31 ideas
6161 | Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands] |
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] |
6163 | If bivalence is rejected, then excluded middle must also be rejected [Rowlands] |
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] |
6155 | Supervenience is a one-way relation of dependence or determination between properties [Rowlands] |
6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
6157 | Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands] |
6159 | Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands] |
17897 | Analytic explanation is wholes in terms of parts; synthetic is parts in terms of wholes or contexts [Belnap] |
6152 | Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands] |
6173 | Content externalism implies that we do not have privileged access to our own minds [Rowlands] |
6174 | If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands] |
6158 | Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands] |
6168 | The content of a thought is just the meaning of a sentence [Rowlands] |
6167 | Action is bodily movement caused by intentional states [Rowlands] |
6177 | Moral intuition seems unevenly distributed between people [Rowlands] |
6156 | The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands] |
6170 | Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands] |
6178 | It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands] |