6 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] |
Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0. | |
From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'. |
9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P). | |
From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false. |
9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid. | |
From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred] |
9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
Full Idea: To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency. | |
From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not] |
21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |