48 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] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| 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] |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [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] |
| 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] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| 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] |
| 18407 | Indexicality is not significantly connected to agency [Cappelen/Dever] |
| 18427 | If some of our thought is tied to its context, it will be hard to communicate it [Cappelen/Dever] |
| 18426 | All information is objective, and purely indexical information is not much use [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] |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| 18413 | Fregeans can't agree on what 'senses' are [Cappelen/Dever] |
| 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] |