But this is scant consolation because, apart from the fact that in the long-run we are all dead, the convergence-of-opinion theorem holds only under limited and very well-defined circumstances that can hardly be met in ordinary scientific cases.
The alternative is to claim that prior probabilities have epistemic force because they express rational degrees of belief, based, for instance, on plausibility or explanatory judgements.
Besides, a more radical (though plausible) thought is that theories may get (indirect) support from pieces of evidence that do not belong to their observational consequences.
Inductive underdetermination takes for granted that any attempt to prove a theory on the basis of evidence is futile.
For instance, no finite amount of evidence of the form Aa can entail an unrestricted universal generalization of the form All A's are B.
Deductive underdetermination rests on the claim that the link between evidence and (interesting) theory is not deductive.A total denial of the legitimacy of any prior probabilities would amount to inductive skepticism.Inductive underdetermination would be inductive skepticism. The more interesting version of inductive underdetermination does not challenge the need to employ prior probabilities, but rather their epistemic credentials.That is, the evidence can raise the probability of a theory.So inductive underdetermination must rest on some arguments that question the confirmatory role of the evidence vis--vis the theory.There is a battery of such arguments, but they may be classified under two types.The first capitalizes on the fact that no evidence can affect the probability of the theory unless the theory is assigned some nonzero initial probability.If, it is argued, prior probabilities have epistemic force, then the evidence can warrant a high degree of belief in a theory (or greater degree of belief in a theory than its rivals).But, it is added, how can prior probabilities have any epistemic force?However, it would be folly to think that deductive underdetermination creates a genuine epistemic problem.There are enough reasons available for the claim that belief in theory can be justified even if the theory is not proven by the evidence: Warrant-conferring methods need not be deductive.