36 ideas
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| 8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| 8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 8452 | Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein] |
| 8475 | The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |