40 ideas
17311 | Real definitions don't just single out a thing; they must also explain its essence [Koslicki] |
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] |
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] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [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] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [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] |
17312 | It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki] |
17314 | The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki] |
17313 | Modern views want essences just to individuate things across worlds and times [Koslicki] |
17309 | For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki] |
17315 | We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
17317 | A good explanation captures the real-world dependence among the phenomena [Koslicki] |
17316 | We can abstract to a dependent entity by blocking out features of its bearer [Koslicki] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |