2005 | Logical Consequence |
Intro | p.1 | 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion |
2 | p.4 | 10689 | A step is a 'material consequence' if we need contents as well as form |
2 | p.5 | 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought |
2 | p.7 | 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation |
3 | p.6 | 10691 | Logical consequence needs either proofs, or absence of counterexamples |
3 | p.6 | 10693 | Models are mathematical structures which interpret the non-logical primitives |
3 | p.6 | 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite |
4 | p.8 | 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises |
2006 | Logical Pluralism |
2.1 | p.8 | 13232 | Logic studies arguments, not formal languages; this involves interpretations |
2.1 | p.12 | 13233 | Propositions commit to content, and not to any way of spelling it out |
2.2 | p.12 | 13234 | The view of logic as knowing a body of truths looks out-of-date |
2.2 | p.13 | 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing |
2.2 | p.13 | 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims |
2.4 | p.16 | 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book |
2.5 | p.19 | 13238 | Syllogisms are only logic when they use variables, and not concrete terms |
2.5 | p.21 | 13239 | Judgement is always predicating a property of a subject |
3.2 | p.29 | 13240 | A sentence follows from others if they always model it |
4.2.1 | p.40 | 13241 | The model theory of classical predicate logic is mathematics |
5.2 | p.53 | 13244 | Relevant necessity is always true for some situation (not all situations) |
5.2 | p.53 | 13242 | It's 'relevantly' valid if all those situations make it true |
5.2 | p.53 | 13243 | Excluded middle must be true for some situation, not for all situations |
5.3.3 | p.55 | 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises |
5.4 | p.55 | 13246 | Relevant logic does not abandon classical logic |
5.5.3 | p.57 | 13247 | A truthmaker is an object which entails a sentence |
5.5.4 | p.58 | 13248 | We can rest truth-conditions on situations, rather than on possible worlds |
6.1.2 | p.64 | 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically |
7.1 | p.75 | 13250 | Free logic terms aren't existential; classical is non-empty, with referring names |
7.4 | p.79 | 13252 | Some truths have true negations |
8 | p.88 | 13253 | There are several different consequence relations |
8 | p.91 | 13255 | Relevant logic may reject transitivity |
8 | p.91 | 13254 | A doesn't imply A - that would be circular |