23 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] |
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] |
3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
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] |
16740 | A power is not a cause, but an aptitude for a cause [Zabarella] |
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] |
16571 | Prime matter is exceptionally obscure [Zabarella] |