I've recently got interested in degrees of belief. (Hang around Canberra long enough and it's bound to happen.) I've been particularly enjoying a paper by Lina Eriksson and Al Hajek called 'What Are Degrees of Belief' (forthcoming in a Studia Logica special issue on formal epistemology, edited by Branden Fitelson, to appear 2007). I won't go into the details of their paper here since it is not publicly available yet. But here's something a bit different that I started thinking about after reading their paper and chatting to Al about it.
(Caveat: I don't know much about the literature on this topic, so I'm making no claims to originality.)
It would be nice to have a unified way of explicating the notions of belief and degree of belief. My hunch is that the notion of commitment - which clearly has both on/off and gradable aspects - can help. Belief could be explicated as commitment in the on/off sense, degrees of belief as degrees of commitment in the gradable sense.
The tricky bit is going to be specifying the right notion of commitment. Here are some of the things it's not:
- the kind of commitment you take on by making a promise
- the kind of commitment you have to a proposition p in virtue of believing something which entails p (thanks to Al for this one)
- the kind of commitment you can have to a cause or a person.
Here are some things that might help pin down the right notion:
- it's a propositional attitude
- we aim to have this kind of commitment in the on/off way to a proposition p only if p is true.
Incidentally, some readers of this blog may be interested to know (if they don't already) that Studia Logica is currently calling for papers on vagueness. (I just spotted this while finding the link for the above reference.)