11 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 |
| 3914 | Language arranges sensory experience to form a world-order [Whorf] |
| Full Idea: Language first of all is a classification and arrangement of the stream of sensory experience which results in a certain world-order. | |
| From: Benjamin Lee Whorf (Punctual and segmentive Hopi verbs [1936], p.55) | |
| A reaction: This is only true to a limited degree. See Davidson's 'On the very idea of a conceptual scheme'. All humans share a world-order, to some extent. |
| 3916 | Hopi consistently prefers verbs and events to nouns and things [Whorf] |
| Full Idea: Hopi, with its preference for verbs, as contrasted to our own liking for nouns, perpetually turns our propositions about things into propositions about events. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.63) | |
| A reaction: This should provoke careful thought about ontology - without concluding that it is entirely relative to language. |
| 3917 | Scientific thought is essentially a specialised part of Indo-European languages [Whorf] |
| Full Idea: What we call "scientific thought" is a specialisation of the western Indo-European type of language. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.246) | |
| A reaction: This is the beginnings of an absurd extreme relativist view of science, based on a confusion about meaning and thought. |
| 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? |
| 3915 | The Hopi have no concept of time as something flowing from past to future [Whorf] |
| Full Idea: A Hopi has no general notion or intuition of time as a smooth flowing continuum in which everything in the universe proceeds at an equal rate, out of a future, through a present, into a past. | |
| From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.57) | |
| A reaction: If true, this would not so much support relativism of language as the view that that conception of time is actually false. |