85 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] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 16554 | Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver] |
| 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] |
| 16556 | Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver] |
| 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] |
| 16562 | We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver] |
| 16563 | The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver] |
| 16555 | Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver] |
| 16528 | Mechanisms are not just push-pull systems [Machamer/Darden/Craver] |
| 16529 | Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver] |
| 16530 | A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver] |
| 16553 | Our account of mechanism combines both entities and activities [Machamer/Darden/Craver] |
| 16559 | Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver] |
| 16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
| 16564 | There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver] |
| 16561 | We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver] |
| 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] |
| 16558 | Laws of nature have very little application in biology [Machamer/Darden/Craver] |
| 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] |