54 ideas
| 18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 9912 | There are no such things as numbers [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] |
| 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] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [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] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [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] |
| 18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
| 15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
| 18459 | Diversity arises from the power of unity [Porphyry] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
| 18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
| 18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
| 18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
| 18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
| 18464 | Justice is each person fulfilling his function [Porphyry] |
| 18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
| 18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
| 18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
| 18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
| 18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
| 7907 | Human killing is worse if the victim is virtuous [Buddhaghosa] |
| 18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
| 18454 | Time is the circular movement of the soul [Porphyry] |
| 18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
| 18460 | God is nowhere, and hence everywhere [Porphyry] |
| 18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
| 18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
| 18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |