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This chapter develops and defends the thesis that we can know probabilistic contents. It is argued that we can get probabilistic knowledge in all the same ways that we get propositional knowledge, including by testimony, inference, memory, and a priori reflection. In addition, there are several reasons to think that we can have perceptual knowledge of probabilistic contents by having perceptual experiences that have probabilistic contents. Probabilistic beliefs can have many traditional epistemic virtues, including factivity, reliability, safety, sensitivity, and aptness. They can also exhibit the same sort of epistemic failure exhibited by justified full beliefs that fail to be knowledge. The chapter concludes by defending several applications of probabilistic knowledge in the philosophy of language. For instance, probabilistic knowledge can help us diagnose misguided criticism of conventionally female speech.

This chapter develops and defends the thesis that we can believe probabilistic contents. Probabilistic contents are not merely propositions about probabilities; rather, they are sets of probability spaces over propositions. For example, you have .6 credence that Jones smokes just in case you believe a certain set of probability spaces, namely those that assign .6 probability to Jones smoking. A central question of this chapter is why we should think that credences are beliefs in probabilistic contents, as opposed to attitudes of degreed belief in propositions. The answer is that the contents of belief are the objects that play various theoretical roles, such as explaining rational action, grounding relations of disagreement between subjects, and grounding relations of consistency and entailment between beliefs—and probabilistic contents do in fact play each of these roles.

This chapter develops and defends the thesis that we can assert probabilistic contents. The chapter begins by recounting some familiar arguments against the standard view that we only ever assert propositions. A probabilistic theory of assertion is then defended with three novel arguments. These arguments are less empirical than familiar arguments against the standard view, and more foundational in character. It is argued that probabilistic contents of assertion provide a unified account of how we communicate probabilistic beliefs and full beliefs, a unified account of belief and assertion, and an adequate account of how probabilistic beliefs can figure in joint reasoning and guide our collective actions. The chapter concludes with some remarks about probabilistic models of communication, as well as remarks about the conclusions that we should draw from contemporary debates about the semantics of epistemic modals.

It is natural to wonder whether we might use traditional notions of epistemic possibility or evidential probability to address the case for probabilistic knowledge in chapter 5, without embracing the revisionary thesis that we can know probabilistic contents. This chapter spells out the shortcomings of several such proposals. For instance, it is argued that these proposals fail to predict that probabilistic knowledge is factive. The second half of the chapter explores this notion of factivity at length. It is argued that ascriptions of probabilistic knowledge can themselves have probabilistic contents. The theory of epistemic vocabulary defended in this book is compared and contrasted with existing expressivist and relativist theories of epistemic modals. Finally, it is argued that the analog of truth for degrees of belief is not agreement with objective chance, but rather truth itself.

This chapter defends a semantics for epistemic modals and probability operators. This semantics is probabilistic—that is, sentences containing these expressions have sets of probability spaces as their semantic values relative to a context. Existing non-truth-conditional semantic theories of epistemic modals face serious problems when it comes to interpreting nested modal constructions such as ‘it must be possible that Jones smokes’. The semantics in this chapter solves these problems, accounting for several significant features of nested epistemic vocabulary. The chapter ends by defending a probabilistic semantics for simple sentences that do not contain any epistemic vocabulary, and by using this semantics to illuminate the relationship between credence and full belief.