24 ideas
14779 | I reason in order to avoid disappointment and surprise [Peirce] |
14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
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] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
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] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |
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] |
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] |