1 Nothing rests on the representation of time here except the rather ordinary intuition that changes of belief can be ordered in terms of their causal dependence on each other. There is for example no reason to think that every segment of time need be the same length, or even that every segment have an effective length at all.

2 See my “Towards a Theory of Rational Inference”, Philosophical Studies, 30 (1976), 259–267Google Scholar, for a more comprehensive account of the significance of these constraints. See also Eberle, R., “A Logic of Believing, Knowing, and Inferring”, Synthese 26 (1974), 356–382CrossRefGoogle Scholar, for a formally developed logic of inference which is similar but not identical to the one presented here.

3 See Chisholm, R.M., “On a Principle of Epistemic Preferability”, Philosophy and Phenomenologial Research 30 (1969), 214–30Google Scholar, and Chisholm, R.M. and Keim, R.G., “A System of Epistemic Logic” Ratio 14 (1972), 99–115Google Scholar, for another approach to epistemic logic based on epistemic preference.

4 Harman, Gilbert, Thought (Princeton University Press, 1973); see especially Chapter 1, pp. 19–23Google Scholar, and Chapters 11 and 12.

5 Edmund L, Gettier, “Is Justified True Belief Knowledge?”, Analysis, Vol. 23, pp. 121–123Google Scholar. The Gettier examples (like the lottery paradox) may be seen to rest on a confusion between the two kinds of knowledge producing relation: the evidential relation embodied in acceptance rules and the justification relation which obtains between a person's beliefs and the inferences a person makes on the strength of those beliefs.

6 Much of the literature on the Gettier examples is obscure because the differences in these two kinds of reactions are ignored. For example Lehrer, in his recent book, Knowledge (Clarendon Press 1974) proposes a complicated coherence account of justification which fails because he confuses the logical relation of inference with the psychological relation which exists between an agent's beliefs as a result of an actual inference. To see this note that on Lehrer's account, A) S is completely justified in believing that p if and only if within the corrected doxastic system of S,p is believed to have a better chance of being true than the denial of p or any other statement that competes with p, and B) S is completely justified in believing thatp in a way that does not depend on any false statement if and only if S is completely justified in believing thatp in the verific alternative to the corrected doxastic system of 5. The effect of these definitions is to make justification a matter of coherence; as a result counter examples are easy to produce, e.g.: S has two roommates Tom and Bill. S is completely justified in believing that Tom has a car and that Bill does not. Both beliefs were true until yesterday when unknown to S Tom sold Bill his car. Asked if exactly one of his roommates has a car S replied affirmatively. His belief that one of his roommates has a car is true, completely justified and completely justified in a way which does not depend upon any false statement. This is so because S's corrected doxastic system contains a) S believes that Tom has a car, b) S believes that Bill has no car and c) S believes that Bill and Tom are his only roommates.; S's verific alternative contains: a˚) S believes that it is false that Tom has a car, b˚) S believes that it is false that Bill has no car, c˚) S believes that Bill and Tom are his only roommates. Both sets entail that exactly one roommate has a car. But S does not known that exactly one roommate has a car, because his belief is based on an inference producing knowledge only on the condition that he knows that Tom has a car and that Bill does not, neither of which he can know as they are false.