89 ideas
| 22611 | Metaphysics can criticise interpretations of science theories, and give good feedback [Ingthorsson] |
| 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] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [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] |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [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] |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| 9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| 9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
| 9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
| 9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9398 | ∧I: Given A and B, 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] |
| 9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| 9393 | A: we may assume any proposition at any stage [Lemmon] |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| 9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
| 9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
| 9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
| 9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
| 9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
| 9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- 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] |
| 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] |
| 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] |
| 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] |
| 22609 | Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory [Ingthorsson] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 22629 | Basic processes are said to be either physical, or organic, or psychological [Ingthorsson] |
| 22633 | Indirect realists are cautious about the manifest image, and prefer the scientific image [Ingthorsson] |
| 22606 | Neo-Humeans say there are no substantial connections between anything [Ingthorsson] |
| 22631 | Properties are said to be categorical qualities or non-qualitative dispositions [Ingthorsson] |
| 22632 | Physics understands the charge of an electron as a power, not as a quality [Ingthorsson] |
| 22627 | Compound objects are processes, insofar as change is essential to them [Ingthorsson] |
| 22613 | Most materialist views postulate smallest indivisible components which are permanent [Ingthorsson] |
| 22612 | Endurance and perdurance just show the consequences of A or B series time [Ingthorsson] |
| 22625 | Science suggests causal aspects of the constitution and persistance of objects [Ingthorsson] |
| 22620 | If causation involves production, that needs persisting objects [Ingthorsson] |
| 22636 | Every philosophical theory must be true in some possible world, so the ontology is hopeless [Ingthorsson] |
| 22638 | Worlds may differ in various respects, but no overall similarity of worlds is implied [Ingthorsson] |
| 1457 | Morality requires a minimum commitment to the self [Rashdall] |
| 6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
| 6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
| 22605 | Humeans describe the surface of causation, while powers accounts aim at deeper explanations [Ingthorsson] |
| 22607 | Time and space are not causal, but they determine natural phenomena [Ingthorsson] |
| 22608 | Casuation is the transmission of conserved quantities between causal processes [Ingthorsson] |
| 22614 | Interventionist causal theory says it gets a reliable result whenever you manipulate it [Ingthorsson] |
| 22621 | Causation as transfer only works for asymmetric interactions [Ingthorsson] |
| 22639 | Causal events are always reciprocal, and there is no distinction of action and reaction [Ingthorsson] |
| 22615 | One effect cannot act on a second effect in causation, because the second doesn't yet exist [Ingthorsson] |
| 22616 | Empiricists preferred events to objects as the relata, because they have observable motions [Ingthorsson] |
| 22617 | Science now says all actions are reciprocal, not unidirectional [Ingthorsson] |
| 22619 | Causes are not agents; the whole interaction is the cause, and the changed compound is the effect [Ingthorsson] |
| 22635 | People only accept the counterfactual when they know the underlying cause [Ingthorsson] |
| 22634 | Counterfactuals don't explain causation, but causation can explain counterfactuals [Ingthorsson] |
| 22637 | Counterfactual theories are false in possible worlds where causation is actual [Ingthorsson] |
| 22624 | A cause can fail to produce its normal effect, by prevention, pre-emption, finks or antidotes [Ingthorsson] |
| 22622 | Any process can go backwards or forwards in time without violating the basic laws of physics [Ingthorsson] |
| 22618 | In modern physics the first and second laws of motion (unlike the third) fail at extremes [Ingthorsson] |
| 22630 | If particles have decay rates, they can't really be elementary, in the sense of indivisible [Ingthorsson] |
| 22610 | It is difficult to handle presentism in first-order logic [Ingthorsson] |
| 1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
| 1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |