One of my very longstanding views is that there are no such things as degrees of belief: degrees of belief, or credences, are fictitious artifacts whose popularity in philosophy is due far more to its flattering the analytical tastes and skills of a certain kind of philosopher than to its actually arising out of a tenable analysis of belief. I always regarded them as a bit speculative and dubious, I think, and have been outright against them since my first reading of Newman's An Essay in Aid of a Grammar of Assent. This is definitely a minority position; for a long time it was very difficult to find anyone rejecting the notion of degrees of belief. Crispin Sartwell and P. M. S. Hacker had come out rejecting it in print when I was in graduate school, and up to that point there hadn't been much else on the Nay side. Nor could one find it even being used as a punching-bag. The only work by a proponent of degrees of belief that even really treated rejection as an option serious enough to look at in some detail was H. H. Price's Belief, from 1969. I have noticed, however, over the past decade that there has been, while not exactly a major shift, an increasing trickle of people willing to question old certainties about the matter, even if such questioning doesn't lead them to rejecting. Eriksson and Hájek, for instance, had a very nice paper in 2007 that noted problems with the usual accounts, although they eventually conclude that 'degrees of belief' should just be taken as a primitive.
Andrew Moon has recently come out with a paper, "Beliefs do not come in degrees", that argues the skeptical position in greater detail than has been done before. Moon argues against three arguments -- really, probably better thought of as classes or families of arguments -- in favor of degrees of belief, which he calls the confidence argument, the argument from natural language, the firmness argument. He presents and defends arguments on the opposing side, including a different argument from natural language, and what he calls the intention argument and the determinables argument. The determinables argument is particularly interesting.
If something comes in degrees, Moon argues, it makes sense to analyze it into two components: there is a determinable property that comes in a determinate form, and it is possible for the determinate forms relative to a determinable to have a certain order relative to each other, as well. So, for instance, being red is a determinable; being light red and being dark red are determinates of it. What is more, these determinates have an orderly relation to each other that we can characterize as more and less red: light red is less red than dark red, even though at the same time light red is red just as dark red is. On the basis of this kind of analysis, Moon proposes his principle for how things with degrees work, the Determinables-Determinates Condition:
If P comes in degrees, then P is a determinable with a corresponding set of determinates that are degree-ordered.
To this Moon adds what he calls the Anti-Threshold Condition:
If P1 is a determinable that comes in degrees with a corresponding set D1 of determinates that are degree-ordered, P2 is a determinable with a corresponding set D2 of determinates, and D2 is a proper subset of D1, then P2 does not come in degrees.
So, for instance, you can be more or less wealthy, but not more or less a millionaire, although millionaires are a proper subset of wealthy people. I think the Anti-Threshold Condition is the part of the argument that needs work. Consider the case of P1 = 'being red', P2 = 'being scarlet'. The determinates for P2 are a proper subset of the determinates for P1, but P2 certainly comes in degrees. Moon is on very plausible ground in thinking that there is some way in which threshold properties are exclusive of degreed properties, but we need a better way of identifying when a property is threshold and when it is degreed. However, Moon's argument primarily turns not on this particular condition so much as the difference between threshold properties and degreed properties -- the bare fact of proper subsethood is not sufficient.
If belief comes in degrees, then, by the Determinable-Determinates Condition, there must be a determinable with a set of ordered determinates. Most of Moon's argument is that there is no plausible candidate for such a determinable. Being confident won't work because a tiny amount of confidence is not belief. If, on the other hand, one holds that belief is reaching a certain threshold of confidence, then belief is a threshold property, not a degreed property: it consists not of degrees but of simply having overtopped a given minimal level of something. Even if confidence and belief are related in this way (which is doubtful, since there are reasons to think that confidence and belief come apart in a number of ways), it would imply that belief is a category rather than a scale.
As noted, I think there is more work needed on this argument; but it is certainly true that the degree-of-belief position needs to be examined more closely in terms of the metaphysics of degrees.
Various Links of Interest
* Dale E. Miller, John Stuart Mill and Charlottesville
* How and Why Did the Viking Age Begin?
* Josef Joffe, The First Totalitarian, reviews Victor Sebestyen's biography of Lenin.
* Andrew Janiak, Who was that Marquise? Rediscovering forgotten voices of women in philosophy.
* An audio version of Charles Williams's ghost story, Et In Sempiternum Pereant. You can also read it online. It is a sequel short story to his novel, Many Dimensions, which was a fortnightly book here in 2013. As with MD, its central action is a self-offering that saves.
Jules Verne, The Mysterious Island
Tanith Lee, The Secret Books of Paradys, I & II
Cajetan, Commentary on St. Thomas Aquinas' On Being & Essence
Edith Stein, The Hidden Life: Essays, Meditations, Spiritual Texts
Jacques Maritain, The Peasant of the Garonne