A Program for Syntax

Abstract

The program for syntax which I describe here is not one I can claim as specially my own. The two basic ideas are due to Frege: analysis of an expression into a main functor and its argument(s), and distinction among categories of functors according to the categories of arguments and values. The development of a handy notation for categories, and of an algorithm to test whether a string of expressions will combine into a complex expression that belongs to a definite category, is due to the Polish logicians, particularly Ajdukiewicz. My own contribution has been confined to working out details. So my program is not original, but I think it is right in essentials; and I am making propaganda for it by working it out in some particular instructive examples. I think this is all the more called for because some recent work in syntax seems to have ignored the insights I am trying to convey.