10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Smith,P on Frege] |
10093 | The ramified theory of types used propositional functions, and covered bound variables [George/Velleman on Russell/Whitehead] |
8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Magidor on Russell] |
10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Musgrave on Russell] |
6409 | The 'simple theory of types' distinguishes levels among properties [Grayling on Ramsey] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Shapiro on Chihara] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Shapiro on Chihara] |
10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
16308 | Set theory was liberated early from types, and recently truth-theories are exploring type-free [Halbach] |