A Recursive Semantics for Defeasible Reasoning

One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. In light of our pervasive ignorance, we cannot get around in the world just reasoning deductively from our prior beliefs together with new perceptual input. As our conclusions are not guaranteed to be true, we must countenance the possibility that new information will lead us to change our minds, withdrawing previously adopted beliefs. In this sense, our reasoning is “defeasible”. The question arises how defeasible reasoning works, or ought to work. In particular we need rules governing what a cognizer ought to believe given a set of interacting arguments some of which defeat others. That is what is called a “semantics” for defeasible reasoning, and this chapter will propose a new semantics that avoids certain clear counter-examples to all existing semantics. 1. Reasoning in the Face of Pervasive Ignorance One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. Reflect on how little you really know about all the individual matters of fact that characterize the world. What, other than vague generalizations, do you know about the apples on the trees of China, individual grains of sand, or even the residents of Cincinnati? But that does not prevent you from eating an apple while visiting China, lying on the beach in Hawaii, or giving a lecture in Cincinnati. Our ignorance of individual matters of fact is many orders of magnitude greater than our knowledge. And the situation does not improve when we turn to knowledge of general facts. Modern science apprises us of some generalizations, and our experience teaches us numerous higher-level although less precise general truths, but surely we are ignorant of most general truths. In light of our pervasive ignorance, we cannot get around in the world just reasoning deductively from our prior beliefs together with new perceptual input. This is obvious when we look at the varieties of reasoning we actually employ. We tend to trust perception, assuming that things are the way they appear to us, even though we know that sometimes they are not. And we tend to assume that facts we have learned perceptually will remain true, at least for awhile, when we are no longer perceiving them, but of course, they might not. And, importantly, we combine our individual observations inductively to form beliefs about both statistical and exceptionless generalizations. None of this reasoning is deductively valid. On the other hand, we cannot be criticized for drawing conclusions on the basis of such non-conclusive evidence, because there is no feasible alternative. Our non-deductive reasoning makes our conclusions reasonable, but does not guarantee their truth. As our conclusions are not guaranteed to be true, we must countenance the possibility that new information will lead us to change our minds, withdrawing previously adopted beliefs. In this sense, our reasoning is “defeasible”. That is, it makes it reasonable for us to form beliefs, but it can be “defeated” by considerations that make it unreasonable to maintain the previously reasonable beliefs. If we are to understand how rational cognition works, we must know how defeasible reasoning works, or ought to work. This chapter attempts to answer that question.