Combining Philosophers

All the ideas for Aeschylus, Antoine Arnauld and Thoralf Skolem

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7 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
16519 No one can conceive of a possible substance, apart from those which God has created [Arnauld]
     Full Idea: I am much mistaken if there is anyone who dares to say that he can conceive of a purely possible substance, …for although one talks so much of them, one never conceives them except according to the notion of those which God has created.
     From: Antoine Arnauld (Letters to Leibniz [1686], 1686.05.13), quoted by David Wiggins - Sameness and Substance 4.2
     A reaction: This idea cashes out in the 'necessitism' of Tim Williamson, and views on the Barcan formulae in modal logic.
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)
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
7810 The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling]
     Full Idea: The 'Eumenides' of Aeschylus tells how the old rule of revenge and blood feud was replaced by a due process of law before a civil jury.
     From: report of Aeschylus (The Eumenides [c.458 BCE]) by A.C. Grayling - What is Good? Ch.2
     A reaction: Compare Idea 1659, where this revolution is attributed to Protagoras (a little later than Aeschylus). I take the rule of law and of society to be above all the rule of reason, because the aim is calm objectivity instead of emotion.