212 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
7504 | Modern science comes from Descartes' view that knowledge doesn't need moral purity [Descartes, by Foucault] |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
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] |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
2857 | Since Plato all philosophers have followed the herd, except Descartes, stuck in superficial reason [Nietzsche on Descartes] |
8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
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] |
13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
13421 | 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock] |
13422 | 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock] |
13355 | 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock] |
13350 | 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock] |
13351 | 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock] |
13356 | The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock] |
13352 | 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock] |
13353 | 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock] |
13354 | 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock] |
13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
13846 | A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock] |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
13346 | Truth is the basic notion in classical logic [Bostock] |
13545 | Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock] |
13822 | Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock] |
13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock] |
13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
13800 | |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock] |
13803 | If we are to express that there at least two things, we need identity [Bostock] |
13799 | The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock] |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
13818 | If we allow empty domains, we must allow empty names [Bostock] |
13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
13757 | Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock] |
13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
13760 | A sequent calculus is good for comparing proof systems [Bostock] |
13364 | Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG] |
13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
13541 | For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock] |
13542 | A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock] |
13540 | A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock] |
13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
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] |
13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
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] |
13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
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] |
13847 | If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock] |
13820 | The idea that anything which can be proved is necessary has a problem with empty names [Bostock] |
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] |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
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] |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
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] |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
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] |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
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] |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
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] |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
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] |
13363 | A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock] |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
2280 | Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes] |
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
2272 | There must be at least as much in the cause as there is in the effect [Descartes] |
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] |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
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] |