In: Statistics and Probability
Is it always possible to construct and carry out a crucial test to determine once and for all which of two competing hypotheses is correct? Explain.
A crucial test is a test (experimental or observational) intended to determine which of two rival hypotheses is true and which is false.
According to Carl Hempel, strictly construed, a crucial experiment is impossible in science.
Because:
1. Auxiliary hypotheses are almost always needed to derive test implications from test hypotheses. It is impossible to disprove either of two competing hypotheses.
2. Test hypotheses cannot be conclusively proved by any set of available data.
At most, a crucial test provides good reason to believe that one of the hypotheses is true and the other is false.
P.S.:
The additional assumptions used to deduce a prediction are called auxiliary hypotheses.
It is a hypothesis other than the test hypothesis which is assumed to be true, and is needed to derive the test implication.
i.e. If H (test hypothesis) and A (auxiliary hypothesis) are true, then I (test implication) is true.