Combining Texts

All the ideas for 'fragments/reports', 'An Introduction to Modal Logic' and 'works'

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6 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
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'.
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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.
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
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]
5. Theory of Logic / K. Features of Logics / 4. Completeness
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]
13. Knowledge Criteria / C. External Justification / 1. External Justification
3568 Surely ALL truths are externally justified, by the facts? [Cross,A]
     Full Idea: Surely ALL truths are externally justified?
     From: Adam Cross (works [2001]), quoted by PG - Db (ideas)
     A reaction: A very nice warning to aspiring externalists. If you actually think the justification is somehow 'out there', then everything is going to be justified, by its own facts. We need to get the justification 'in here'.
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
     Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
     From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8