102 ideas
13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
13477 | The problems are the monuments of philosophy [Hart,WD] |
14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
14764 | I am saturated with the spirit of physical science [Peirce] |
13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
2392 | Properties supervene if you can't have one without the other [Chalmers] |
2393 | Logical supervenience is when one set of properties must be accompanied by another set [Chalmers] |
2394 | Natural supervenience is when one set of properties is always accompanied by another set [Chalmers] |
2398 | Reduction requires logical supervenience [Chalmers] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
16048 | Physicalism says in any two physically indiscernible worlds the positive facts are the same [Chalmers, by Bennett,K] |
2401 | All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers] |
16424 | Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers] |
16425 | Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers] |
16426 | How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers] |
13956 | Kripke is often taken to be challenging a priori insights into necessity [Chalmers] |
13963 | Maybe logical possibility does imply conceivability - by an ideal mind [Chalmers] |
2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
2390 | We attribute beliefs to people in order to explain their behaviour [Chalmers] |
14768 | Infallibility in science is just a joke [Peirce] |
13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
2397 | 'Perception' means either an action or a mental state [Chalmers] |
2422 | The structure of the retina has already simplified the colour information which hits it [Chalmers] |
14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
2396 | Reductive explanation is not the be-all and the end-all of explanation [Chalmers] |
2426 | Why are minds homogeneous and brains fine-grained? [Chalmers] |
2391 | Can we be aware but not conscious? [Chalmers] |
2412 | Can we explain behaviour without consciousness? [Chalmers] |
2386 | Hard Problem: why brains experience things [Chalmers] |
2416 | What turns awareness into consciousness? [Chalmers] |
2423 | Going down the scale, where would consciousness vanish? [Chalmers] |
2403 | Nothing in physics even suggests consciousness [Chalmers] |
2400 | Is intentionality just causal connections? [Chalmers] |
2389 | Sometimes we don't notice our pains [Chalmers] |
2419 | Why should qualia fade during silicon replacement? [Chalmers] |
2402 | It seems possible to invert qualia [Chalmers] |
2415 | In blindsight both qualia and intentionality are missing [Chalmers] |
2414 | When distracted we can totally misjudge our own experiences [Chalmers] |
2409 | Maybe dualist interaction is possible at the quantum level? [Chalmers] |
2411 | Supervenience makes interaction laws possible [Chalmers] |
2424 | It is odd if experience is a very recent development [Chalmers] |
2413 | If I can have a zombie twin, my own behaviour doesn't need consciousness [Chalmers] |
2417 | Does consciousness arise from fine-grained non-reductive functional organisation? [Chalmers] |
2428 | Maybe the whole Chinese Room understands Chinese, though the person doesn't [Chalmers] |
2418 | The Chinese Mind doesn't seem conscious, but then nor do brains from outside [Chalmers] |
2406 | H2O causes liquidity, but no one is a dualist about that [Chalmers] |
2405 | Perhaps consciousness is physically based, but not logically required by that base [Chalmers] |
2395 | Zombies imply natural but not logical supervenience [Chalmers] |
9318 | Phenomenal consciousness is fundamental, with no possible nonphenomenal explanation [Chalmers, by Kriegel/Williford] |
2404 | Nothing external shows whether a mouse is conscious [Chalmers] |
2429 | Temperature (etc.) is agreed to be reducible, but it is multiply realisable [Chalmers] |
18403 | Indexicals may not be objective, but they are a fact about the world as I see it [Chalmers] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
14708 | Rationalist 2D semantics posits necessary relations between meaning, apriority, and possibility [Chalmers, by Schroeter] |
13958 | The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers] |
2399 | Meaning has split into primary ("watery stuff"), and secondary counterfactual meaning ("H2O") [Chalmers] |
13959 | The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers] |
13957 | Primary and secondary intensions are the a priori (actual) and a posteriori (counterfactual) aspects of meaning [Chalmers] |
13961 | We have 'primary' truth-conditions for the actual world, and derived 'secondary' ones for counterfactual worlds [Chalmers] |
13962 | Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement [Chalmers] |
13960 | In two-dimensional semantics we have two aspects to truth in virtue of meaning [Chalmers] |
16427 | Presumably God can do anything which is logically possible [Chalmers] |