15 ideas
9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |