Combining Texts

Ideas for 'fragments/reports', 'Essays on Intellectual Powers 5: Abstraction' and 'An Introduction to Modal Logic'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

5 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

8077	Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
	Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic).

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 / 2. Tools of Propositional Logic / e. Axioms of PL

20791	Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
	Full Idea: Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81
	A reaction: [from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable.

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]