ABSTRACT
A full century after the publication o f his Grundgesetze der Arithmetik, Gottlob Frege (1848-1925) remains among the most discussed, articulated, praised and criticized philosophical thinkers. However, his work has yet to be fully explicated or evaluated. This is in part because a full assessment o f his logical, semantic and philosophical views could only be possible if those views were developed in greater detail than Frege himself managed in his lifetime. In particular, he failed to develop his logical system sufficiently in order to capture fully within it the complexity o f his notable theories regarding semantics, meaning and language. Filling in this gap in the interpretation o f Frege’s philosophical position is necessary in part simply because doing so will give us a better understanding of what his logical and semantic views actually were. Moreover, there are certain prominent criticisms and potential problems with his philosophy that can only be properly recognized and evaluated when this gap is
filled in. The primary purpose o f this work is to redress this void in Frege’s work. In
later chapters, I shall expand upon his logical system so that it does better justice to his core tenets in the philosophy o f language, namely, the theory o f Sinn and Bedeutung. Before doing so, it will be necessary to discuss, develop and explicate certain aspects o f his logical and semantic views, which will involve engaging in controversial matters of interpretation. It will also require examining previous attempts at capturing broadly Fregean semantics within systems o f logic. Once a truly Fregean logical calculus is in place, we shall then be in a better place to evaluate Frege’s philosophical views. It will be discovered that eliminating this gap in his work provides him with the ability to respond to
certain objections to his views that appeared threatening only because certain aspects o f those views had not been fully explicated. However, perhaps o f greater interest, it will also be discovered that his views contain internal problems and inconsistencies that have hitherto gone unnoticed and unaddressed for the very same reason. In particular, I show that if Frege’s logical system is developed to include his semantic views, it becomes possible to demonstrate certain Cantorian and semantical paradoxes within it, including paradoxes that do not rely on the questionable aspects of his extant system responsible for previously identified paradoxes. These findings are then further discussed in the attempt to understand the source o f the difficulties within Frege’s views, in general, and vis-à-vis the views o f others.
