Combining Texts

Ideas for 'talk', 'The Semantic Tradition from Kant to Carnap' 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 / A. Syllogistic Logic / 1. Aristotelian Logic

639	Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle]
	Full Idea: Socrates aimed to establish formal logic, of whose syllogisms essences are the foundations. He developed inductive arguments and also general definitions.
	From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1078b

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 / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

18270	Choice suggests that intensions are not needed to ensure classes [Coffa]
	Full Idea: The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log')
	A reaction: The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist.