93 ideas
| 23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
| 3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
| 22864 | Philosophy is the study and criticsm of cultural beliefs, to achieve new possibilities [Dewey] |
| 23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
| 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] |
| 22873 | Liberalism should improve the system, and not just ameliorate it [Dewey] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| 17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
| 20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
| 3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
| 556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
| 563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
| 557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
| 565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
| 9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
| 13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| 11237 | Only universals have essence [Plato, by Politis] |
| 11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
| 22869 | Knowledge is either the product of competent enquiry, or it is meaningless [Dewey] |
| 22867 | The quest for certainty aims for peace, and avoidance of the stress of action [Dewey] |
| 22870 | No belief can be so settled that it is not subject to further inquiry [Dewey] |
| 17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
| 22866 | Mind is never isolated, but only exists in its interactions [Dewey] |
| 1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
| 3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
| 7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
| 2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
| 9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
| 94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
| 17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
| 6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
| 2912 | Plato is boring [Nietzsche on Plato] |
| 22872 | Liberals aim to allow individuals to realise their capacities [Dewey] |
| 22880 | The things in civilisation we prize are the products of other members of our community [Dewey] |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
| 22879 | 'God' is an imaginative unity of ideal values [Dewey] |
| 22877 | We should try attaching the intensity of religious devotion to intelligent social action [Dewey] |
| 22878 | Religions are so shockingly diverse that they have no common element [Dewey] |