46 ideas
| 6675 | The heart has its reasons of which reason knows nothing [Pascal] |
| 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] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 22011 | The first principles of truth are not rational, but are known by the heart [Pascal] |
| 6681 | We only want to know things so that we can talk about them [Pascal] |
| 6676 | Painting makes us admire things of which we do not admire the originals [Pascal] |
| 6680 | It is a funny sort of justice whose limits are marked by a river [Pascal] |
| 6677 | Imagination creates beauty, justice and happiness, which is the supreme good [Pascal] |
| 295 | The good is beautiful [Plato] |
| 6678 | We live for the past or future, and so are never happy in the present [Pascal] |
| 294 | People say that friendship exists only between good men [Plato] |
| 20732 | If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal] |
| 6682 | Majority opinion is visible and authoritative, although not very clever [Pascal] |
| 6679 | It is not good to be too free [Pascal] |
| 7455 | Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking] |
| 7457 | Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal] |
| 7456 | The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal] |
| 6684 | If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal] |