96 ideas
| 16604 | Philosophy consists of choosing between Plato, Aristotle and Democritus [Pasnau] |
| 16606 | Original philosophers invariably seek inspiration from past thinkers [Pasnau] |
| 16586 | The commentaries of Averroes were the leading guide to Aristotle [Pasnau] |
| 16568 | Modernity begins in the late 12th century, with Averroes's commentaries on Aristotle [Pasnau] |
| 16653 | Once accidents were seen as real, 'Categories' became the major text for ontology [Pasnau] |
| 16704 | In 1347, the Church effectively stopped philosophy for the next 300 years [Pasnau] |
| 16605 | After c.1450 all of Plato was available. Before that, only the first half of 'Timaeus' was known [Pasnau] |
| 16607 | Renaissance Platonism is peripheral [Pasnau] |
| 16715 | Plato only made an impact locally in 15th century Italy [Pasnau] |
| 16610 | Philosophy could easily have died in 17th century, if it weren't for Descartes [Pasnau] |
| 16781 | The 17th century is a metaphysical train wreck [Pasnau] |
| 16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| 16598 | Priority was a major topic of dispute for scholastics [Pasnau] |
| 16727 | In mixtures, the four elements ceased to exist, replaced by a mixed body with a form [Pasnau] |
| 16732 | 17th C qualities are either microphysical, or phenomenal, or powers [Pasnau] |
| 16733 | 17th century authors only recognised categorical properties, never dispositions [Pasnau] |
| 16662 | The biggest question for scholastics is whether properties are real, or modes of substances [Pasnau] |
| 16767 | There is no centralised power, but we still need essence for a metaphysical understanding [Pasnau] |
| 16788 | Instead of adding Aristotelian forms to physical stuff, one could add dispositions [Pasnau] |
| 16738 | Scholastics reject dispositions, because they are not actual, as forms require [Pasnau] |
| 16649 | Scholastics say there is a genuine thing if it is 'separable' [Pasnau] |
| 16785 | If you reject essences, questions of individuation become extremely difficult [Pasnau] |
| 16680 | Scholastics thought Quantity could be the principle of individuation [Pasnau] |
| 16628 | Corpuscularianism promised a decent account of substance [Pasnau] |
| 16617 | Corpuscularian critics of scholasticism say only substances exist [Pasnau] |
| 16741 | Scholastics wanted to treat Aristotelianism as physics, rather than as metaphysics [Pasnau] |
| 16777 | If crowds are things at all, they seem to be Substances, since they bear properties [Pasnau] |
| 16615 | Scholastics use 'substantia' for thick concrete entities, and for thin metaphysical ones [Pasnau] |
| 16775 | For corpuscularians, a substance is just its integral parts [Pasnau] |
| 16769 | If clay survives destruction of the statue, the statue wasn't a substance, but a mere accident [Pasnau] |
| 16602 | Corpuscularianism rejected not only form, but also the dependence of matter on form [Pasnau] |
| 16612 | Hylomorphism may not be a rival to science, but an abstract account of unity and endurance [Pasnau] |
| 16613 | Hylomorphism declined because scholastics made it into a testable physical theory [Pasnau] |
| 16747 | Scholastics made forms substantial, in a way unintended by Aristotle [Pasnau] |
| 16759 | Scholastics began to see substantial form more as Aristotle's 'efficient' cause [Pasnau] |
| 16748 | Aquinas says a substance has one form; Scotists say it has many forms [Pasnau] |
| 16671 | Scholastic Quantity either gives a body parts, or spreads them out in a unified way [Pasnau] |
| 16579 | There may be different types of substrate, or temporary substrates [Pasnau] |
| 16596 | A substratum can't be 'bare', because it has a job to do [Pasnau] |
| 16584 | If a substrate gives causal support for change, quite a lot of the ingredients must endure [Pasnau] |
| 16580 | A substrate may be 'prime matter', which endures through every change [Pasnau] |
| 16749 | Aristotelians deny that all necessary properties are essential [Pasnau] |
| 16694 | Typical successive things are time and motion [Pasnau] |
| 16583 | Weak ex nihilo says it all comes from something; strong version says the old must partly endure [Pasnau] |
| 16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 16609 | Atomists say causation is mechanical collisions, and all true qualities are microscopic [Pasnau] |
| 16603 | In the 17th C matter became body, and was then studied by science [Pasnau] |
| 16592 | Atomism is the commonest version of corpuscularianism, but isn't required by it [Pasnau] |
| 16750 | If there are just arrangements of corpuscles, where are the boundaries between substances? [Pasnau] |
| 16722 | Scholastic causation is by changes in the primary qualities of hot, cold, wet, dry [Pasnau] |
| 16760 | Substantial forms were a step towards scientific essentialism [Pasnau] |
| 16581 | Scholastic authors agree that matter was created by God, out of nothing [Pasnau] |
| 16642 | Transubstantion says accidents of bread and wine don't inhere in the substance [Pasnau] |