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] |
| 16669 | Everything that exists is either a being, or some mode of a being [Malebranche] |
| Full Idea: It is absolutely necessary that everything in the world be either a being or a mode [manière] of a being. | |
| From: Nicolas Malebranche (The Search After Truth [1675], III.2.8.ii), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.4 |
| 2594 | A true cause must involve a necessary connection between cause and effect [Malebranche] |
| Full Idea: A true cause as I understand it is one such that the mind perceives a necessary connection between it and its effects. | |
| From: Nicolas Malebranche (The Union of Body and Soul [1675], p.116) |
| 12726 | In a true cause we see a necessary connection [Malebranche] |
| Full Idea: A true cause is one in which the mind perceives a necessary connection between the cause and its effect. | |
| From: Nicolas Malebranche (The Search After Truth [1675], 1.649 (450)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
| A reaction: Presumably Hume was ignorant of 'true' causes, since he says he never saw this connection. But then is the perception done by the mind, or by the senses? |
| 15314 | Faraday's single field of variable forces introduces a criterion of Unity into what is ultimate [Faraday, by Harré/Madden] |
| Full Idea: In Faraday lines of force picture the directional structure of powers,...so the fundamental entity is a single, unified field. ...A new criterion of the ultimate has stepped in: Unity. The universal field is still the final explanation, but not invariant. | |
| From: report of Michael Faraday (Experimental Researches in Electricity [1859]) by Harré,R./Madden,E.H. - Causal Powers 9.II.B | |
| A reaction: Almost Parmenides, except that the field is not invariant. But that was always the ancient objection to the One - that it offered no explanation of change. |