As I understand the term “acceptability,” it designates justified or rational believability. To say that a given proposition is acceptable for a person is to say that it is epistemically all right for the person to adopt that proposition as a belief. In Section 3.2, it was already mentioned that the term “acceptability” is used both in a categorical and in a graded sense. Both the categorical and the graded notion of acceptability play a vital role in our epistemic life; we go routinely back and forth between thinking and speaking about what we deem acceptable and about the degrees to which we deem various things acceptable. Neither mode is to be dismissed off-hand as being loose talking and thinking, nor is it even clear on what grounds one mode could be said to be inferior or subservient to the other. Accordingly, many philosophers hold that we need both an epistemology of belief and an epistemology of degrees of belief.

It would seem that we can have both the attitude of deeming categorically acceptable and the attitude of deeming acceptable to a certain degree vis-à-vis conditionals as well. That, at any rate, is what a number of authors have been supposing in their work on either the categorical acceptability conditions of conditionals or their graded acceptability conditions (or both). It was noted in Section 1.1 that the issue of the acceptability of conditionals is one of the rare topics on which philosophers tend to agree. In the previous chapter, we saw that most philosophers agree – wrongly, as was argued – on what the probabilities of conditionals cannot be, whereas the question of what these probabilities are is a matter of ongoing debate. With respect to the issue of acceptability, the agreement is more substantial. Many philosophers agree on what the graded acceptability conditions of conditionals are, and there is also a good deal of agreement on the categorical acceptability conditions.

Thus one might think that if a whole chapter of this book is to be devoted at all to issues – graded and categorical acceptability of conditionals – on which virtually everyone agrees, the chapter will be a short one. Instead, this chapter is the longest in the book. The reason for this is that I believe the near-consensus on both issues to be misguided, and arguing against the mainstream requires proper backing.