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] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
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] |
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] |
16628 | Corpuscularianism promised a decent account of substance [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] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |