102 ideas
| 20262 | Don't use wisdom in order to become clever! [Nietzsche] |
| 20255 | Early 19th century German philosophers enjoyed concepts, rather than scientific explanations [Nietzsche] |
| 20260 | Carlyle spent his life vainly trying to make reason appear romantic [Nietzsche] |
| 20256 | What we think is totally dictated by the language available to express it [Nietzsche] |
| 20265 | The desire for a complete system requires making the weak parts look equal to the rest [Nietzsche] |
| 20380 | Why should truth be omnipotent? It is enough that it is very powerful [Nietzsche] |
| 20235 | Like animals, we seek truth because we want safety [Nietzsche] |
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| 9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
| 9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| 9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
| 9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
| 9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
| 9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
| 9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9393 | A: we may assume any proposition at any stage [Lemmon] |
| 9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
| 9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
| 9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| 9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| 9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
| 9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
| 9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
| 9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
| 9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
| 9537 | Truth-tables are good for showing invalidity [Lemmon] |
| 9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
| 9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
| 9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
| 13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
| 13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
| 13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
| 13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
| 13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
| 13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
| 13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
| 13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
| 13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
| 13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
| 13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 20258 | Most people treat knowledge as a private possession [Nietzsche] |
| 20250 | We may be unable to remember, but we may never actually forget [Nietzsche] |
| 20270 | There is no one scientific method; we must try many approaches, and many emotions [Nietzsche] |
| 20131 | We can cultivate our drives, of anger, pity, curiosity, vanity, like a gardener, with good or bad taste [Nietzsche] |
| 20242 | Things are the boundaries of humanity, so all things must be known, for self-knowledge [Nietzsche] |
| 20249 | Our knowledge of the many drives that constitute us is hopelessly incomplete [Nietzsche] |
| 20231 | People used to think that outcomes were from God, rather than consequences of acts [Nietzsche] |
| 20266 | It is essential that wise people learn to express their wisdom, possibly even as foolishness [Nietzsche] |
| 20251 | Actions done for a purpose are least understood, because we complacently think it's obvious [Nietzsche] |
| 20271 | Beauty in art is the imitation of happiness [Nietzsche] |
| 20230 | The very idea of a critique of morality is regarded as immoral! [Nietzsche] |
| 20234 | Morality prevents us from developing better customs [Nietzsche] |
| 20237 | Moral feelings are entirely different from the moral concepts used to judge actions [Nietzsche] |
| 20238 | Treating morality as feelings is just obeying your ancestors [Nietzsche] |
| 20243 | Human beings are not majestic, either through divine origins, or through grand aims [Nietzsche] |
| 20268 | Most dying people have probably lost more important things than what they are about to lose [Nietzsche] |
| 20252 | Marriage is too serious to be permitted for people in love! [Nietzsche] |
| 20236 | Marriage upholds the idea that love, though a passion, can endure [Nietzsche] |
| 20263 | Fear reveals the natures of other people much more clearly than love does [Nietzsche] |
| 20233 | Punishment has distorted the pure innocence of the contingency of outcomes [Nietzsche] |
| 20248 | People do nothing for their real ego, but only for a phantom ego created by other people [Nietzsche] |
| 20246 | If you feel to others as they feel to themselves, you must hate a self-hater [Nietzsche] |
| 20272 | Honesty is a new young virtue, and we can promote it, or not [Nietzsche] |
| 20240 | The Jews treated great anger as holy, and were in awe of those who expressed it [Nietzsche] |
| 20244 | Christianity replaces rational philosophical virtues with great passions focused on God [Nietzsche] |
| 20274 | The cardinal virtues want us to be honest, brave, magnanimous and polite [Nietzsche] |
| 20257 | Cool courage and feverish bravery have one name, but are two very different virtues [Nietzsche] |
| 20259 | Teach youth to respect people who differ with them, not people who agree with them [Nietzsche] |
| 20267 | Seeing duty as a burden makes it a bit cruel, and it can thus never become a habit [Nietzsche] |
| 20275 | Most people think they are already complete, but we can cultivate ourselves [Nietzsche] |
| 20229 | No authority ever willingly accepts criticism [Nietzsche] |
| 20254 | People govern for the pleasure of it, or just to avoid being governed [Nietzsche] |
| 20273 | The French Revolution gave trusting Europe the false delusion of instant recovery [Nietzsche] |
| 20232 | Get rid of the idea of punishment! It is a noxious weed! [Nietzsche] |
| 20253 | Modern wars arise from the study of history [Nietzsche] |
| 20261 | History does not concern what really happened, but supposed events, which have all the influence [Nietzsche] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 20241 | Enquirers think finding our origin is salvation, but it turns out to be dull [Nietzsche] |
| 20245 | Christianity hoped for a short cut to perfection, that skipped the hard labour of morality [Nietzsche] |
| 20247 | Christianity was successful because of its heathen rituals [Nietzsche] |
| 20269 | 'I believe because it is absurd' - but how about 'I believe because I am absurd' [Nietzsche] |
| 20264 | The easy and graceful aspects of a person are called 'soul', and inner awkwardness is called 'soulless' [Nietzsche] |