a taste for desert landscapes

Suppose the following expresses a strict implication:

If H then O

The letter H is supposed to remind you of “hypothesis”, and the letter O of “observation” (or better, a datum or description of an observation). But H needn’t be thought of as a singular hypothesis in isolation — it might be a large conjunction of hypotheses and assumptions. And O needn’t be an observational claim at all, let alone a “theory neutral” observational claim, if indeed such things exist.

Now suppose we deny that O counts as “evidence for” H, but allow that not-O counts as “evidence against” H. Why would we do such a thing?

Trivially, “evidence against” H is the same thing as “evidence for” not-H. The only obvious reason why someone would say that not-O counts as “evidence for” not-H, at the same time as denying that O is “evidence for” H is that not-O strictly implies not-H, but O does not strictly imply H.

But that is to assimilate “evidence” to “strict implication”.  And that would be sloppy. It would be like Sherlock Holmes wrongly attributing his solution of a crime to “deduction”.

Evidence takes many forms. Perhaps occasionally, some axioms that we are happy to accept imply a theorem that we initially find implausible. In that situation, the axioms function as “evidence” for the theorem. (Strictly speaking, it is the axioms together with the rules of inference we use to deduce the theorem using the axioms as premises.) But that is the exception rather than the rule.