66 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] |
| 6653 | Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe] |
| 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] |
| 6618 | A 'substance' is a thing that remains the same when its properties change [Lowe] |
| 6635 | Causal theories of belief make all beliefs true, and can't explain belief about the future [Lowe] |
| 6619 | Perhaps 'I' no more refers than the 'it' in 'it is raining' [Lowe] |
| 6643 | 'Ecological' approaches say we don't infer information, but pick it up directly from reality [Lowe] |
| 6638 | One must be able to visually recognise a table, as well as knowing its form [Lowe] |
| 6644 | Computationalists object that the 'ecological' approach can't tell us how we get the information [Lowe] |
| 6647 | Comparing shapes is proportional in time to the angle of rotation [Lowe] |
| 6639 | The 'disjunctive' theory of perception says true perceptions and hallucinations need have nothing in common [Lowe] |
| 6640 | A causal theorist can be a direct realist, if all objects of perception are external [Lowe] |
| 6645 | If blindsight shows we don't need perceptual experiences, the causal theory is wrong [Lowe] |
| 6637 | How could one paraphrase very complex sense-data reports adverbially? [Lowe] |
| 6667 | There are memories of facts, memories of practical skills, and autobiographical memory [Lowe] |
| 6642 | Psychologists say illusions only occur in unnatural and passive situations [Lowe] |
| 6641 | Externalists say minds depend on environment for their very existence and identity [Lowe] |
| 6617 | The main questions are: is mind distinct from body, and does it have unique properties? [Lowe] |
| 6626 | 'Phenomenal' consciousness is of qualities; 'apperceptive' consciousness includes beliefs and desires [Lowe] |
| 6646 | The brain may have two systems for vision, with only the older one intact in blindsight [Lowe] |
| 6665 | Persons are selves - subjects of experience, with reflexive self-knowledge [Lowe] |
| 6670 | If my brain could survive on its own, I cannot be identical with my whole body [Lowe] |
| 6671 | It seems impossible to get generally applicable mental concepts from self-observation [Lowe] |
| 6666 | All human languages have an equivalent of the word 'I' [Lowe] |
| 6625 | If qualia are causally inert, how can we even know about them? [Lowe] |
| 6621 | You can only identify behaviour by ascribing belief, so the behaviour can't explain the belief [Lowe] |
| 6654 | A computer program is equivalent to the person AND the manual [Lowe] |
| 6629 | Functionalism commits us to bizarre possibilities, such as 'zombies' [Lowe] |
| 6623 | Functionalism can't distinguish our experiences in spectrum inversion [Lowe] |
| 6628 | Functionalism only discusses relational properties of mental states, not intrinsic properties [Lowe] |
| 6622 | Non-reductive physicalism accepts token-token identity (not type-type) and asserts 'supervenience' of mind and brain [Lowe] |
| 6634 | Physicalists must believe in narrow content (because thoughts are merely the brain states) [Lowe] |
| 6630 | Eliminativism is incoherent if it eliminates reason and truth as well as propositional attitudes [Lowe] |
| 6648 | Some behaviourists believe thought is just suppressed speech [Lowe] |
| 6651 | People are wildly inaccurate in estimating probabilities about an observed event [Lowe] |
| 6652 | 'Base rate neglect' makes people favour the evidence over its background [Lowe] |
| 6655 | The 'Frame Problem' is how to program the appropriate application of general knowledge [Lowe] |
| 6657 | Computers can't be rational, because they lack motivation and curiosity [Lowe] |
| 6656 | The Turing test is too behaviourist, and too verbal in its methods [Lowe] |
| 6636 | The naturalistic views of how content is created are the causal theory and the teleological theory [Lowe] |
| 6633 | Twin Earth cases imply that even beliefs about kinds of stuff are indexical [Lowe] |
| 6632 | The same proposition provides contents for the that-clause of an utterance and a belief [Lowe] |
| 6631 | If propositions are abstract entities, how can minds depend on their causal powers? [Lowe] |
| 6659 | The three main theories of action involve the will, or belief-plus-desire, or an agent [Lowe] |
| 6661 | Libet gives empirical support for the will, as a kind of 'executive' mental operation [Lowe] |
| 6662 | We feel belief and desire as reasons for choice, not causes of choice [Lowe] |
| 6663 | People's actions are explained either by their motives, or their reasons, or the causes [Lowe] |
| 21996 | Freedom only comes when labour is no longer necessary [Marx] |