1913 | Principia Mathematica |
p.17 | 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules |
p.47 | 10093 | The ramified theory of types used propositional functions, and covered bound variables |
p.50 | 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic |
p.51 | 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality |
p.70 | 8691 | The Russell/Whitehead type theory was limited, and was not really logic |
p.122 | 18248 | A real number is the class of rationals less than the number |
p.127 | 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it |
p.148 | 10025 | Russell and Whitehead took arithmetic to be higher-order logic |
p.285 | 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers |
p.448 | 10037 | 'Principia' lacks a precise statement of the syntax |
p.448 | 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied |
p.452 | 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory |
p.459 | 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element |
I p.57 | p.175 | 12033 | An object is identical with itself, and no different indiscernible object can share that |
p.267 | p.267 | 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains |
p.44 | p.145 | 18275 | Only the act of judging completes the meaning of a statement |
p.72 | p.172 | 18208 | We regard classes as mere symbolic or linguistic conveniences |