94 ideas
12644 | Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor] |
12633 | Definitions often give necessary but not sufficient conditions for an extension [Fodor] |
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] |
12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
12648 | Names in thought afford a primitive way to bring John before the mind [Fodor] |
12650 | 'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor] |
12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
12653 | There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor] |
12651 | Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor] |
12628 | Knowing that must come before knowing how [Fodor] |
12625 | Pragmatism is the worst idea ever [Fodor] |
12636 | Mental states have causal powers [Fodor] |
12661 | The different types of resemblance don't resemble one another [Fodor] |
12632 | In the Representational view, concepts play the key linking role [Fodor] |
12624 | Only the labels of nodes have semantic content in connectionism, and they play no role [Fodor] |
12640 | Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor] |
12641 | Connectionism gives no account of how constituents make complex concepts [Fodor] |
12643 | Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor] |
12647 | Mental representations name things in the world, but also files in our memory [Fodor] |
12649 | We think in file names [Fodor] |
12655 | Frame Problem: how to eliminate most beliefs as irrelevant, without searching them? [Fodor] |
12630 | If concept content is reference, then my Twin and I are referring to the same stuff [Fodor] |
12658 | Nobody knows how concepts are acquired [Fodor] |
12662 | We have an innate capacity to form a concept, once we have grasped the stereotype [Fodor] |
12635 | Having a concept isn't a pragmatic matter, but being able to think about the concept [Fodor] |
12652 | Concepts have two sides; they are files that face thought, and also face subject-matter [Fodor] |
12626 | Cartesians put concept individuation before concept possession [Fodor] |
12637 | Frege's puzzles suggest to many that concepts have sense as well as reference [Fodor] |
12638 | If concepts have sense, we can't see the connection to their causal powers [Fodor] |
12639 | Belief in 'senses' may explain intentionality, but not mental processes [Fodor] |
12654 | You can't think 'brown dog' without thinking 'brown' and 'dog' [Fodor] |
12659 | Maybe stereotypes are a stage in concept acquisition (rather than a by-product) [Fodor] |
12660 | One stereotype might be a paradigm for two difference concepts [Fodor] |
12629 | For the referential view of thought, the content of a concept is just its reference [Fodor] |
12631 | Compositionality requires that concepts be atomic [Fodor] |
12657 | Abstractionism claims that instances provide criteria for what is shared [Fodor] |
12634 | 'Inferential-role semantics' says meaning is determined by role in inference [Fodor] |
12642 | Co-referring terms differ if they have different causal powers [Fodor] |
12663 | We refer to individuals and to properties, and we use singular terms and predicates [Fodor] |
12645 | Semantics (esp. referential semantics) allows inferences from utterances to the world [Fodor] |
12646 | Semantics relates to the world, so it is never just psychological [Fodor] |
12627 | Before you can plan action, you must decide on the truth of your estimate of success [Fodor] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |