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Ideas for 'fragments/reports', 'The Concept of Law' and 'Which Logic is the Right Logic?'

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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

10773	The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
	Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox').
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)

10777	Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
	Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7)
	A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'.