39 ideas
| 3745 | Must sentences make statements to qualify for truth? [O'Connor] |
| 3742 | Beliefs must match facts, but also words must match beliefs [O'Connor] |
| 3744 | The semantic theory requires sentences as truth-bearers, not propositions [O'Connor] |
| 3749 | What does 'true in English' mean? [O'Connor] |
| 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] |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| 3746 | Logic seems to work for unasserted sentences [O'Connor] |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| 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] |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| 3747 | Events are fast changes which are of interest to us [O'Connor] |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| 3743 | We can't contemplate our beliefs until we have expressed them [O'Connor] |
| 3748 | Without language our beliefs are particular and present [O'Connor] |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |