38 ideas
| 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] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [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] |
| 15127 | A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne] |
| 15123 | Is the causal profile of a property its essence? [Hawthorne] |
| 15124 | If properties are more than their powers, we could have two properties with the same power [Hawthorne] |
| 15122 | Could two different properties have the same causal profile? [Hawthorne] |
| 14590 | If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne] |
| 15128 | We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne] |
| 15121 | An individual essence is a necessary and sufficient profile for a thing [Hawthorne] |
| 14591 | Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne] |
| 8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
| 14589 | A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne] |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 15126 | Maybe scientific causation is just generalisation about the patterns [Hawthorne] |
| 15125 | We only know the mathematical laws, but not much else [Hawthorne] |
| 14588 | Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne] |