117 ideas
| 3426 | If one theory is reduced to another, we make fewer independent assumptions about the world [Kim] |
| 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] |
| 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] |
| 3431 | Supervenience suggest dependence without reduction (e.g. beauty) [Kim] |
| 3437 | 'Physical facts determine all the facts' is the physicalists' slogan [Kim] |
| 3430 | Resemblance or similarity is the core of our concept of a property [Kim] |
| 3432 | Is weight a 'resultant' property of water, but transparency an 'emergent' property? [Kim] |
| 3434 | Emergent properties are 'brute facts' (inexplicable), but still cause things [Kim] |
| 3436 | Should properties be individuated by their causal powers? [Kim] |
| 3406 | Counterfactuals are either based on laws, or on nearby possible worlds [Kim, by PG] |
| 3368 | Mind is basically qualities and intentionality, but how do they connect? [Kim] |
| 3392 | Mind is only interesting if it has causal powers [Kim] |
| 3396 | Experiment requires mental causation [Kim] |
| 3397 | Beliefs cause other beliefs [Kim] |
| 3367 | Both thought and language have intentionality [Kim] |
| 3365 | Intentionality involves both reference and content [Kim] |
| 3360 | Are pains pure qualia, or do they motivate? [Kim] |
| 3366 | Pain has no reference or content [Kim] |
| 3389 | Inverted qualia and zombies suggest experience isn't just functional [Kim] |
| 3391 | Crosswiring would show that pain and its function are separate [Kim, by PG] |
| 3422 | Externalism about content makes introspection depend on external evidence [Kim] |
| 3412 | How do we distinguish our anger from embarrassment? [Kim] |
| 3363 | We often can't decide what emotion, or even sensation, we are experiencing [Kim] |
| 3409 | Mental substance causation makes physics incomplete [Kim] |
| 3399 | If epiphenomenalism were true, we couldn't report consciousness [Kim] |
| 3390 | Are inverted or absent qualia coherent ideas? [Kim] |
| 3414 | What could demonstrate that zombies and inversion are impossible? [Kim] |
| 3359 | Cartesian dualism fails because it can't explain mental causation [Kim] |
| 3369 | Logical behaviourism translates mental language to behavioural [Kim] |
| 3428 | Behaviourism reduces mind to behaviour via bridging principles [Kim] |
| 3380 | Are dispositions real, or just a type of explanation? [Kim] |
| 3371 | Behaviour depends on lots of mental states together [Kim] |
| 3372 | Behaviour is determined by society as well as mental states [Kim] |
| 3373 | Snakes have different pain behaviour from us [Kim] |
| 3370 | What behaviour goes with mathematical beliefs? [Kim] |
| 3379 | Neurons seem to be very similar and interchangeable [Kim] |
| 3388 | Machine functionalism requires a Turing machine, causal-theoretical version doesn't [Kim] |
| 3384 | The person couldn't run Searle's Chinese Room without understanding Chinese [Kim] |
| 3393 | How do functional states give rise to mental causation? [Kim] |
| 3439 | Reductionism gets stuck with qualia [Kim] |
| 3427 | Reductionism is impossible if there aren't any 'bridge laws' between mental and physical [Kim] |
| 3376 | We can't assess evidence about mind without acknowledging phenomenal properties [Kim] |
| 3424 | Most modern physicalists are non-reductive property dualists [Kim] |
| 3413 | Zombies and inversion suggest non-reducible supervenience [Kim] |
| 3362 | Supervenience says all souls are identical, being physically indiscernible [Kim] |
| 3374 | Token physicalism isn't reductive; it just says all mental events have some physical properties [Kim] |
| 3433 | The core of the puzzle is the bridge laws between mind and brain [Kim] |
| 3377 | Elimination can either be by translation or by causal explanation [Kim] |
| 3438 | Reductionists deny new causal powers at the higher level [Kim] |
| 3440 | Without reductionism, mental causation is baffling [Kim] |
| 3375 | If an orange image is a brain state, are some parts of the brain orange? [Kim] |
| 3411 | How do we distinguish our attitudes from one another? [Kim] |
| 3386 | Folk psychology has been remarkably durable [Kim] |
| 3394 | Maybe folk psychology is a simulation, not a theory [Kim] |
| 3387 | A culture without our folk psychology would be quite baffling [Kim] |
| 3410 | Folk psychology has adapted to Freudianism [Kim] |
| 3382 | A machine with a mind might still fail the Turing Test [Kim] |
| 3383 | The Turing Test is too specifically human in its requirements [Kim] |
| 3408 | Two identical brain states could have different contents in different worlds [Kim] |
| 3420 | Two types of water are irrelevant to accounts of behaviour [Kim] |
| 3418 | 'Arthritis in my thigh' requires a social context for its content to be meaningful [Kim] |
| 3421 | Content is best thought of as truth conditions [Kim] |
| 3416 | Content may match several things in the environment [Kim] |
| 3419 | Pain, our own existence, and negative existentials, are not external [Kim] |
| 3417 | Content depends on other content as well as the facts [Kim] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 3403 | We assume people believe the obvious logical consequences of their known beliefs [Kim] |
| 3402 | If someone says "I do and don't like x", we don't assume a contradiction [Kim] |
| 22187 | Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha] |
| 3401 | A common view is that causal connections must be instances of a law [Kim] |
| 3407 | Laws are either 'strict', or they involve a 'ceteris paribus' clause [Kim] |