Consistency— What’s Logic Got to Do with It?

Most modern philosophers who study logic as part of their training, know something about the development of modern logic and something about the fact that the issue of consistency had something to do with this development. In this paper, I want to explore the origin of the modern conception of the idea of consistency in logic in the work of German mathematician David Hilbert. My interest in the development of the modern idea of consistency arises from my belief that an overriding concern with a strict requirement of consistency, borrowed primarily from the rigors of modern developments in logic, has prevented latter day twentieth century philosophers from producing philosophical systems of the type produced in earlier times. To give an idea of what I mean, let me attempt to discuss the following question: How, if in any way, does an overriding concern with consistency affect philosophy? Well, it seems that some notion of consistency is operative when philosophers reason about anything. On the other hand, philosophers do not always expect that the objects of their study satisfy some consistency criteria. With only rare exceptions, do we hear a call for consistency in love, which has been an object of philosophical musing at least since Plato wrote his Symposium [Ham89] and probably long before. In fact, when asked “Consistency—What’s Love Got to Do with It?”, we would probably say “not much” unless we insist on interpreting consistency in love as love’s consistency with scientific theories about anthropology and human physiology and genetics. But that sort of perspective will take us philosophers perhaps too far from the original ideas found in the Symposium and I’m not sure how far philosophers want to get from Plato. However, if we interpret the consistency in love as love’s fitness in a philosophical system, it seems we will be back in a philosophical sort of business. Leaving the detailed discussion of the connection between modern philosophy and the notion of consistency to another occasion, let me return to the main topic of