38 ideas
| 1708 | In "Callias is just/not just/unjust", which of these are contraries? [Aristotle] |
| 1703 | It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle] |
| 1704 | Statements are true according to how things actually are [Aristotle] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 22272 | Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle] |
| 9405 | Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle] |
| 9728 | Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn] |
| 9729 | Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| 9730 | Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| 9731 | Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| 9732 | Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| 9733 | Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 21593 | In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson] |
| 1701 | A prayer is a sentence which is neither true nor false [Aristotle] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 1706 | Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle] |
| 1707 | Maybe necessity and non-necessity are the first principles of ontology [Aristotle] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 2337 | For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam] |
| 13763 | Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle] |
| 1705 | It doesn't have to be the case that in opposed views one is true and the other false [Aristotle] |
| 1702 | Things may be necessary once they occur, but not be unconditionally necessary [Aristotle] |