ABSTRACT
The calculus of classical first-order predicate logic is much more complex than that of classical propositional logic; and what is also more complex are its interpretations in natural language. Beside this, we can import, into predicate logic, all the modifications and extensions of classical propositional logic that we have considered. We can also consider introducing brand new kinds of logical constants, such as new quantifiers or constants of wholly new categories (such as, for example, Russell’s iota inversum or Hilbert’s epsilon). What comes especially naturally is the introduction of predicates of higher-orders, which leads us to predicate logic of the second- and higher-orders and ultimately to categorial and lambda-categorial grammar, which appears to be the most general type of logical language.
