30 ideas
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
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] |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
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] |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
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] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
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] |
8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |