29 ideas
15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
13070 | If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne] |
11197 | The definitions expressing identity are used to sort things [Aquinas] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
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] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [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] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
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] |
11195 | If affirmative propositions express being, we affirm about what is absent [Aquinas] |
11201 | Properties have an incomplete essence, with definitions referring to their subject [Aquinas] |
11205 | If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas] |
13090 | The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne] |
11202 | It is by having essence that things exist [Aquinas] |
11203 | Specific individual essence is defined by material, and generic essence is defined by form [Aquinas] |
11200 | The definition of a physical object must include the material as well as the form [Aquinas] |
11196 | Essence is something in common between the natures which sort things into categories [Aquinas] |
11208 | A simple substance is its own essence [Aquinas] |
11198 | Definition of essence makes things understandable [Aquinas] |
11206 | The mind constructs complete attributions, based on the unified elements of the real world [Aquinas] |
11207 | A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas] |