Wednesday, August 24, 2016

Two Conflicting Hypotheses


I invite you to join me in a tedious thought experiment. Suppose we have two hypotheses, which we will call H1 and H2, exactly one of which must be true.

This supposition implies that H1 and H2 contradict each other directly. H2 may as well say, "H1 is false."

How can we decide which hypothesis to accept and which to reject? Epistemology tells us we should accept the hypothesis with the strongest supporting evidence. So let's introduce some evidence.

Suppose we have a body of evidence which supports H1 to some degree, and call that evidence V1. Suppose we have a different body of evidence which supports H2 to some degree, and call that evidence V2.

Suppose further that the bulk of the evidence supports H1 rather than H2. In mathematical notation, we would say that V1 > V2.

If we were asked to select one hypothesis over the other, purely on the basis of evidence, we could do so quite simply. Since V1 > V2, we would say H1 appears to be true, so we would accept H1, and reject H2.

But that would be too easy a problem for serious and talented people such as ourselves. This thought experiment may be tedious, but it's not trivial.

Aside from evidence actually bearing on the question, we also have other reasons why it would be advantageous to accept H1, and we call those reasons R1. Similarly, we have other reasons why it would be advantageous to accept H2, and we call those reasons R2.

If we took stock of all these reasons and found that R1 > R2, we would still have a trivial problem. Since V1 > V2, we would prefer H1 based on the evidence. And since R1 > R2, we would prefer H1 for other reasons as well. So it would be easy to accept H1 and reject H2.

But if R2 > R1, we would have a dilemma. H1 would still appear to be true, because V1 > V2. But this would no longer settle the question, because R2 > R1, so accepting H2 would appear to be advantageous.

We've been discussing this in abstract, philosophical terms.

But in concrete reality, this is a common dilemma:

What do we do when V1 > V2 but R2 > R1?