92 ideas
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 16728 | Logicians acknowledge too few things, while others acknowledge too many [Fitzralph] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 4098 | The theory of descriptions supports internalism, since they are thinkable when the object is non-existent [Crane] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 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] |
| 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] |
| 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] |
| 4104 | One can taste that the wine is sour, and one can also taste the sourness of the wine [Crane] |
| 4105 | The traditional supports for the sense datum theory were seeing double and specks before one's eyes [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] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 4071 | Causation can be seen in counterfactual terms, or as increased probability, or as energy flow [Crane] |
| 4076 | Causes are properties, not events, because properties are what make a difference in a situation [Crane] |
| 4066 | It seems that 'exists' could sometimes be a predicate [Crane] |