110 ideas
3807 | Reason is and ought to be the slave of the passions [Hume] |
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] |
8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
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] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [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] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
21291 | There is no medium state between existence and non-existence [Hume] |
11942 | Power is the possibility of action, as discovered by experience [Hume] |
11949 | There may well be powers in things, with which we are quite unacquainted [Hume] |
11950 | We have no idea of powers, because we have no impressions of them [Hume] |
11941 | The distinction between a power and its exercise is entirely frivolous [Hume] |
11098 | Momentary impressions are wrongly identified with one another on the basis of resemblance [Hume, by Quine] |
7954 | If we see a resemblance among objects, we apply the same name to them, despite their differences [Hume] |
21293 | Individuation is only seeing that a thing is stable and continuous over time [Hume] |
12048 | The only meaning we have for substance is a collection of qualities [Hume] |
13424 | Aristotelians propose accidents supported by substance, but they don't understand either of them [Hume] |
21299 | Changing a part can change the whole, not absolutely, but by its proportion of the whole [Hume] |
21300 | A change more obviously destroys an identity if it is quick and observed [Hume] |
1321 | If identity survives change or interruption, then resemblance, contiguity or causation must unite the parts of it [Hume] |
1330 | If a republic can retain identity through many changes, so can an individual [Hume] |
21302 | If a ruined church is rebuilt, its relation to its parish makes it the same church [Hume] |
21303 | We accept the identity of a river through change, because it is the river's nature [Hume] |
21301 | The purpose of the ship makes it the same one through all variations [Hume] |
21290 | Multiple objects cannot convey identity, because we see them as different [Hume] |
1207 | Both number and unity are incompatible with the relation of identity [Hume] |
21289 | 'An object is the same with itself' is meaningless; it expresses unity, not identity [Hume] |
21292 | Saying an object is the same with itself is only meaningful over a period of time [Hume] |
9428 | Nothing we clearly imagine is absolutely impossible [Hume] |
4766 | Necessity only exists in the mind, and not in objects [Hume] |
6526 | Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H] |
6489 | Associationism results from having to explain intentionality just with sense-data [Robinson,H on Hume] |
6182 | Even Hume didn't include mathematics in his empiricism [Hume, by Kant] |
12417 | Mathematicians only accept their own proofs when everyone confims them [Hume] |
5548 | Hume became a total sceptic, because he believed that reason was a deception [Hume, by Kant] |
7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
7295 | Maybe induction is only reliable IF reality is stable [Mitchell,A] |
21806 | Memory, senses and understanding are all founded on the imagination [Hume] |
3819 | Hume's 'bundle' won't distinguish one mind with ten experiences from ten minds [Searle on Hume] |
1317 | A person is just a fast-moving bundle of perceptions [Hume] |
1331 | The parts of a person are always linked together by causation [Hume] |
1388 | Hume gives us an interesting sketchy causal theory of personal identity [Perry on Hume] |
21297 | A person is simply a bundle of continually fluctuating perceptions [Hume] |
1316 | Introspection always discovers perceptions, and never a Self without perceptions [Hume] |
1333 | Memory only reveals personal identity, by showing cause and effect [Hume] |
1332 | We use memory to infer personal actions we have since forgotten [Hume] |
21305 | Memory not only reveals identity, but creates it, by producing resemblances [Hume] |
21307 | Who thinks that because you have forgotten an incident you are no longer that person? [Hume] |
21306 | Causation unites our perceptions, by producing, destroying and modifying each other [Hume] |
21294 | A continuous lifelong self must be justified by a single sustained impression, which we don't have [Hume] |
21295 | When I introspect I can only observe my perceptions, and never a self which has them [Hume] |
21298 | We pretend our perceptions are continuous, and imagine a self to fill the gaps [Hume] |
21304 | Identity in the mind is a fiction, like that fiction that plants and animals stay the same [Hume] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
20030 | If one event causes another, the two events must be wholly distinct [Hume, by Wilson/Schpall] |
6692 | For Hume, practical reason has little force, because we can always modify our desires [Hume, by Graham] |
8257 | Reason alone can never be a motive to any action of the will [Hume] |
22374 | You can only hold people responsible for actions which arise out of their character [Hume] |
22382 | We cannot discover vice by studying a wilful murder; that only arises from our own feelings [Hume] |
4008 | Modern science has destroyed the Platonic synthesis of scientific explanation and morality [Hume, by Taylor,C] |
8067 | The problem of getting to 'ought' from 'is' would also apply in getting to 'owes' or 'needs' [Anscombe on Hume] |
4578 | You can't move from 'is' to 'ought' without giving some explanation or reason for the deduction [Hume] |
3650 | Total selfishness is not irrational [Hume] |
14301 | We have no good concept of solidity or matter, because accounts of them are all circular [Hume] |
8382 | For Hume a constant conjunction is both necessary and sufficient for causation [Hume, by Crane] |
19274 | Hume seems to presuppose necessary connections between mental events [Kripke on Hume] |
21296 | If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume] |