100 ideas
| 7834 | Great philosophies are confessions by the author, growing out of moral intentions [Nietzsche] |
| 7080 | Metaphysics divided the old unified Greek world into two [Nietzsche, by Critchley] |
| 11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
| 11090 | Why do we want truth, rather than falsehood or ignorance? The value of truth is a problem [Nietzsche] |
| 9535 | 'Contradictory' propositions always differ in truth-value [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] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [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] |
| 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] |
| 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] |
| 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] |
| 7079 | Nietzsche resists nihilism through new values, for a world of becoming, without worship [Nietzsche, by Critchley] |
| 11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
| 11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
| 11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
| 11096 | Discourse generally departmentalizes itself to some degree [Quine] |
| 11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
| 11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
| 11097 | Red is the largest red thing in the universe [Quine] |
| 17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
| 11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
| 2878 | We see an approximation of a tree, not the full detail [Nietzsche] |
| 20140 | We shouldn't object to a false judgement, if it enhances and preserves life [Nietzsche] |
| 2877 | Morality becomes a problem when we compare many moralities [Nietzsche] |
| 20355 | The ranking of a person's innermost drives reveals their true nature [Nietzsche] |
| 2291 | A thought comes when 'it' wants, not when 'I' want [Nietzsche] |
| 2871 | Wanting 'freedom of will' is wanting to pull oneself into existence out of the swamp of nothingness by one's own hair [Nietzsche] |
| 20381 | It is psychology which reveals the basic problems [Nietzsche] |
| 11104 | Concepts are language [Quine] |
| 11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |
| 2860 | The most boring and dangerous of all errors is Plato's invention of pure spirit and goodness [Nietzsche] |
| 1568 | Nietzsche felt that Plato's views downgraded the human body and its brevity of life [Nietzsche, by Roochnik] |
| 2883 | Noble people see themselves as the determiners of values [Nietzsche] |
| 23440 | Nietzsche's judgement of actions by psychology instead of outcome was poisonous [Foot on Nietzsche] |
| 2875 | That which is done out of love always takes place beyond good and evil [Nietzsche] |
| 2868 | Nature is totally indifferent, so you should try to be different from it, not live by it [Nietzsche] |
| 2882 | Morality originally judged people, and actions only later on [Nietzsche] |
| 2872 | In the earliest phase of human history only consequences mattered [Nietzsche] |
| 2885 | The noble soul has reverence for itself [Nietzsche] |
| 20134 | Moralities extravagantly address themselves to 'all', by falsely generalising [Nietzsche] |
| 2881 | Virtue has been greatly harmed by the boringness of its advocates [Nietzsche] |
| 20382 | The four virtues are courage, insight, sympathy, solitude [Nietzsche] |
| 2879 | In ancient Rome pity was considered neither good nor bad [Nietzsche] |
| 2859 | The idea of the categorical imperative is just that we should all be very obedient [Nietzsche] |
| 2884 | The morality of slaves is the morality of utility [Nietzsche] |
| 2880 | The greatest possibilities in man are still unexhausted [Nietzsche] |
| 2876 | The thought of suicide is a great reassurance on bad nights [Nietzsche] |
| 7078 | The freedom of the subject means the collapse of moral certainty [Nietzsche, by Critchley] |
| 6869 | Nietzsche thinks the human condition is to overcome and remake itself [Nietzsche, by Ansell Pearson] |
| 2874 | Man is the animal whose nature has not yet been fixed [Nietzsche] |
| 20137 | The great person engages wholly with life, and is happy to endlessly relive the life they created [Nietzsche] |
| 20139 | Only aristocratic societies can elevate the human species [Nietzsche] |
| 20373 | A healthy aristocracy has no qualms about using multitudes of men as instruments [Nietzsche] |
| 22394 | Democracy diminishes mankind, making them mediocre and lowering their value [Nietzsche] |
| 2867 | Christianity is Platonism for the people [Nietzsche] |