Note in Confirmation

In his article "Sqme proposals for the solution of the Carnap-Popper discussion on 'inductive logic''', this journal, vol. 6 (1968), pp. 5-25, Batens distinguishes, in section 4, two explicanda of the intuitive concept 'confirmation'. The first, confl' is concerned with degrees of certainty, the second, conf2, with the degree to which a hypothesis is confirmed by facts. Batens divides the possible explicata of conf2 into two sorts of functions. TCb-functions are such that only confirmation-aspects are judged, whereas TCa-functions judge contentand confirmation-aspects together. As an adequate TCb-function Batens proposes, in section 6, his K-function (P is an inductive probability function): P(e,h) K(h,e) = ----P( e,h) + P( e,h) The K-values range from 0, falsification, via !, neutral confirmation, to 1, verification. Batens does not propose a TCa-function but he formulates, in section 5, three properties which such a function must have in any case: a with respect to tautological evidence, hypotheses with a higher content must receive a higher value, b the same must hold for verified hypotheses, c the value of a hypothesis must increase, if the relative probability of the hypothesis increases, and decrease, if the relative probability decreases. The properties a and b can be combined and generalised in a very natural way to the following property (K is Batens' TCb-function, L is a TCafunction): abo ifK(hl,e) = K(h2,e) then, ifP(hl) ~ P(h2), then L(hl,e) ~ L(h2,e). It is easy to verify that the following definition of L has the properties ab and c, and hence a, band c: