49 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] |
| 3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
| 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] |
| 7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
| 3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
| 2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
| 3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
| 2994 | In CRTT thought may be represented, content must be [Fodor] |
| 15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
| 7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
| 3001 | Behaviourism has no theory of mental causation [Fodor] |
| 2993 | Any piece of software can always be hard-wired [Fodor] |
| 3011 | Causal powers must be a crucial feature of mental states [Fodor] |
| 5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
| 2995 | Supervenience gives good support for mental causation [Fodor] |
| 2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
| 3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
| 2992 | We may be able to explain rationality mechanically [Fodor] |
| 2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
| 3010 | Belief and desire are structured states, which need mentalese [Fodor] |
| 2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
| 3012 | Do identical thoughts have identical causal roles? [Fodor] |
| 2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
| 3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
| 3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
| 3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
| 3000 | Meaning holism is a crazy doctrine [Fodor] |
| 3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
| 2996 | Mental states may have the same content but different extensions [Fodor] |
| 22817 | Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D] |
| 22816 | Socialists reject nationality as a false source of identity [Miller,D] |