In the philosophy of science, underdetermination refers to situations where the evidence available is insufficient to identify which belief one should hold about that evidence. For example, if all that was known was that exactly $10 was spent on apples and oranges, and that apples cost $1 and oranges $2, then one would know enough to eliminate some possibilities (e.g., 6 oranges could not have been purchased), but one would not have enough evidence to know which specific combination of apples and oranges was purchased. In this example, one would say that belief in what combination was purchased is underdetermined by the available evidence.
Ancient Greek skeptics argued for equipollence, the view that reasons for and against claims are equally balanced. This captures at least one sense of saying that the claims themselves are underdetermined.
Underdetermination, again under different labels, arises in the modern period in the work of René Descartes. Among other skeptical arguments, Descartes presents two arguments involving underdetermination. His dream argument points out that experiences perceived while dreaming (for example, falling) do not necessarily contain sufficient information to deduce the true situation (being in bed). He concluded that since one cannot always distinguish dreams from reality, one cannot rule out the possibility that one is dreaming rather than having veridical experiences; thus the conclusion that one is having a veridical experience is underdetermined. His demon argument posits that all of one's experiences and thoughts might be manipulated by a very powerful and deceptive "evil demon". Once again, so long as the perceived reality appears internally consistent to the limits of one's limited ability to tell, the situation is indistinguishable from reality and one cannot logically determine that such a demon does not exist.
To show that a conclusion is underdetermined, one must show that there is a rival conclusion that is equally well supported by the standards of evidence. A trivial example of underdetermination is the addition of the statement "whenever we look for evidence" (or more generally, any statement which cannot be falsified). For example, the conclusion "objects near earth fall toward it when dropped" might be opposed by "objects near earth fall toward it when dropped but only when one checks to see that they do." Since one may append this to any conclusion, all conclusions are at least trivially underdetermined. If one considers such statements to be illegitimate, e.g. by applying Occam's Razor, then such "tricks" are not considered demonstrations of underdetermination.