As may be apparent, the contradiction in this example arises from step (2), where the string '~x' is assumed to represent a valid proposition x. This assumption, however, is consistent with the formalist view, which contends that logic is concerned only with the external form of propositions and not with their semantic content. Here the string ~x is syntactically correct ("well-formed," in logicians' language). It is neither true nor false, however, because it does not represent a valid proposition—that is, one formed in a coherent manner from properly grounded concepts.

In this course, therefore, logic will be understood, not merely as a method for manipulating symbolic strings, but as the tool by which we grasp truths about reality. The methods of formal and symbolic logic will be applied only to concepts and propositions grounded in the real world.