50 ideas
| 16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
| 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] |
| 16949 | Klein summarised geometry as grouped together by transformations [Quine] |
| 16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
| 16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
| 16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 16944 | Science is common sense, with a sophisticated method [Quine] |
| 16940 | Induction is just more of the same: animal expectations [Quine] |
| 16941 | Induction relies on similar effects following from each cause [Quine] |
| 16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
| 16934 | General terms depend on similarities among things [Quine] |
| 16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
| 8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
| 16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
| 16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
| 19698 | Deviant causal chain: a reason causes an action, but isn't the reason for which it was performed [Davidson, by Neta] |
| 7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
| 16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
| 16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
| 16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
| 16942 | It is hard to see how regularities could be explained [Quine] |