Combining Texts

Ideas for 'The Sayings of Confucius', 'The Metaphysics of Causation' and 'Mathematical logic and theory of types'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

10373	Logical form can't dictate metaphysics, as it may propose an undesirable property [Schaffer,J]
	Full Idea: Logical form should not have the last word in metaphysics, since it might predicate a property that we have theoretical reason to reject.
	From: Jonathan Schaffer (The Metaphysics of Causation [2007], 1.3.1)
	A reaction: These kind of warnings need to be sounded all the time, to prevent logicians and language experts from pitching their tents in the middle of metaphysics. They are welcome guests only,

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.