87 ideas
| 7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| 7004 | The view that truth making is entailment is misguided and misleading [Heil] |
| 21544 | It seems that when a proposition is false, something must fail to subsist [Russell] |
| 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] |
| 7035 | God does not create the world, and then add the classes [Heil] |
| 21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell] |
| 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] |
| 7017 | The reductionist programme dispenses with levels of reality [Heil] |
| 7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
| 21538 | If two people perceive the same object, the object of perception can't be in the mind [Russell] |
| 7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
| 7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
| 7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
| 21534 | The only thing we can say about relations is that they relate [Russell] |
| 21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
| 7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
| 7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
| 7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
| 7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
| 7025 | Are a property's dispositions built in, or contingently added? [Heil] |
| 7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
| 7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
| 7009 | Similarity among modes will explain everthing universals were for [Heil] |
| 7041 | Similar objects have similar properties; properties are directly similar [Heil] |
| 7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
| 7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
| 7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
| 21536 | When I perceive a melody, I do not perceive the notes as existing [Russell] |
| 21535 | Objects only exist if they 'occupy' space and time [Russell] |
| 7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
| 7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
| 7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
| 7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
| 21533 | Contingency arises from tensed verbs changing the propositions to which they refer [Russell] |
| 21537 | I assume we perceive the actual objects, and not their 'presentations' [Russell] |
| 7030 | Properties don't possess ways they are, because that just is the property [Heil] |
| 7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
| 7029 | Can we distinguish the way a property is from the property? [Heil] |
| 7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
| 7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
| 7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
| 7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
| 21532 | Full empiricism is not tenable, but empirical investigation is always essential [Russell] |
| 7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
| 7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
| 7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
| 7060 | One form of explanation is by decomposition [Heil] |
| 7010 | Dispositionality provides the grounding for intentionality [Heil] |
| 7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
| 7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
| 7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
| 7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
| 7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
| 7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
| 7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
| 7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
| 7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
| 7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
| 21542 | Do incorrect judgements have non-existent, or mental, or external objects? [Russell] |
| 21541 | The complexity of the content correlates with the complexity of the object [Russell] |
| 7058 | Externalism is causal-historical, or social, or biological [Heil] |
| 7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
| 7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
| 21543 | If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell] |
| 7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
| 7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
| 7036 | The real natural properties are sparse, but there are many complex properties [Heil] |