It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but on the ``logical'' conception of *set* which motivates naive set theory. The accepted solution is to replace this with the ``iterative'' conception of *set*.

I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of *set* and the thesis of absolutism that should be rejected.

This dissertation considers this question and develops two new Bayesian updating rules as a response to it. These rules refine the requirements that Bayesianism already provides us with by supplementing these requirements with two formal accounts of evidence.

In chapter two, I set some of the groundwork for the dissertation by comparing the problem of how evidence, and the experience that gives rise to it, constrain an update to two problems in the Bayesian literature that have similar structures, but that are better understood.

In chapters three and four, I look at some places where the literature has foundered on the lack of an account of evidence. I consider two discussions that illustrate how the lack of a constraint on how experience gives rise to an update causes us to see problems where there aren't any and to overlook problems where they do indeed exist.

In chapter five, I develop a new account of the structure of Bayesian justification, which I call Bayesian coherentism. Bayesian coherentism is an updating norm that is motivated, both by the problems of the previous chapters and by the desire to provide a unified account of the structure from which updates on certain and uncertain evidence proceed.

Finally, in chapter six, I develop a different norm that is guided by considerations similar to those that motivate Bayesian coherentism, but that is also compatible with the recently popular idea that there are no norms of diachronic rationality.

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