171 ideas
| 7504 | Modern science comes from Descartes' view that knowledge doesn't need moral purity [Descartes, by Foucault] |
| 1569 | Descartes impoverished the classical idea of logos, and it no longer covered human experience [Roochnik on Descartes] |
| 2248 | Reason says don't assent to uncertain principles, just as much as totally false ones [Descartes] |
| 2857 | Since Plato all philosophers have followed the herd, except Descartes, stuck in superficial reason [Nietzsche on Descartes] |
| 2290 | Once it is clear that there is a God who is no deceiver, I conclude that clear and distinct perceptions must be true [Descartes] |
| 3641 | It is circular to make truth depend on believing God's existence is true [Arnauld on Descartes] |
| 4524 | Descartes is right that in the Christian view only God can guarantee the reliability of senses [Nietzsche on Descartes] |
| 2266 | My general rule is that everything that I perceive clearly and distinctly is true [Descartes] |
| 4301 | Someone may think a thing is 'clear and distinct', but be wrong [Leibniz on Descartes] |
| 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] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 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] |
| 10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
| 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] |
| 2252 | Surely maths is true even if I am dreaming? [Descartes] |
| 2430 | I can learn the concepts of duration and number just from observing my own thoughts [Descartes] |
| 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] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 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] |
| 2297 | If I can separate two things in my understanding, then God can separate them in reality [Descartes] |
| 3628 | Substance cannot be conceived or explained to others [Gassendi on Descartes] |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| 16631 | If we remove surface qualities from wax, we have an extended, flexible, changeable thing [Descartes] |
| 17865 | Descartes gives an essence by an encapsulating formula [Descartes, by Almog] |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| 2301 | We know by thought that what is done cannot be undone [Descartes] |
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| 20190 | Belief is not an intellectual state or act, because propositions are affirmed or denied by the will [Descartes, by Zagzebski] |
| 1585 | Descartes tried to model reason on maths instead of 'logos' [Roochnik on Descartes] |
| 1582 | Labelling slightly doubtful things as false is irrational [Roochnik on Descartes] |
| 2256 | Maybe there is only one certain fact, which is that nothing is certain [Descartes] |
| 2260 | If I don't think, there is no reason to think that I exist [Descartes] |
| 6929 | Modern philosophy set the self-conscious ego in place of God [Descartes, by Feuerbach] |
| 3849 | "I think therefore I am" is the absolute truth of consciousness [Sartre on Descartes] |
| 2258 | I must even exist if I am being deceived by something [Descartes] |
| 2259 | "I am, I exist" is necessarily true every time I utter it or conceive it in my mind [Descartes] |
| 3160 | The Cogito is a transcendental argument, not a piece of a priori knowledge [Rey on Descartes] |
| 6914 | Descartes transformed 'God is thinkable, so he exists' into 'I think, so I exist' [Descartes, by Feuerbach] |
| 4641 | In the Meditations version of the Cogito he says "I am; I exist", which avoids presenting it as an argument [Descartes, by Baggini /Fosl] |
| 1117 | The Cogito proves subjective experience is basic, but makes false claims about the Self [Russell on Descartes] |
| 2873 | Maybe 'I' am not the thinker, but something produced by thought [Nietzsche on Descartes] |
| 1369 | It is a precondition of the use of the word 'I' that I exist [Ayer on Descartes] |
| 5360 | The thing which experiences may be momentary, and change with the next experience [Russell on Descartes] |
| 2870 | 'I think' assumes I exist, that thinking is known and caused, and that I am doing it [Nietzsche on Descartes] |
| 5188 | A thought doesn't imply other thoughts, or enough thoughts to make up a self [Ayer on Descartes] |
| 3623 | The Cogito only works if you already understand what thought and existence are [Mersenne on Descartes] |
| 3624 | That I perform an activity (thinking) doesn't prove what type of thing I am [Hobbes on Descartes] |
| 3120 | Autistic children seem to use the 'I' concept without seeing themselves as thinkers [Segal on Descartes] |
| 4526 | The Cogito assumes a priori the existence of substance, when actually it is a grammatical custom [Nietzsche on Descartes] |
| 5579 | How can we infer that all thinking involves self-consciousness, just from my own case? [Kant on Descartes] |
| 5580 | My self is not an inference from 'I think', but a presupposition of it [Kant on Descartes] |
| 5587 | We cannot give any information a priori about the nature of the 'thing that thinks' [Kant on Descartes] |
| 5588 | The fact that I am a subject is not enough evidence to show that I am a substantial object [Kant on Descartes] |
| 13923 | Descartes' claim to know his existence before his essence is misleading or absurd [Descartes, by Lowe] |
| 6930 | Modern self-consciousness is a doubtful abstraction; only senses and feelings are certain [Feuerbach on Descartes] |
| 2261 | My perceiving of things may be false, but my seeming to perceive them cannot be false [Descartes] |
| 2257 | I myself could be the author of all these self-delusions [Descartes] |
| 2279 | A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes] |
| 6490 | For Descartes, objects have one primary quality, which is geometrical [Descartes, by Robinson,H] |
| 2295 | Why does pain make us sad? [Descartes] |
| 2265 | We perceive objects by intellect, not by senses or imagination [Descartes] |
| 3627 | Dogs can make the same judgements as us about variable things [Gassendi on Descartes] |
| 2264 | We don't 'see' men in heavy clothes, we judge them to be men [Descartes] |
| 2263 | The wax is not perceived by the senses, but by the mind alone [Descartes] |
| 2247 | To achieve good science we must rebuild from the foundations [Descartes] |
