51 ideas
| 13567 | Ontology should give insight into or an explanation of the world revealed by science [Ellis] |
| 18241 | Sufficient reason is implied by contradiction, of an insufficient possible which exists [Wolff, by Korsgaard] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 13604 | Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis] |
| 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] |
| 13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
| 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] |
| 13584 | The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis] |
| 13587 | There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis] |
| 13577 | Typical 'categorical' properties are spatio-temporal, such as shape [Ellis] |
| 9436 | The property of 'being an electron' is not of anything, and only electrons could have it [Ellis] |
| 13582 | 'Being a methane molecule' is not a property - it is just a predicate [Ellis] |
| 13580 | Causal powers must necessarily act the way they do [Ellis] |
| 13598 | Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis] |
| 13568 | Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis] |
| 13586 | Maybe dispositions can be explained by intrinsic properties or structures [Ellis] |
| 13585 | The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis] |
| 13596 | A causal power is a disposition to produce forces [Ellis] |
| 13599 | Powers are dispositions of the essences of kinds that involve them in causation [Ellis] |
| 13572 | There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis] |
| 13573 | Universals are all types of natural kind [Ellis] |
| 13571 | Scientific essentialism doesn't really need Kripkean individual essences [Ellis] |
| 13578 | The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis] |
| 13576 | Necessities are distinguished by their grounds, not their different modalities [Ellis] |
| 13570 | Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis] |
| 13607 | If events are unconnected, then induction cannot be solved [Ellis] |
| 13597 | Good explanations unify [Ellis] |
| 13601 | Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis] |
| 13569 | To give essentialist explanations there have to be natural kinds [Ellis] |
| 13600 | The point of models in theories is not to idealise, but to focus on what is essential [Ellis] |
| 13583 | There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis] |
| 13574 | Natural kinds are distinguished by resting on essences [Ellis] |
| 13575 | If there are borderline cases between natural kinds, that makes them superficial [Ellis] |
| 13595 | Laws don't exist in the world; they are true of the world [Ellis] |
| 13566 | A proton must have its causal role, because without it it wouldn't be a proton [Ellis] |
| 13579 | What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis] |
| 13581 | Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis] |
| 13594 | The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis] |
| 13603 | A primary aim of science is to show the limits of the possible [Ellis] |
| 18242 | Confucius shows that ethics can rest on reason, rather than on revelation [Wolff, by Korsgaard] |