Non-Additive Degrees of Belief

This paper starts from the position that belief is primarily quantitative and not categorical, i.e. we generally assume the existence of various degrees of belief. This corresponds to the observation that most human beings experience belief as a matter of degree. We follow the usual convention that such degrees of belief are values in the [0, 1]-interval, including the two extreme cases 0 for “no belief” and 1 for “full belief”.1 Any other value in the unit interval represents its own level of certitude, thus allowing the quantification of statements like “I strongly believe . . .” or “I can hardly believe ...”. In this sense, we make a strict distinction between belief and faith, the latter always being absolute. This position is in perfect accordance with the following definition of belief: