Combining Texts

Ideas for 'Physics', 'An Introduction to Modal Logic' and 'The Logical Structure of the World (Aufbau)'

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4 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]
4. Formal Logic / G. Formal Mereology / 1. Mereology
13270 Are a part and whole one or many? Either way, what is the cause? [Aristotle]
     Full Idea: There is a difficulty about part and whole, ...whether the part and the whole are one or more than one, and in what way they can be one or many, and, if they are more than one, in what way they are more than one.
     From: Aristotle (Physics [c.337 BCE], 185b11), quoted by Kathrin Koslicki - The Structure of Objects 6.3
     A reaction: He only states the problem here, but doesn't pursue it. I take the real question of mereology to be what makes a many into a one. I don't see a problem with a many being simultaneously a one.