29 ideas
7493 | Let us reason together, saith the Lord [Isaiah] |
2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
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] |
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] |
15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |
7608 | The world is established, and cannot be moved [Isaiah] |
7343 | Beside me there is no God [Isaiah] |