95 ideas
| 7846 | Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson] |
| 20107 | How many mediocre thinkers are occupied with influential problems! [Nietzsche] |
| 20352 | Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson] |
| 20379 | Reason is just another organic drive, developing late, and fighting for equality [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] |
| 20123 | First see nature as non-human, then fit ourselves into this view of nature [Nietzsche] |
| 15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
| 15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
| 15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| 15436 | Universals are meant to give an account of resemblance [Lewis] |
| 15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
| 15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
| 15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
| 15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
| 15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
| 15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
| 15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
| 15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
| 15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| 20376 | We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche] |
| 15450 | Maybe abstraction is just mereological subtraction [Lewis] |
| 15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |
| 22501 | Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot] |
| 22500 | Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche] |
| 20128 | Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter] |
| 22503 | Nietzsche could only revalue human values for a different species [Nietzsche, by Foot] |
| 8041 | The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche] |
| 20135 | Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter] |
| 20353 | The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson] |
| 20113 | Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche] |
| 22475 | Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot] |
| 22476 | Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot] |
| 20104 | Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche] |
| 7847 | Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson] |
| 9782 | Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek] |
| 20102 | Flight from boredom leads to art [Nietzsche] |
| 20106 | Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski] |
| 20124 | Reliving life countless times - this gives the value back to life which religion took away [Nietzsche] |
| 20367 | Individual development is more important than the state, but a community is necessary [Nietzsche] |
| 20371 | Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson] |
| 20108 | Every culture loses its identity and power if it lacks a major myth [Nietzsche] |