167 ideas
| 2319 | Metaphysics is the clarification of the ontological relationships between different areas of thought [Kim] |
| 6601 | Science rules the globe because of colonising power, not inherent rationality [Feyerabend] |
| 3426 | If one theory is reduced to another, we make fewer independent assumptions about the world [Kim] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 4779 | For Kim, events are exemplifications of properties by objects at particular times [Kim, by Psillos] |
| 10369 | How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J] |
| 8976 | If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim] |
| 8975 | Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons] |
| 8974 | Events are composed of an object with an attribute at a time [Kim, by Simons] |
| 8977 | Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim] |
| 8980 | Kim's theory results in too many events [Simons on Kim] |
| 2317 | Reductionism is good on light, genes, temperature and transparency [Kim, by PG] |
| 3536 | Supervenient properties must have matching base properties [Kim] |
| 2310 | Supervenience is linked to dependence [Kim] |
| 2315 | Mereological supervenience says wholes are fixed by parts [Kim] |
| 13745 | Supervenience is not a dependence relation, on the lines of causal, mereological or semantic dependence [Kim] |
| 13746 | Supervenience is just a 'surface' relation of pattern covariation, which still needs deeper explanation [Kim] |
| 3431 | Supervenience suggest dependence without reduction (e.g. beauty) [Kim] |
| 2329 | Causal power is a good way of distinguishing the real from the unreal [Kim] |
| 3437 | 'Physical facts determine all the facts' is the physicalists' slogan [Kim] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 15456 | Extrinsic properties, unlike intrinsics, imply the existence of a separate object [Kim, by Lewis] |
| 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] |
| 2320 | Properties can have causal powers lacked by their constituents [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] |
| 8825 | It seems impossible to logically deduce physical knowledge from indubitable sense data [Kim] |
| 530 | There are two contradictory arguments about everything [Kim] |
| 13314 | Protagoras says arguments on both sides are always equal [Kim, by Seneca] |
| 2065 | Not every person is the measure of all things, but only wise people [Plato on Kim] |
| 1550 | Why didn't Protagoras begin by saying "a tadpole is the measure of all things"? [Plato on Kim] |
| 2561 | For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty] |
| 14470 | Explanatory exclusion: there cannot be two separate complete explanations of a single event [Kim] |
| 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] |
| 2318 | Agency, knowledge, reason, memory, psychology all need mental causes [Kim, by PG] |
| 3397 | Beliefs cause other beliefs [Kim] |
| 3367 | Both thought and language have intentionality [Kim] |
| 3365 | Intentionality involves both reference and content [Kim] |
| 2325 | It seems impossible that an exact physical copy of this world could lack intentionality [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] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 3422 | Externalism about content makes introspection depend on external evidence [Kim] |
| 3363 | We often can't decide what emotion, or even sensation, we are experiencing [Kim] |
| 3412 | How do we distinguish our anger from embarrassment? [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] |
| 2324 | Intentionality as function seems possible [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] |
| 2314 | Maybe intentionality is reducible, but qualia aren't [Kim] |
| 3376 | We can't assess evidence about mind without acknowledging phenomenal properties [Kim] |
| 3424 | Most modern physicalists are non-reductive property dualists [Kim] |
| 2313 | Emergentism says there is no explanation for a supervenient property [Kim] |
| 2328 | The only mental property that might be emergent is that of qualia [Kim] |
| 2309 | Non-Reductive Physicalism relies on supervenience [Kim] |
| 3362 | Supervenience says all souls are identical, being physically indiscernible [Kim] |
| 3413 | Zombies and inversion suggest non-reducible supervenience [Kim] |
| 2311 | Maybe strong supervenience implies reduction [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] |
| 2308 | Identity theory was overthrown by multiple realisations and causal anomalies [Kim] |
| 2322 | Multiple realisation applies to other species, and even one individual over time [Kim] |
| 2327 | Knowledge and inversion make functionalism about qualia doubtful [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] |
| 2323 | Emotions have both intentionality and qualia [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] |
| 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] |
| 8430 | Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim] |
| 3535 | All observable causes are merely epiphenomena [Kim] |
| 3401 | A common view is that causal connections must be instances of a law [Kim] |
| 8396 | Many counterfactuals have nothing to do with causation [Kim, by Tooley] |
| 8429 | Counterfactuals can express four other relations between events, apart from causation [Kim] |
| 8428 | Causation is not the only dependency relation expressed by counterfactuals [Kim] |
| 3407 | Laws are either 'strict', or they involve a 'ceteris paribus' clause [Kim] |
| 4781 | Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos] |