79 ideas
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
9108 | From an impossibility anything follows [William of Ockham] |
16676 | Why use more things when fewer will do? [William of Ockham] |
6806 | Do not multiply entities beyond necessity [William of Ockham] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
16654 | Our words and concepts don't always correspond to what is out there [William of Ockham] |
18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
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] |
22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
9103 | A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
18459 | Diversity arises from the power of unity [Porphyry] |
16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
16792 | If parts change, the whole changes [William of Ockham] |
9089 | Knowledge is a quality existing subjectively in the soul [William of Ockham] |
9091 | Sometimes 'knowledge' just concerns the conclusion, sometimes the whole demonstration [William of Ockham] |
9100 | Our intellect only assents to what we believe to be true [William of Ockham] |
9090 | Knowledge is certain cognition of something that is true [William of Ockham] |
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] |
9101 | Abstractive cognition knows universals abstracted from many singulars [William of Ockham] |
9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
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] |
9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
9104 | A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
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] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
9115 | To love God means to love whatever God wills to be loved [William of Ockham] |
16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
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] |