84 ideas
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
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] |
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] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
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] |
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] |
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] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
16427 | Presumably God can do anything which is logically possible [Chalmers] |