Combining Texts

All the ideas for 'Scientific Explanation', 'An Axiomatization of Set Theory' and 'Logical Analysis of Gestalt Concepts'

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4 ideas

2. Reason / F. Fallacies / 4. Circularity
9355 One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt]
     Full Idea: An argument is 'premise-circular' if it aims to establish a conclusion that is assumed as a premise of that very argument. An argument is 'rule-circular' if it aims to establish a conclusion that asserts the goodness of the rule used in that argument.
     From: report of R.B. Braithwaite (Scientific Explanation [1953], p.274-8) by Michael Devitt - There is no a Priori §2
     A reaction: Rule circularity is the sort of thing Quine is always objecting to, but such circularities may be unavoidable, and even totally benign. All the good things in life form a mutually supporting team.
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
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
     Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.
     From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2
     A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this.
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
12887 A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
     Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
     From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
     A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.