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] |
9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |