John Pollock

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all relevant reasons.

As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle(□p⊃□□p)should be considered valid. However, when philosophers and logiciansapplymodal logic to concrete problems, they rarely need principles which involve iterated modalities. For most practical purposes, principles involving only one layer of modalities are all that are needed. This suggests that if we try to construct a theory of modal logic in which there are no iterated modalities, we can avoid most of the controversy and still have a theory that is strong enough for all of the normal uses to which modal logic is put.

Epistemology is about how we can know the various things we claim to know. Epistemology is driven by attempts to answer the question, “How do you know?” This gives rise to investigations on several different levels. At the lowest level, philosophers investigate particular kinds of knowledge claims. Thus we find theories of perceptual knowledge (“How do you know the things you claim to know directly on the basis of perception?”), theories of induction and abduction (“How do you know the general truths you infer from observation of particular cases?”), theories of our knowledge of other minds, theories of mathematical knowledge, and so forth. At an intermediate level, topics are investigated that pertain to all or most of the specific kinds of knowledge discussed at the lowest level. Theories of reasoning, both deductive and defeasible, occur at this level. At the highest level we find general epistemological theories that attempt to explain how knowledge in general is possible. At this level we encounter versions of foundationalism, coherentism, probabilism, reliabilism, and direct realism. One can be doing epistemology by working at any of these levels. The levels cannot be isolated from each other, however. Work at any level tends to presuppose something about the other levels. For example, work on inductive reasoning at least presupposes that reasoning plays a role in the acquisition or justification of beliefs and normally presupposes something about the structure of defeasible reasoning.

Cognitive agents form beliefs representing the world, evaluate the world as represented, form plans for making the world more to their liking, and perform actions executing the plans. Then the cycle repeats. This is the doxastic-conative loop, diagrammed in figure one.1 Both human beings and the autonomous rational agents envisaged in AI are cognitive agents in this sense. The cognition of a cognitive agent can be subdivided into two parts. Epistemic cognition is that kind of cognition responsible for producing and maintaining beliefs. Practical cognition evaluates the world, adopts plans, and initiates action. There is a massive literature both in philosophy and artificial intelligence concerning various aspects of epistemic cognition, and large parts of it are well understood. Practical cognition is less well understood. We can usefully divide practical cognition into five parts: (1) the evaluation of the world as represented by the agent’s beliefs, (2) the adoption of goals for changing it, (3) the construction of plans for achieving goals, (4) the adoption of plans, and (5) the execution of plans. There is a substantial literature in AI concerning the construction and execution of plans, and I will say nothing further about those topics here. This paper will focus on the evaluative aspects of practical cognition. Evaluation plays an essential role in both goal selection and plan adoption. My concern here is the investigation of evaluation as a cognitive enterprise performed by cognitive agents. I am interested both in how it is performed in human beings and how it might be performed in artificial rational agents.