29 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |