22 ideas
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |