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] |
| 8507 | Some think of reality as made of things; I prefer facts or states of affairs [Armstrong] |
| Full Idea: Some philosophers (like Devitt) think of reality as made up of things. Others, like me, think of it as made up of facts or states of affairs. | |
| From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §3) | |
| A reaction: Devitt is a follower of Quine on this. Personally I rather like 'processes'. Unanalysed things with predication (Quine) don't look promising. I currently favour things with active powers, which give rise to properties. See Shoemaker and Ellis. |
| 8506 | Particulars and properties are distinguishable, but too close to speak of a relation [Armstrong] |
| Full Idea: I favour the Realist view that while we can distinguish the particularity of a particular from its properties, but the two 'factors' are too intimately together to speak of a relation between them. | |
| From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §3) | |
| A reaction: Is Armstrong being a bit of an ostrich here? We could talk of part-whole relationships, or internal relations, or set membership, or coinciding objects, or bundles. We certainly ought to have a go. Armstrong approaches Quine here! |
| 8505 | Refusal to explain why different tokens are of the same type is to be an ostrich [Armstrong] |
| Full Idea: A philosophical account of a general sort is required of what it is for different tokens to be of the same type. To refuse to give such an account is to be a metaphysical ostrich. | |
| From: David M. Armstrong (Against 'Ostrich Nominalism' [1980], §1) | |
| A reaction: This defines Ostrich Nominalism (a label Armstrong aims at Quine). I certainly sympathise with Armstrong. If there is no more to a class (a type) than just having members (tokens), nothing is explain. What is natural, essential, intensional etc.? |
| 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? |