Assessing Arguments for Incompatible Conclusions

§5.2

We have been discussing why refutations of propositions are not needed (though they are sometimes possible) once the arguments in favor of a proposition have been refuted. But how should we assess a conclusion when we have two arguments one for it and one against, neither of which have been refuted. There are two ways in which this situation can come about. First, someone who denies the conclusion of an argument might present an independent argument against it, instead of trying to refute the original argument. Second, different people might independently present you with arguments for logically incompatible conclusions. For example, there may be one argument that pleasure is the only thing of value and another argument that wisdom is the only thing of value. Since two different things cannot each be the only thing of value, the conclusion of each argument entails that the conclusion of the other is false. Thus, for each of the two conclusions, you have an argument that it is true and another that it is false.

How then should we proceed when we have separate arguments for incompatible conclusions? The first step is to make sure that the conclusions are in fact in compatible—they may merely appear to be so. But assuming that you have done this you should proceed to the following steps.

First, evaluate each argument on its own. In doing so you might refute one or both of them, in which case there is no further question of how to proceed. You assess the remaining argument (if there is one) as though it was the only argument that was given.

If neither argument is refuted, the next question to ask is whether either argument, when taken in isolation, seems to establish its conclusion as certain. If both arguments seem to do so, then you know that there must be an error that you have not found in one of them. Until you identify the error, both conclusions remain possible, but neither is probable or certain.

Now let’s consider a situation in which one of two arguments—we’ll call it Argument A—seems to establish its conclusion with certainty, while the other—Argument B—seems to establish the contrary proposition as merely possible or probable. In this situation, you should reexamine Argument A in light of Argument B, to see if there is anything in B that casts doubt on any of A’s premises or in its inference. (This last part is especially important if A is not a deduction.) If there is nothing in B to cast doubt on A, then A’s conclusion remains certain and B’s is disproven.

In a situation where each argument, taken independently, seems to establish its conclusion as probable, you need to consider each in the light of the other. Either one will undermine the premises or inference of the other in which case that argument’s conclusion emerges as probable and the others as either possible or unfounded, or the two arguments will partially undermine one another, in which case both conclusions will probably emerge as possible, with neither as probable. For example, if both arguments are inferences to the best explanation, then it cannot be true that two incompatible explanations are each the best: either one is better than the other, in which case only that one is the best explanation, and only the conclusion of that argument is probable; or else the explanations are equally good, in which case neither is best, and the each of two conclusions is (at most) possible.