The structure of the differential method in the special sciences seems to have been somewhat neglected and taken for granted. It is presupposed by such practitioners that the application of the methodology increases the epistemic status of the remaining competing hypotheses while those that are eliminated are considered to be of lower epistemic status.
For example, let’s suppose that we have four competing hypotheses to account for X: H1 v H2 v H3 v H4. If all four hypotheses are plausible then we have no reason to prefer one over another. Now if we assume that additional evidence is presented (E) that disconfirms H3 and H4, does that mean H1 is “confirmed” given its probability has increased?
There are two arguments that can be made. The first is that H1 probability of being true increases as a result of E thus giving good reasons to possibly accept H1 as true. On the other hand, one can argue that E does not render H1 as true and as such the epistemic status of H1 is the same as that of H2. Now if we assume that E disconfirmed all the hypotheses except H1, then E can be considered as confirmatory evidence for H1. This would mean that H1 is more likely to be true than its rival hypotheses and can be argued that by definition it has a higher epistemic status. There are two questions that can be asked: does E actually confirm H1 in the epistemic sense and does it really increase the probability of H1 being true?
Some might argue that we can use “confirmation” in a non-epistemic sense. However, that would seem to eliminate the possibility of a hypothesis being true for reasons that we think are objectively true. As a result, any disagreements would be trivialized and disregarded for non-epistemic reasons. However, it is just as problematic to consider confirmation as epistemic. If we assume that E confirms H if and only if the probability of H1, new evidence, and the background evidence is greater than the probability of H2 and the background evidence, then this presupposes that any increase in probability should be sufficient to count as a confirmation. However, the removal of H2 does not seem to warrant the epistemic status of H1 as being confirmed.
To further elucidate this point let’s look at a billiard ball analogy. Let’s suppose that I have standard set of billiard balls in an opaque bag. I then speculate that the first ball I grab would be the eight ball. Now if I remove some of the other balls I have then increased the probability of selecting the eight ball. However, the removal of some balls does not confirm that the next ball I draw out would in fact be the eight ball. If we were to consider the removal of some the balls as evidence for my speculation then it could also be of equal evidence for any other non-eight ball that I would have chosen.
There is a distinction that needs to be made here, is E a strong or a weak confirmatory evidence? To determine this E must be evaluated in relation to the remaining hypotheses and the background evidence, in this case H1 and H2. It is tempting to argue that if E disconfirms H2 then it must be strong evidence for H1. However, this is not necessarily the case. It could be the case that E disconfirmed H2 on the basis that it offers slightly stronger reasons to believe in H1. Thus E does not actually confirm H1 but rather confirms our belief that the disjunction H1 v H2 stands. Furthermore, if E is considered to be strong evidence then it defeats the purpose of the differential method. Thus although the the differential method is practical it does not seem to justify higher epistemic status–it is to an extent subjective