Underdetermination is a relation between evidence and theory.More accurately, it is a relation between the propositions that express the (relevant) evidence and the propositions that constitute the theory.
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.
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.
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.
Both kinds of claims are supposed to have a certain epistemic implication, namely that belief in theory is never warranted by the evidence. Deductive underdetermination is pervasive in all interesting cases of scientific theory.
If the theory is not just a summary of the evidence, the evidence cannot determine, in the sense of proving, the theory.