Combining Philosophers

All the ideas for Herodotus, GE Hughes/M Cresswell and Cratylus

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7 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]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
     Full Idea: Cratylus was appalled that Heraclitus said you could not step twice into the same river, because it was already going too far to admit stepping into the same river once.
     From: report of Cratylus (fragments/reports [c.425 BCE]) by Aristotle - Metaphysics 1010a
     A reaction: Compare Idea 427.
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
     Full Idea: Cratylus thought speech of any kind was radically inappropriate and that expression should be restricted exclusively to the movement of the finger.
     From: report of Cratylus (fragments/reports [c.425 BCE]) by Aristotle - Metaphysics 1010a
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]
     Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born.
     From: Herodotus (The Histories [c.435 BCE], 2.123.2)