7 ideas
| 22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
| Full Idea: It was an early Romantic idea that there is necessarily a plurality of systems in which individuality is expressed; for a complete system would destroy freedom. | |
| From: Vittorio Hösle (A Short History of German Philosophy [2013], 7) | |
| A reaction: I'm not clear why you are free because you are locked into system that differs from that of other people. True freedom seems to be either no system, or continually remaking one's own system. Why is such freedom valuable? Freedom v truth? |
| 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] |
| 490 | Everything happens by reason and necessity [Leucippus] |
| Full Idea: Nothing happens at random; everything happens out of reason and by necessity. | |
| From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where? |
| 22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |
| Full Idea: The turning point in the history of the philosophy of history occurs in the eighteenth century, when the ancient cyclical model of Vico is superseded by the idea of progress. | |
| From: Vittorio Hösle (A Short History of German Philosophy [2013], 6) | |
| A reaction: He says that Hegel merely inherited this progressive view, rather than creating it. I'm not sure how widely held the cyclical view was. I don't recognise it in Shakespeare. Science and technology must have suggested progress. |