Abstract

Godel wrote an ontological argument, which he worked on sporadically for thirty years. Godel was allegedly enthralled by the argument and believed it to be a satisfactory logical investigation in favor of the existence of God. The argument was later revised by C. Anthony Anderson. Although the argument itself is a formal one given in a third order modal logic with a property abstraction operator, the formal semantics for the argument have never been worked out. The focus of most of the philosophical discussion of the argument to date has been centered on the viability of the axioms themselves. In this dissertation, however, I want to explore some of the implicit philosophical assumptions in the argument that may have been overlooked, for I contend that problems with the argument have more to do with the problem of developing an applied semantics for Modal Logic in general, than with the specific nature of the axioms. To show this, I first develop the formal semantics of third order modal logic necessary to interpret the argument and prove a completeness result for the system. I then examine the philosophical implications of applying NL-interpretations to the third order structures for the Ontological Argument. I conclude that the argument is untenable because an adequate applied semantics can not be demonstrated