Carnap-Confirmation, Content-Cutting, & Real Confirmation

Since Carnap's notion of confirmation as probabilistic favorable relevance violates the intuitive Hempelian transmittability condition that confirmation of a hypothesis be transmitted to all the content of the hypothesis it cannot capture some key aspects of our intuitive notions of confirmation and inductive support. After all, if confirming a theory does not mean confirming those parts of the theory concerning the future why should we care about confirmation? An alternative notion of confirmation, called real confirmation, which satisfies the transmittability condition is defined through recourse to the new notion of (logical) content I have explicated elsewhere. Basically, evidence e is taken to really confirm h iff e raises the probability of every content part of h. Under the traditional notion of content, where every contingent consequence of h counts as a content part of h, this definition would be of little use, since typically e always is unfavorably relevant to some consequence of h, in particular, the consequence h v ~e. The important point is that under the new notion of content not every consequence of a proposition counts as part of its content, for instance ~e v h is not part of the content of h. This new notion of content is then used to define the notion of evidence e cutting the untested content of hypothesis h. The important point here is that there is a tendency to believe that where evidence e raises the probability of h but e does not deductively entail h, then e inductively confirms h. Against this it is argued that there are cases where e does not entail h yet e deductively confirms h through deductively cutting the untested content of h. Thus ‘Ken is in Sydney’ content cuts ‘Ken is in Sydney and all electrons are negatively charged’ without lending any inductive support to that claim. Note, again, that for Carnap, who subscribed to the traditional account of content as consequence class, content-cutting would be a trivial relationship because just about any e cuts the untested content of any h, since it eliminates the questionability of h’s consequence h v e. It is argued that the paradoxes of confirmation pose no particular threat to probabilistic notions of confirmation since they all involve cases of content cutting in the absence of real confirmation. The new notion of content is also used to define a notion of irrelevance stronger than simple Carnapian probabilistic irrelevance. The point here is that evidence that is intuitively very relevant to a proposition can by the standard Carnapian notion of probabilistic irrelevance be irrelevant to it. For Carnap the evidence ‘Die A came up even and Die B came up 1,3,5, or 6’ and the evidence ‘Ken is in Sydney’ are both equally and wholly irrelevant to the claim that ‘Both die A and die B came up even’. Finally, we consider how the notion of real confirmation bears on the distinction between the confirmation of simple law-like statements and the broader question of the confirmation of theories. What this paper shows is that Bayesian probabilistic accounts of confirmation can avoid the strongly counter-intuitive consequences which make them so questionable.