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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox

[problem with concepts which describe themselves]

2 ideas

16475	A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell]
	Full Idea: A predicate is 'heterological' when it cannot be predicated of itself; thus 'long' is heterological because it is not a long word, but 'short' is homological. So is 'heterological' heterological? Either answer leads to a contradiction.
	From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5)
	A reaction: [Grelling's Paradox] Yes: 'heterological' is heterological because it isn't heterological; No: it isn't, because it is. Russell says we therefore need a hierarchy of languages (types), and the word 'word' is outside the system.

10631	If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
	Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not.
	From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)