31 ideas
| 23657 | The existence of tensed verbs shows that not all truths are necessary truths [Reid] |
| 23655 | An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 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] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 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] |
| 23659 | If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid] |
| 23662 | The existence of ideas is no more obvious than the existence of external objects [Reid] |
| 23661 | We are only aware of other beings through our senses; without that, we are alone in the universe [Reid] |
| 23654 | In obscure matters the few must lead the many, but the many usually lead in common sense [Reid] |
| 23660 | The theory of ideas, popular with philosophers, means past existence has to be proved [Reid] |
| 23658 | Consciousness is an indefinable and unique operation [Reid] |
| 23656 | The structure of languages reveals a uniformity in basic human opinions [Reid] |
| 23653 | If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| 23663 | There are axioms of taste - such as a general consensus about a beautiful face [Reid] |