According to decision theory, the rational initial action in a sequential decision-problem may be found by backward induction or folding back. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the depth of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, first, that (...) the traditional solutions of certain games depend on knowledge which exceeds depth limits, and that these solutions therefore cannot be shown rational in the usual sense. Then, for that related reason even folding back solutions of one-person problems cannot be! A revision of our notion of rational choice is proposed, analogous to the reliabilist account of knowledge of Goldman and others, by which this paradox is resolved. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

Positive thinkers love Watty Piper's The little engine that could. The story features a train laden with toys for deserving children on the other side of the mountain. After the locomotive breaks down, a sequence of snooty locomotives come up the track. Each engine refuses to pull the train up the mountain. They are followed by a weary old locomotive that declines, saying "I cannot. I cannot. I cannot." But then a bright blue engine comes up the track. He manages (...) to chug over the mountain by averring "I think I can. I think I can. I think can.". (shrink)

The problem of cooperation for rational actors comprises two sub problems: the problem of the intentional object (under what description does each actor perceive the situation?) and the problem of common knowledge for finite minds (how much belief iteration is required?). I will argue that subdoxastic signalling can solve the problem of the intentional object as long as this is confined to a simple coordination problem. In a more complex environment like an assurance game signals may become unreliable. Mutual beliefs (...) can then bolster the earlier attained equilibrium. I will first address these two problems by means of an example, in order to draw some more general lessons about combining evolutionary theory and rationality later on. (shrink)

This paper is intended to show how epistemologists can profit from the study of ways in which 'know' is vague. Topics include the kk thesis, Incorrigibility of sense data, A resemblance between infinity and vagueness, Common knowledge, Naive holism, Question-Begging, Epistemic universalizability, The prediction paradox, The completability of epistemology, And harman's social knowledge cases.

Epistemologists have profited from studies of the ways in which ‘know’ is ambiguous. We can also profit by studying the ways in which ‘know’ is vague. After classifying sources of vagueness for ‘know,’ I spend the second section examining theories of vagueness. With the exception of the theory that vague predicates are incoherent, which I try to refute, we need not take a stand on a particular theory to show that the vagueness of knowledge has substantive epistemological implications. The third (...) section supports the thesis through a survey of ways in which appeals to vagueness can be applied to the field's issues. First, I show how higher order vagueness is evidence against the KK thesis, the incorrigibility of sense data, and the completability of epistemology. An interesting resemblance between infinity and vagueness provides the point of departure for the next type of application. For this resemblance suggests a new way of handling apparently infinite belief structures. The approach is illustrated with an analysis of common knowledge. The third type of application concerns the ways in which disguised sorites creep into our thinking about knowledge. In addition to brief illustrations concerning naive holism, question begging, and an objection to incorrigibilism, I provide more detailed illustrations involving Jonathan Adler's sceptical appeal to epistemic universalizability, the prediction paradox, and William Lycan's objection to Gilbert Harman's social knowledge cases. I conclude with some general remarks on the lessons to be learned from the vagueness of knowledge. (shrink)