21 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
23291 | Without truth, both language and thought are impossible [Davidson] |
23284 | Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson] |
23286 | Truth can't be a goal, because we can neither recognise it nor confim it [Davidson] |
23292 | Correspondence can't be defined, but it shows how truth depends on the world [Davidson] |
23288 | When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson] |
23287 | Disquotation only accounts for truth if the metalanguage contains the object language [Davidson] |
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] |
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] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
23285 | If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson] |
23289 | Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson] |
23290 | It could be that the use of a sentence is explained by its truth conditions [Davidson] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |