33 ideas
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] |
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
23285 | If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
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] |