37 ideas
| 23449 | Interpreting a text is representing it as making sense [Morris,M] |
| 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] |
| 23484 | Bipolarity adds to Bivalence the capacity for both truth values [Morris,M] |
| 23494 | Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M] |
| 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] |
| 13531 | Model theory reveals the structures of mathematics [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] |
| 23452 | Discriminating things for counting implies concepts of identity and distinctness [Morris,M] |
| 23451 | Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M] |
| 23460 | To count, we must distinguish things, and have a series with successors in it [Morris,M] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 22227 | For Sartre there is only being for-itself, or being in-itself (which is beyond experience) [Sartre, by Daigle] |
| 20743 | Appearances do not hide the essence; appearances are the essence [Sartre] |
| 6151 | Sartre says consciousness is just directedness towards external objects [Sartre, by Rowlands] |
| 6164 | Sartre rejects mental content, and the idea that the mind has hidden inner features [Sartre, by Rowlands] |
| 23491 | There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M] |
| 7074 | Man is a useless passion [Sartre] |
| 6687 | Man is the desire to be God [Sartre] |
| 22228 | Sartre's freedom is not for whimsical action, but taking responsibility for our own values [Sartre, by Daigle] |
| 22233 | Love is the demand to be loved [Sartre] |
| 20755 | Fear concerns the world, but 'anguish' comes from confronting my self [Sartre] |
| 20760 | Sincerity is not authenticity, because it only commits to one particular identity [Sartre, by Aho] |
| 22231 | We flee from the anguish of freedom by seeing ourselves objectively, as determined [Sartre] |