21 ideas
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
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] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
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] |
8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
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] |
8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
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] |