Combining Philosophers

All the ideas for John Austin, Theodosius and Thoralf Skolem

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879	Axiomatising set theory makes it all relative [Skolem]
	Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296)

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

13536	Skolem did not believe in the existence of uncountable sets [Skolem]
	Full Idea: Skolem did not believe in the existence of uncountable sets.
	From: Thoralf Skolem (works [1920], 5.3)
	A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view.

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

17878	If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
	Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293)

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880	Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
	Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299)
	A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881	Mathematician want performable operations, not propositions about objects [Skolem]
	Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300)

15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds

1799	If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]
	Full Idea: We can't say the school of Pyrrho is sceptical, because the motion of the mind in each individual is incomprehensible to others, so we don't know Pyrrho's disposition.
	From: report of Theodosius (Chapters on Scepticism [c.100 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.8

25. Social Practice / D. Justice / 2. The Law / d. Legal positivism

20930	The existence of law is one thing, its merits and demerits another [Austin,J]
	Full Idea: The existence of law is one thing; its merit and demerit another. Whether it be or be not is one enquiry; whether it be or be not conformable to an assumed standard is a different enquiry.
	From: John Austin (Lectures on Jurisprudence [1858], p.214), quoted by Jens Zimmermann - Hermeneutics: a very short introduction 6 'Positivism'
	A reaction: It is impossible to contest this point, but the issue is whether there is nothing more to law than its written existence.