ABSTRACT

This conclusion presents some closing remarks on the preceding chapters of the book. Semantic categories of natural language do not coincide with those of the predicate calculus, and that some are implemented in them in different ways. Many, probably most sentences of natural language cannot be translated by sentences of the predicate calculus with the same, or even roughly the same semantic characteristics. Frege showed that contrary to what the grammar of natural language has led us to think, common nouns, as used in natural language, are not logical subjects but logical predicates. The book showed that Frege was wrong in his analyses. The predicate calculus is hardly ever used in mathematics outside mathematical logic. In the book, a deductive system for natural language, comparable in its deductive power to the first order predicate calculus, was developed. Logicians' interest in a system of formal inferences with propositional combinations of multiply quantified sentences may be served by that system as well.