38 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
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] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
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] |
16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
16551 | Grasping an essence is just grasping a real definition [Lowe] |
16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |