42 ideas
| 11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
| 11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
| 11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
| 11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
| 11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
| 11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
| 11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
| 11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
| 16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
| 11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
| 11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
| 10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
| 10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
| 11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
| 11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
| 11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
| 11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
| 11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
| 11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
| 11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |
| 23688 | Noncognitivism tries to avoid both naturalism and mysterious morality [Hacker-Wright] |