45 ideas
18405 | A 'teepee' argument has several mutually supporting planks to it [Cappelen/Dever] |
13520 | A 'tautology' must include connectives [Wolf,RS] |
13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
14221 | Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski] |
14222 | Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski] |
14226 | We distinguish objects by their attributes, not by their essences [Shalkowski] |
14225 | Critics say that essences are too mysterious to be known [Shalkowski] |
14223 | De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski] |
9220 | Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider] |
18422 | Prioprioception focuses on your body parts, not on your self, or indexicality [Cappelen/Dever] |
18425 | We can acquire self-knowledge with mirrors, not just with proprioception and introspection [Cappelen/Dever] |
18421 | Proprioception is only immune from error if you are certain that it represents the agent [Cappelen/Dever] |
18419 | Folk Functionalism is a Ramsification of our folk psychology [Cappelen/Dever] |
18404 | It is assumed that indexical content is needed to represent the perspective of perception [Cappelen/Dever] |
18426 | All information is objective, and purely indexical information is not much use [Cappelen/Dever] |
18427 | If some of our thought is tied to its context, it will be hard to communicate it [Cappelen/Dever] |
18428 | You don't remember your house interior just from an experienced viewpoint [Cappelen/Dever] |
18429 | Our beliefs and desires are not organised around ourselves, but around the world [Cappelen/Dever] |
18407 | Indexicality is not significantly connected to agency [Cappelen/Dever] |
18413 | Fregeans can't agree on what 'senses' are [Cappelen/Dever] |
14224 | Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski] |
18417 | Possible worlds accounts of content are notoriously coarse-grained [Cappelen/Dever] |
18408 | Indexicals are just non-constant in meaning, and don't involve any special concepts [Cappelen/Dever] |
18414 | Fregeans say 'I' differs in reference, so it must also differ in sense [Cappelen/Dever] |
18423 | All indexicals can be expressed non-indexically [Cappelen/Dever] |
18406 | The basic Kaplan view is that there is truth-conditional content, and contextual character [Cappelen/Dever] |
18411 | It is proposed that a huge range of linguistic items are context-sensitive [Cappelen/Dever] |
18420 | We deny that action involves some special class of beliefs [Cappelen/Dever] |