161 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] |
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] |
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] |
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] |
10073 | There cannot be a set theory which is complete [Smith,P] |
10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
10605 | Two functions are the same if they have the same extension [Smith,P] |
10075 | A 'partial function' maps only some elements to another set [Smith,P] |
10074 | A 'total function' maps every element to one element in another set [Smith,P] |
10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
10613 | No nice theory can define truth for its own language [Smith,P] |
10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
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] |
10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
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] |
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] |
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] |
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] |
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] |
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] |
2260 | If I don't think, there is no reason to think that I exist [Descartes] |
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] |
3623 | The Cogito only works if you already understand what thought and existence are [Mersenne 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] |
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] |
3627 | Dogs can make the same judgements as us about variable things [Gassendi on Descartes] |
2265 | We perceive objects by intellect, not by senses or imagination [Descartes] |
2263 | The wax is not perceived by the senses, but by the mind alone [Descartes] |
2264 | We don't 'see' men in heavy clothes, we judge them to be men [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] |
2296 | If pain is felt in a lost limb, I cannot be certain that a felt pain exists in my real limbs [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] |
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] |
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] |
2286 | The idea of a supremely perfect being is within me, like the basic concepts of mathematics [Descartes] |
2280 | Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
2272 | There must be at least as much in the cause as there is in the effect [Descartes] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
2289 | Nothing apart from God could have essential existence, and such a being must be unique and eternal [Descartes] |
2269 | God the creator is an intelligent, infinite, powerful substance [Descartes] |
2275 | It is self-evident that deception is a natural defect, so God could not be a deceiver [Descartes] |
2287 | Existence and God's essence are inseparable, like a valley and a mountain, or a triangle and its properties [Descartes] |
2274 | The idea of God in my mind is like the mark a craftsman puts on his work [Descartes] |
2268 | One idea leads to another, but there must be an initial idea that contains the reality of all the others [Descartes] |
2288 | I cannot think of a supremely perfect being without the supreme perfection of existence [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] |
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] |
2277 | Since God does not wish to deceive me, my judgement won't make errors if I use it properly [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] |