19 ideas
9470 | Modal logic is not an extensional language [Parsons,C] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
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] |
9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
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] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |