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.
In fact, given the fact that two or more rival theories are assigned different prior probabilities, the evidence can confirm one more than the others, or even make one highly probable.
Let us call the first deductive underdetermination and the second inductive (or ampliative) underdetermination.
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.
Given that the link is not deductive, it is claimed that we can never justifiably believe in the truth of a theory, no matter what the evidence is.
However, it would be folly to think that deductive underdetermination creates a genuine epistemic problem.
More accurately, it is a relation between the propositions that express the (relevant) evidence and the propositions that constitute the theory.
The basic problem is that individual theoretical claims are unable to be confirmed or falsified on their own, in isolation from surrounding hypotheses.
Two or more rival theories (together with suitable initial conditions) may entail exactly the same observational consequences.
Given the above presupposition, it follows that the observational consequences cannot warrant belief in one theory over its rivals.
Though simplistic accounts of the hypothetico-deductive method need to be jettisoned, there are ways to meet the challenge of deductive underdetermination, even if we stay close to hypothetico-deductivism.
Since theories entail observational consequences only with the aid of auxiliary assumptions, and since the available auxiliary assumptions may change over time, the set of observational consequences of a theory is not circumscribed once and for all.