23 ideas
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
18915 | If facts are the truthmakers, they are not in the world [Engelbretsen] |
18919 | There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen] |
18913 | Traditional term logic struggled to express relations [Engelbretsen] |
18907 | Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen] |
18912 | Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen] |
18922 | Logical syntax is actually close to surface linguistic form [Engelbretsen] |
18905 | Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen] |
18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
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] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
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] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
18917 | Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen] |
18916 | Facts are not in the world - they are properties of the world [Engelbretsen] |
18921 | Individuals are arranged in inclusion categories that match our semantics [Engelbretsen] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
18918 | Terms denote objects with properties, and statements denote the world with that property [Engelbretsen] |
18920 | 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen] |
18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |