impredicativity造句

• A prototypical example is intuitionistic type theory, which retains ramification but discards impredicativity.
• By this method impredicativity could be avoided.
• Hermann Weyl's interest in intuitionistic logic and impredicativity appears to have resulted from his reading of Husserl.
• But this separation into orders makes it impossible to construct the familiar analysis, which [ see Kleene's example at Impredicativity ] contains impredicative definitions.
• "' Russell's no-class theory is the root of the problem "': G鰀el believes that impredicativity is not " absurd ", as it appears throughout mathematics.
• The opposite of impredicativity is predicativity, which essentially entails building stratified ( or ramified ) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over.
• This is a predicativity restriction, though NFI is not a predicative theory : it admits enough impredicativity to define the set of natural numbers ( defined as the intersection of all inductive sets; note that the inductive sets quantified over are of the same type as the set of natural numbers being defined ).
• "' A pernicious impredicativity : ? = NOT-? "': To create a pernicious paradox, apply input ? to the simple algebraic-logic equivalent of the symbolic-logical ? = NOT-? for truth values 1 and 0 rather than " true " and " false ".
• "' Fatal impredicativity in the definition of the unit class "': The problem that bedeviled the logicists ( and set theorists too, but with a different resolution ) derives from the ? = NOT-? paradox Russell discovered in Frege's 1879 " Begriffsschrift " that Frege had allowed a function to derive its input " functional " ( value of its variable ) not only from an object ( thing, term ), but from the function's own output as well.