59 ideas
| 21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
| 4588 | There is no such thing as 'science'; there are just many different sciences [Heil] |
| 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] |
| 6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
| 4616 | A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil] |
| 4603 | Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil] |
| 4617 | A stone does not possess the property of being a stone; its other properties make it a stone [Heil] |
| 4615 | Complex properties are not new properties, they are merely new combinations of properties [Heil] |
| 4612 | Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil] |
| 4587 | From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil] |
| 4611 | The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil] |
| 4592 | If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil] |
| 4586 | You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil] |
| 4591 | Idealism explains appearances by identifying appearances with reality [Heil] |
| 4610 | Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil] |
| 4618 | If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil] |
| 4621 | Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil] |
| 4623 | Propositional attitudes are not the only intentional states; there is also mental imagery [Heil] |
| 4626 | The widespread externalist view says intentionality has content because of causal links of agent to world [Heil] |
| 4622 | Error must be possible in introspection, because error is possible in all judgements [Heil] |
| 4590 | If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil] |
| 4614 | Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil] |
| 4595 | No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil] |
| 4599 | Hearts are material, but functionalism says the property of being a heart is not a material property [Heil] |
| 4624 | If you are a functionalist, there appears to be no room for qualia [Heil] |
| 4601 | Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil] |
| 4602 | Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil] |
| 4593 | 'Property dualism' says mind and body are not substances, but distinct families of properties [Heil] |
| 4597 | Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil] |
| 4609 | It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil] |
| 4596 | The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil] |
| 4598 | Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil] |
| 4619 | 'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil] |
| 4620 | Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil] |
| 4594 | A scientist could know everything about the physiology of headaches, but never have had one [Heil] |
| 4625 | Is mental imagery pictorial, or is it propositional? [Heil] |
| 4607 | Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil] |
| 4605 | Truth-conditions correspond to the idea of 'literal meaning' [Heil] |
| 4606 | To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil] |
| 4604 | If propositions are abstract entities, how do human beings interact with them? [Heil] |