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Ideas for 'Parmenides', 'Principles of Theoretical Logic' and 'Ontology and Mathematical Truth'

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2 ideas

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC

17750	The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]
	Full Idea: The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann.
	From: report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9967	'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
	Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory.
	From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116)
	A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets.