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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.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.
For on any theory of confirmation, the evidence (even if it is restricted to observational consequences) can render a theory probable or more probable than its rivals.
That is, the evidence can raise the probability of a theory.
More accurately, it is a relation between the propositions that express the (relevant) evidence and the propositions that constitute the theory.
The claim that evidence underdetermines theory may mean two things: first, that the evidence cannot prove the truth of the theory, and second, that the evidence cannot render the theory probable.
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.
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.
If the theory is not just a summary of the evidence, the evidence cannot determine, in the sense of proving, 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.