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Ideas for 'fragments/reports', 'Mathematical logic and theory of types' and 'The Semantic Conception of Truth'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

19192	The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
	Full Idea: With our definition of truth we can prove the laws of contradiction and excluded middle. These semantic laws should not be identified with the related logical laws, which belong to the sentential calculus, and do not involve 'true' at all.
	From: Alfred Tarski (The Semantic Conception of Truth [1944], 12)
	A reaction: Very illuminating. I wish modern thinkers could be so clear about this matter. The logic contains 'P or not-P'. The semantics contains 'P is either true or false'. Critics say Tarski has presupposed 'classical' logic.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox

6407	The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
	Full Idea: The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox.
	From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2
	A reaction: A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory.

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

19187	The Liar makes us assert a false sentence, so it must be taken seriously [Tarski]
	Full Idea: In my judgement, it would be quite wrong and dangerous from the point of view of scientific progress to depreciate the importance of nhtinomies like the Liar Paradox, and treat them as jokes. The fact is we have been compelled to assert a false sentence.
	From: Alfred Tarski (The Semantic Conception of Truth [1944], 07)
	A reaction: This is the heartfelt cry of the perfectionist, who wants everything under control. It was the dream of the age of Frege to Hilbert, which gradually eroded after Gödel's Incompleteness proof. Short ordinary folk panic about the Liar?