75 ideas
| 2930 | The main aim of philosophy must be to determine the order of rank among values [Nietzsche] |
| 20143 | Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche] |
| 23722 | Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche] |
| 4417 | Only that which has no history is definable [Nietzsche] |
| 23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche] |
| 13591 | Quantified modal logic collapses if essence is withdrawn [Quine] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 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] |
| 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] |
| 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] |
| 13590 | Essences can make sense in a particular context or enquiry, as the most basic predicates [Quine] |
| 8483 | Necessity is relative to context; it is what is assumed in an inquiry [Quine] |
| 13589 | Possible worlds are a way to dramatise essentialism, and yet they presuppose essentialism [Quine] |
| 13588 | A rigid designator (for all possible worlds) picks out an object by its essential traits [Quine] |
| 13592 | Beliefs can be ascribed to machines [Quine] |
| 4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
| 23719 | Forgetfulness is a strong positive ability, not mental laziness [Nietzsche] |
| 4420 | There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche] |
| 4414 | Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche] |
| 4419 | People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche] |
| 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] |
| 4411 | It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche] |
| 3793 | We must question the very value of moral values [Nietzsche] |
| 4408 | The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche] |
| 23716 | A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche] |
| 20129 | All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche] |
| 4409 | Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche] |
| 3259 | Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel] |
| 4416 | Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche] |
| 4418 | A masterful and violent person need have nothing to do with contracts [Nietzsche] |
| 4407 | Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche] |
| 4415 | Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche] |
| 23718 | If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche] |
| 23717 | Modern nihilism is now feeling tired of mankind [Nietzsche] |
| 23721 | Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche] |
| 20142 | The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche] |
| 23720 | Punishment makes people harder, more alienated, and hostile [Nietzsche] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 4410 | The truly great haters in world history have always been priests [Nietzsche] |