41 ideas
| 3656 | The greatest good for a state is true philosophers [Descartes] |
| 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] |
| 16744 | All powers can be explained by obvious features like size, shape and motion of matter [Descartes] |
| 5016 | Five universals: genus, species, difference, property, accident [Descartes] |
| 5015 | A universal is a single idea applied to individual things that are similar to one another [Descartes] |
| 16630 | If we perceive an attribute, we infer the existence of some substance [Descartes] |
| 5013 | A substance needs nothing else in order to exist [Descartes] |
| 16633 | A substance has one principal property which is its nature and essence [Descartes] |
| 3658 | Total doubt can't include your existence while doubting [Descartes] |
| 5005 | I think, therefore I am, because for a thinking thing to not exist is a contradiction [Descartes] |
| 5006 | 'Thought' is all our conscious awareness, including feeling as well as understanding [Descartes] |
| 5012 | 'Nothing comes from nothing' is an eternal truth found within the mind [Descartes] |
| 5004 | We can know basic Principles without further knowledge, but not the other way round [Descartes] |
| 19508 | Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S] |
| 19509 | The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S] |
| 5014 | We can understand thinking occuring without imagination or sensation [Descartes] |
| 5017 | In thinking we shut ourselves off from other substances, showing our identity and separateness [Descartes] |
| 5010 | Our free will is so self-evident to us that it must be a basic innate idea [Descartes] |
| 5011 | There are two ultimate classes of existence: thinking substance and extended substance [Descartes] |
| 5018 | Even if tightly united, mind and body are different, as God could separate them [Descartes] |
| 5007 | Most errors of judgement result from an inaccurate perception of the facts [Descartes] |
| 5009 | We do not praise the acts of an efficient automaton, as their acts are necessary [Descartes] |
| 5008 | The greatest perfection of man is to act by free will, and thus merit praise or blame [Descartes] |
| 15987 | Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes] |
| 12730 | We will not try to understand natural or divine ends, or final causes [Descartes] |
| 16601 | Matter is not hard, heavy or coloured, but merely extended in space [Descartes] |