Combining Texts

Ideas for 'Phenomenalism', 'The Principles of Mathematics' and 'Summa Theologicae'

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3 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

23173	If a syllogism admits one absurdity, others must follow [Aquinas]
	Full Idea: In syllogistic arguments, granted one absurdity, others must follow too.
	From: Thomas Aquinas (Summa Theologicae [1265], I-II Q19 6)
	A reaction: This asserts the necessity of logical consequence, which he derives from Aristotle.

5. Theory of Logic / B. Logical Consequence / 8. Material Implication

14106	Implication cannot be defined [Russell]
	Full Idea: A definition of implication is quite impossible.
	From: Bertrand Russell (The Principles of Mathematics [1903], §016)

14108	It would be circular to use 'if' and 'then' to define material implication [Russell]
	Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication.
	From: Bertrand Russell (The Principles of Mathematics [1903], §037)
	A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'.