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] |
| 9879 | NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett] |
| Full Idea: Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions. | |
| From: report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded. |
| 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] |
| 15675 | We don't condemn people for being bad at reasoning [Finlayson] |
| Full Idea: We do not morally disapprove of people who are incompetent reasoners. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.6:83) | |
| A reaction: Well, we don't morally disapprove simply of their lack of reasoning ability, but we may morally disapprove of their actions, which have arisen entirely from the disability. |
| 15674 | One can universalise good advice, but that doesn't make it an obligation [Finlayson] |
| Full Idea: 'Early to bed and early to rise' is a universalizable maxim, but, though it might be good advice, there is obviously no such obligation. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.6:83) | |
| A reaction: I take it that Kant's rule won't distinguish moral guidance from prudential guidance. Unfair, I think. I may be a lark, but when I universalise this maxim I see that it can't be willed as a universal rule, because we should tolerate the owls. |
| 15662 | The 'culture industry' is an advertisement for the way things are [Finlayson] |
| Full Idea: Critical theory said that culture unwittingly played the role of an advertisement for the way things are. Horkheimer and Adorno referred to this phenomenon as the 'culture industry'. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.1:04) | |
| A reaction: An interesting perspective. However, absolutely everything is an advertisement for what it offers. I think this is especially true of moral (and immoral) actions. |