205 ideas
| 7504 | Modern science comes from Descartes' view that knowledge doesn't need moral purity [Descartes, by Foucault] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
| 4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 4222 | If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe] |
| 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] |
| 4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
| 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] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 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] |
| 4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
| 4202 | Change can be of composition (the component parts), or quality (properties), or substance [Lowe] |
| 4201 | Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG] |
| 4219 | Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe] |
| 4221 | Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe] |
| 4220 | Maybe an event is the exemplification of a property at a time [Lowe] |
| 4225 | Events are changes in the properties of or relations between things [Lowe] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 4196 | The main categories of existence are either universal and particular, or abstract and concrete [Lowe] |
| 4234 | Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe] |
| 4235 | Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe] |
| 4236 | Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe] |
| 4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
| 4232 | Nominalists believe that only particulars exist [Lowe] |
| 4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
| 4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
| 4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
| 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] |
| 4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
| 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] |
| 4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe] |
| 4198 | If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe] |
| 4199 | A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe] |
| 4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
| 4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
| 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] |
| 4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
| 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] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 2279 | A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 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] |
| 4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
| 4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe] |
| 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] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 4238 | The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe] |
| 4237 | Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe] |
| 2280 | Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes] |
| 4210 | If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe] |
| 4215 | It seems proper to say that only substances (rather than events) have causal powers [Lowe] |
| 4209 | The theories of fact causation and event causation are both worth serious consideration [Lowe] |
| 4211 | Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe] |
| 2272 | There must be at least as much in the cause as there is in the effect [Descartes] |
| 4213 | Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe] |
| 4212 | Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe] |
| 14581 | The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum] |
| 4208 | 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe] |
| 4224 | If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe] |
| 4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
| 4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |
| 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] |
| 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] |
| 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] |
| 3636 | God didn't give us good judgement even about our own lives [Gassendi on Descartes] |
| 2278 | Error arises because my faculty for judging truth is not infinite [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] |