31 ideas
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
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] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
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] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |