utilitarianism is wrong precisely because it can't distinguish animals from people [Scruton] |
| 4287 | Utilitarianism merely guides us (by means of sympathy) when the moral law is silent [Scruton] |
| 4282 | Morality is not a sort of calculation, it is what sets the limits to when calculation is appropriate [Scruton] |
| 4281 | Utilitarianism says we can't blame Stalin yet, but such a theory is a sick joke [Scruton] |
| 5660 | Allegiance is prior to the recognition of individual rights [Scruton] |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| 8989 | The benefits of social freedom outweigh the loneliness, doubt and alienation it brings [Scruton] |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| 8990 | So-called 'liberation' is the enemy of freedom, destroying the very structures that are needed [Scruton] |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| 5653 | A right is a power which is enforced in the name of justice [Scruton] |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
| 18554 | Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton] |
| 4268 | Animals command our sympathy and moral concern initially because of their intentionality [Scruton] |
| 4291 | Letting your dog kill wild rats, and keeping rats for your dog to kill, are very different [Scruton] |
| 4263 | Many of the stranger forms of life (e.g. worms) interest us only as a species, not as individuals [Scruton] |
| 4276 | An animal has individuality if it is nameable, and advanced animals can respond to their name [Scruton] |
| 4277 | I may avoid stepping on a spider or flower, but fellow-feeling makes me protect a rabbit [Scruton] |
| 4278 | Lucky animals are eaten by large predators, the less lucky starve, and worst is death by small predators [Scruton] |
| 4279 | We can easily remove the risk of suffering from an animal's life, but we shouldn't do it [Scruton] |
| 4289 | Sheep and cattle live comfortable lives, and die an enviably easy death [Scruton] |
| 4292 | Concern for one animal may harm the species, if the individual is part of a bigger problem [Scruton] |
| 4294 | Animals are outside the community of rights, but we still have duties towards them [Scruton] |
| 4295 | We favour our own animals over foreign ones because we see them as fellow citizens [Scruton] |
| 4296 | Brutal animal sports are banned because they harm the personality of the watcher [Scruton] |
| 4288 | Many breeds of animals have needs which our own ancestors planted in them [Scruton] |
| 4293 | Introducing a natural means of controlling animal population may not be very compassionate [Scruton] |
| 3890 | 'Cause' used to just mean any valid explanation [Scruton] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 3904 | Measuring space requires no movement while I do it [Scruton] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 3905 | 'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton] |