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Ideas for 'Science and Method', 'Laudatio: Prof Ruth Barcan Marcus' and 'An Axiomatization of Set Theory'

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2 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
15130 If a property is possible, there is something which can have it [Williamson]
     Full Idea: Barcan's axiom says if there can be something that has a certain property, then there is something that can have that property. It and its converse are not obviously correct or incorrect. They claim that it is non-contingent what individuals there are.
     From: Timothy Williamson (Laudatio: Prof Ruth Barcan Marcus [2011], p.1)
     A reaction: Williamson defends the two Barcan formulas, but the more I understand them the less plausible they sound to me.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
     Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong.
     From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1