91 ideas
13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
19079 | For idealists reality is like a collection of beliefs, so truths and truthmakers are not distinct [Young,JO] |
19076 | Coherence theories differ over the coherence relation, and over the set of proposition with which to cohere [Young,JO] |
19077 | Two propositions could be consistent with your set, but inconsistent with one another [Young,JO] |
19078 | Coherence with actual beliefs, or our best beliefs, or ultimate ideal beliefs? [Young,JO] |
19084 | Coherent truth is not with an arbitrary set of beliefs, but with a set which people actually do believe [Young,JO] |
19083 | How do you identify the best coherence set; and aren't there truths which don't cohere? [Young,JO] |
19075 | Deflationary theories reject analysis of truth in terms of truth-conditions [Young,JO] |
9535 | 'Contradictory' propositions always differ in truth-value [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] |
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] |
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] |
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] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [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] |
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] |
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] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9393 | A: we may assume any proposition at any stage [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] |
13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
13393 | Any entity has the unique property of being that specific entity [Jubien] |
13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
13391 | Modality concerns relations among platonic properties [Jubien] |
13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
19074 | Are truth-condtions other propositions (coherence) or features of the world (correspondence)? [Young,JO] |
19082 | Coherence truth suggests truth-condtions are assertion-conditions, which need knowledge of justification [Young,JO] |
13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |