101 ideas
3426 | If one theory is reduced to another, we make fewer independent assumptions about the world [Kim] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
3406 | Counterfactuals are either based on laws, or on nearby possible worlds [Kim, by PG] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
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] |
3373 | Snakes have different pain behaviour from us [Kim] |
3371 | Behaviour depends on lots of mental states together [Kim] |
3372 | Behaviour is determined by society as well as mental states [Kim] |
3370 | What behaviour goes with mathematical beliefs? [Kim] |
3388 | Machine functionalism requires a Turing machine, causal-theoretical version doesn't [Kim] |
3379 | Neurons seem to be very similar and interchangeable [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] |
3424 | Most modern physicalists are non-reductive property dualists [Kim] |
3376 | We can't assess evidence about mind without acknowledging phenomenal properties [Kim] |
3362 | Supervenience says all souls are identical, being physically indiscernible [Kim] |
3413 | Zombies and inversion suggest non-reducible supervenience [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] |
3416 | Content may match several things in the environment [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] |
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] |
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] |