Conditionalization and observation

I take bayesianism to be the doctrine which maintains that (i) a set of reasonable beliefs can be represented by a probability function defined over sentences or propositions, and that (ii) reasonable changes of belief can be represented by a process called conditionalization. Bayesians have produced several ingenious arguments in support of (i); but the equally important second condition they often seem to take completely for granted. My main aim is to fill this gap in those bayesian positions which characterize reasonable belief directly as a probability function. Thus, what follows applies equally to the bayesian personalists' views which characterize reasonable belief as having subjective sources and to views such as that of Carnap which attempt to explicitly define a function which characterizes the degree of belief it would be objectively reasonable for an idealized rational agent to have in a given proposition in stated circumstances. Many frequentist views are also classifiable as bayesian, and I will briefly discuss the justification of condition (ii) from the point of view of a frequency interpretation of probability or reasonable degree of belief. Along the way I will also have occasion to touch on the connection between conditionalization and observation. Throughout the discussion I will rely on several common bayesian presuppositions. The object of study is a notion of belief, perhaps most aptly described as degree of confidence, which can be ordered as to strength and admits of quantatization. Such beliefs, or degrees of confidence, are assumed to reveal themselves in an agent's disposition to make bets voluntarily or under duress. The agent whose beliefs are under discussion is assumed to be an ideal logician, and the set of propositions about which the agent has beliefs is assumed to be closed under all logical operations. Also, the set of propositions for which the agent entertains beliefs is assumed to be fixed. Quite clearly, when this assumption is violated, the bayesian model does not apply; and the most cogent arguments against