A Research On R.Montague’s Intensional Logic

According to Frege’s thought about intensional problem, this paper proposes two standards evaluating the intensional logic, i.e. the standard of describing the intension of an expression and the standard of solving the intensional puzzles. As to this, there are two approaches in modern intensional logic, that is, the reductionism approach (founded by R.Carnap) and the intensionism approach (founded by A.Church). From the view of the history of intensional logic, R.Montague’s intensional logic inherits not only the syntax of the simple type system by Church, but also the construction of intensional semantics by Carnap. This paper aims to interpret Montague’s "universal grammar" and IL system’s syntax and semantics from the motivation he proposed the intensional logic, and then evaluates it. In this paper’s view, Montague trys to solve the contradiction, between the rigor of extensional logic and natural language’s ambiguity and intensionality, in a rigorous mathematical way. This is an ambitious attempt, anyway. However, Montague’s IL system can solve the puzzlel only, but cannot solve the puzzle2and puzzle3. In post-Montague times, many logicians attempt to cover the shortage of Montague’s system, thus further improving the study of the intensional problem. For these work, this paper reveals the dilemma faced by intesional logic, and proposes it is impossible to use one general intensional standard to improve intesional logic.