H. P. Grice's Gradualism

degree of belief Logic, epistemology, philosophy of science The central notion of an account holding that belief comes in degrees rather than being a simple matter of “yes” or “no.” That we have different degrees of subjective confidence in our beliefs is a basic tenet of Bayesianism, which argues that the subjective probability or degree of belief of propositions can be altered by new evidence, according to a procedure recommended by Bayes’s theorem. Beliefs can be compared in the sense that the degree of belief or subjective probability of one belief is greater than another. Degrees of belief can be analyzed in terms of the degree of belief with which a belief is actually held or of the degree of belief with which it rationally should be held. Bayesian theory allows purely subjective initial assignments of degrees of belief, but applies rational discipline to the alteration of beliefs in light of new evidence, with the expectation that there will be convergence in the degrees of belief assigned to beliefs by different investigators. For personalists such as Ramsey and de Finetti, the consistent degrees of beliefs must conform to the rules of probability calculus. This notion implies a perspective from which we may quantify beliefs and suggests a possible approach to a rigorous science of behavior. “The degree of belief that a person S has in the sentence P is a numerical measure of S’s confidence in the truth of P, and is manifested in the choices S makes among bets, actions, etc.” Garber, “Old Evidence and Logical Omniscience in Bayesian Confirmation Theory,” in Minnesota Studies in the Philosophy of Science, vol. X -- degree of confirmation Logic, philosophy of science A term introduced by Carnap. If one knows what observations would be relevant to the truth or falsity of a statement, the statement is said to be confirmable. How much evidence, then, is required for one to say that the statement is actually confirmed? The degree of confirmation is the measure by which generalized statements may be ranked in order of acceptability. It is a quantitative concept of confirmation and of probability. If we take h to be a statement, e to be evidence, q to be a real number between 0 and 1, and c to be a symbol for degree of confirmation, then c(h.e) = q or the degree of confirmation of h with respect to e is q. “Given certain observations e and a hypothesis h (in the form, say, of a prediction or even of a set of laws), then I believe it is in many cases possible to determine, by mechanical procedures, the logical probability, or degree of confirmation, of h on the basis of e.” Carnap, Philosophical Foundations of Physics