| 2255 | Only one certainty is needed for progress (like a lever's fulcrum) [Descartes] |
| 2251 | Even if my body and objects are imaginary, there may be simpler things which are true [Descartes] |
| 6347 | Descartes can't begin again, because sceptics doubt cognitive processes as well as beliefs [Pollock/Cruz on Descartes] |
| 3620 | We correct sense errors with other senses, not intellect [Mersenne on Descartes] |
| 3619 | The senses can only report, so perception errors are in the judgment [Gassendi on Descartes] |
| 2249 | It is prudent never to trust your senses if they have deceived you even once [Descartes] |
| 2296 | If pain is felt in a lost limb, I cannot be certain that a felt pain exists in my real limbs [Descartes] |
| 2253 | God may have created nothing, but made his creation appear to me as it does now [Descartes] |
| 2254 | To achieve full scepticism, I imagine a devil who deceives me about the external world and my own body and senses [Descartes] |
| 2305 | Waking actions are joined by memory to all our other actions, unlike actions of which we dream [Descartes] |
| 2294 | I can only sense an object if it is present, and can't fail to sense it when it is [Descartes] |
| 4862 | Can the pineal gland be moved more slowly or quickly by the mind than by animal spirits? [Spinoza on Descartes] |
| 3850 | We discovers others as well as ourselves in the Cogito [Sartre on Descartes] |
| 2302 | Faculties of the mind aren't parts, as one mind uses them [Descartes] |
| 3151 | Descartes put thought at the centre of the mind problem, but we put sensation [Rey on Descartes] |
| 21800 | Descartes mentions many cognitive faculties, but reduces them to will and intellect [Descartes, by Schmid] |
| 1399 | Imagination and sensation are non-essential to mind [Descartes] |
| 1400 | Some cause must unite the separate temporal sections of a person [Descartes] |
| 1401 | Since I only observe myself to be thinking, I conclude that that is my essence [Descartes] |
| 2299 | I can exist without imagination and sensing, but they can't exist without me [Descartes] |
| 6907 | For Descartes a person's essence is the mind because objects are perceived by mind, not senses [Descartes, by Feuerbach] |
| 2283 | Our 'will' just consists of the feeling that when we are motivated to do something, there are no external pressures [Descartes] |
| 2282 | My capacity to make choices with my free will extends as far as any faculty ever could [Descartes] |
| 2276 | The mind is a non-extended thing which thinks [Descartes] |
| 2298 | Mind is not extended, unlike the body [Descartes] |
| 3423 | Descartes is a substance AND property dualist [Descartes, by Kim] |
| 2303 | The mind is utterly indivisible [Descartes] |
| 6153 | Interaction between mental and physical seems to violate the principle of conservation of energy [Rowlands on Descartes] |
| 3625 | The 'thinking thing' may be the physical basis of the mind [Hobbes on Descartes] |
| 2552 | Knowing different aspects of brain/mind doesn't make them different [Rorty on Descartes] |
| 4305 | Descartes gives no clear criterion for individuating mental substances [Cottingham on Descartes] |
| 4861 | Does Descartes have a clear conception of how mind unites with body? [Spinoza on Descartes] |
| 6540 | Even Descartes may concede that mental supervenes on neuroanatomical [Lycan on Descartes] |
| 7733 | Superman's strength is indubitable, Clark Kent's is doubtful, so they are not the same? [Maslin on Descartes] |
| 5686 | In some thoughts I grasp a subject, but also I will or fear or affirm or deny it [Descartes] |
| 4017 | Descartes created the modern view of rationality, as an internal feature instead of an external vision [Descartes, by Taylor,C] |
| 2284 | I make errors because my will extends beyond my understanding [Descartes] |
| 5685 | True ideas are images, such as of a man, a chimera, or God [Descartes] |
| 3629 | All ideas are adventitious, and come from the senses [Gassendi on Descartes] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 2286 | The idea of a supremely perfect being is within me, like the basic concepts of mathematics [Descartes] |
| 2273 | The ideas of God and of my self are innate in me [Descartes] |
| 2285 | I can think of innumerable shapes I have never experienced [Descartes] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
| 2280 | Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes] |
| 2272 | There must be at least as much in the cause as there is in the effect [Descartes] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 2269 | God the creator is an intelligent, infinite, powerful substance [Descartes] |
| 2289 | Nothing apart from God could have essential existence, and such a being must be unique and eternal [Descartes] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 2275 | It is self-evident that deception is a natural defect, so God could not be a deceiver [Descartes] |
| 2288 | I cannot think of a supremely perfect being without the supreme perfection of existence [Descartes] |
| 2287 | Existence and God's essence are inseparable, like a valley and a mountain, or a triangle and its properties [Descartes] |
| 2268 | One idea leads to another, but there must be an initial idea that contains the reality of all the others [Descartes] |
| 2274 | The idea of God in my mind is like the mark a craftsman puts on his work [Descartes] |
| 3632 | We mustn't worship God as an image because we have no idea of him [Hobbes on Descartes] |
| 3633 | We can never conceive of an infinite being [Gassendi on Descartes] |
| 5036 | Descartes cannot assume that a most perfect being exists without contradictions [Leibniz on Descartes] |
| 3638 | Existence is not a perfection; it is what makes perfection possible [Gassendi on Descartes] |
| 2277 | Since God does not wish to deceive me, my judgement won't make errors if I use it properly [Descartes] |
| 2278 | Error arises because my faculty for judging truth is not infinite [Descartes] |
| 3636 | God didn't give us good judgement even about our own lives [Gassendi on Descartes] |
| 2281 | If we ask whether God's works are perfect, we must not take a narrow viewpoint, but look at the universe as a whole [Descartes] |