77 ideas
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 4098 | The theory of descriptions supports internalism, since they are thinkable when the object is non-existent [Crane] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 4077 | Aesthetic properties of thing supervene on their physical properties [Crane] |
| 4078 | Constitution (as in a statue constituted by its marble) is supervenience without identity [Crane] |
| 8386 | Events are picked out by descriptions, and facts by whole sentences [Crane] |
| 4082 | The distinction between 'resultant' properties (weight) and 'emergent' properties is a bit vague [Crane] |
| 4083 | If mental properties are emergent they add a new type of causation, and physics is not complete [Crane] |
| 4079 | Properties are causes [Crane] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 4068 | Traditional substance is separate from properties and capable of independent existence [Crane] |
| 4096 | Maybe beliefs don't need to be conscious, if you are not conscious of the beliefs guiding your actions [Crane] |
| 4097 | Maybe there are two kinds of belief - 'de re' beliefs and 'de dicto' beliefs [Crane] |
| 4093 | Many cases of knowing how can be expressed in propositional terms (like how to get somewhere) [Crane] |
| 4108 | Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless, so which is it? [Crane] |
| 4105 | The traditional supports for the sense datum theory were seeing double and specks before one's eyes [Crane] |
| 4104 | One can taste that the wine is sour, and one can also taste the sourness of the wine [Crane] |
| 4101 | If we smell something we are aware of the smell separately, but we don't perceive a 'look' when we see [Crane] |
| 4102 | The problems of perception disappear if it is a relation to an intentional state, not to an object or sense datum [Crane] |
| 4109 | If perception is much richer than our powers of description, this suggests that it is non-conceptual [Crane] |
| 4103 | The adverbial theory of perceptions says it is the experiences which have properties, not the objects [Crane] |
| 4065 | Is knowledge just a state of mind, or does it also involve the existence of external things? [Crane] |
| 4092 | The core of the consciousness problem is the case of Mary, zombies, and the Hard Question [Crane] |
| 4087 | Intentionalism does not require that all mental states be propositional attitudes [Crane] |
| 4095 | Object-directed attitudes like love are just as significant as propositional attitudes [Crane] |
| 4106 | If someone removes their glasses the content of experience remains, but the quality changes [Crane] |
| 4089 | Pains have a region of the body as their intentional content, not some pain object [Crane] |
| 4090 | Weak intentionalism says qualia are extra properties; strong intentionalism says they are intentional [Crane] |
| 4107 | With inverted qualia a person's experiences would change, but their beliefs remain the same [Crane] |
| 4069 | Descartes did not think of minds as made of a substance, because they are not divisible [Crane] |
| 4074 | Functionalism defines mental states by their causal properties, which rules out epiphenomenalism [Crane] |
| 4091 | The problems of misrepresentation and error have dogged physicalist reductions of intentionality [Crane] |
| 4070 | Properties dualism says mental properties are distinct from physical, despite a single underlying substance [Crane] |
| 4084 | Non-reductive physicalism seeks an explanation of supervenience, but emergentists accept it as basic [Crane] |
| 4080 | If mental supervenes on the physical, then every physical cause will be accompanied by a mental one [Crane] |
| 4075 | Identity theory is either of particular events, or of properties, depending on your theory of causation [Crane] |
| 4085 | Physicalism may be the source of the mind-body problem, rather than its solution [Crane] |
| 4073 | Overdetermination occurs if two events cause an effect, when each would have caused it alone [Crane] |
| 4072 | The completeness of physics must be an essential component of any physicalist view of mind [Crane] |
| 4094 | Experience teaches us propositions, because we can reason about our phenomenal experience [Crane] |
| 4100 | The Twin Earth argument depends on reference being determined by content, which may be false. [Crane] |
| 4067 | Broad content entails the existence of the object of the thought [Crane] |
| 4063 | In intensional contexts, truth depends on how extensions are conceived. [Crane] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 4071 | Causation can be seen in counterfactual terms, or as increased probability, or as energy flow [Crane] |
| 8387 | A cause has its effects in virtue of its properties [Crane] |
| 4076 | Causes are properties, not events, because properties are what make a difference in a situation [Crane] |
| 8384 | The regularity theory explains a causal event by other items than the two that are involved [Crane] |
| 4066 | It seems that 'exists' could sometimes be a predicate [Crane] |