Implication and What There is

Abstract

There is one other relation in logic that needs to be considered. That is the relation symbolized by ‘ → ’ and interpreted as ’implies, or ‘if ..., then ...’ These two interpretations reveal the existence of an ambiguity in the semantics of ‘ →. ’ My problem may be stated somewhat in this fashion: what, if anything, about what there is does the relation symbolized by ‘ → ’ and interpreted in various ways intend to mirror ? What others thought it represented is an historical question whose answer is to be found in the works of Leibniz, Aristotle, and all other logicians who laid the foundations of logical theory. But even if I should turn this into an historical study. I would then have indicated what these philosophers intended. And I am not here concerned with that type of historical study. Rather, what I want to determine is the underlying element that causes this type of relation to be introduced. In other words, why is it necessary to have such an element in a language at all?