13 ideas
9470 | Modal logic is not an extensional language [Parsons,C] |
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
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] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
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] |
23217 | All of our happiness and misery arises entirely from the brain [Hippocrates] |