8 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] |
| 18278 | Kant showed that our perceptions are partly constructed from our concepts [Reichenbach] |
| Full Idea: It was Kant's great discovery that the object of knowledge is not simply given but constructed, and that it contains conceptual elements not contained in pure perception. | |
| From: Hans Reichenbach (The Theory of Relativity and A Priori Knowledge [1965], p.49), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap |
| 23104 | Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes] |
| Full Idea: Egalitarians believe that most often it is by promoting equality that autonomy is increased; this is the egalitarianism of such liberals as Ronald Dworkin. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by John Kekes - Against Liberalism 05.1 | |
| A reaction: Not my idea of equality. The whole point is to ascribe reasonable equality to everyone, including those with a limited capacity for autonomy. Equality is a consequence of universal respect. |
| 23257 | We can treat people as equals, or actually treat them equally [Dworkin, by Grayling] |
| Full Idea: Dworkin distinguishes between treating people as equals, that is, 'with equal concern and respect', and treating them equally. This latter can be unjust. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by A.C. Grayling - The Good State 2 | |
| A reaction: The big difference I see between them is that the first is mere words, and the second is actions. Cf. 'thoughts and prayers' after US school shootings. How about equal entitlements, all things being equal? |
| 18621 | Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka] |
| Full Idea: Dworkin suggests that every plausible political theory has the same ultimate value, which is equality - in the more abstract and fundamental sense of treating people 'as equals'. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977], 179-83) by Will Kymlicka - Contemporary Political Philosophy (1st edn) | |
| A reaction: I associate this idea with Kant (who says they are equal by virtue of their rationality), so that's a pretty influential idea. I would associate the main challenge to this with Nietzsche. |