74 ideas
| 5333 | Philosophy needs wisdom about who we are, as well as how we ought to be [Flanagan] |
| 5334 | We resist science partly because it can't provide ethical wisdom [Flanagan] |
| 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] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 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] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [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] |
| 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] |
| 18149 | There are many criteria for the identity of numbers [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] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [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] |
| 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] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 16643 | Accidents always remain suited to a subject [Bonaventura] |
| 16696 | Successive things reduce to permanent things [Bonaventura] |
| 5340 | Explanation does not entail prediction [Flanagan] |
| 5346 | In the 17th century a collisionlike view of causation made mental causation implausible [Flanagan] |
| 5341 | Only you can have your subjective experiences because only you are hooked up to your nervous system [Flanagan] |
| 5351 | We only have a sense of our self as continuous, not as exactly the same [Flanagan] |
| 5353 | The self is an abstraction which magnifies important aspects of autobiography [Flanagan] |
| 5354 | We are not born with a self; we develop a self through living [Flanagan] |
| 5349 | For Buddhists a fixed self is a morally dangerous illusion [Flanagan] |
| 5338 | Normal free will claims control of what I do, but a stronger view claims control of thought and feeling [Flanagan] |
| 5344 | Free will is held to give us a whole list of desirable capacities for living [Flanagan] |
| 5332 | People believe they have free will that circumvents natural law, but only an incorporeal mind could do this [Flanagan] |
| 5345 | We only think of ourselves as having free will because we first thought of God that way [Flanagan] |
| 5343 | People largely came to believe in dualism because it made human agents free [Flanagan] |
| 5347 | Behaviourism notoriously has nothing to say about mental causation [Flanagan] |
| 5339 | Cars and bodies obey principles of causation, without us knowing any 'strict laws' about them [Flanagan] |
| 5342 | Physicalism doesn't deny that the essence of an experience is more than its neural realiser [Flanagan] |
| 5335 | Emotions are usually very apt, rather than being non-rational and fickle [Flanagan] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 5348 | Intellectualism admires the 'principled actor', non-intellectualism admires the 'good character' [Flanagan] |
| 5355 | Cognitivists think morals are discovered by reason [Flanagan] |
| 5336 | Ethics is the science of the conditions that lead to human flourishing [Flanagan] |
| 5350 | The Hindu doctrine of reincarnation only appeared in the eighth century CE [Flanagan] |
| 5352 | The idea of the soul gets some support from the scientific belief in essential 'natural kinds' [Flanagan] |