Perhaps you're using a Frequentist definition of "likelihood" whereas I'm using a Bayesian one?

There's a difference? Probability is probability.

So, if you mean to suggest that figuring out which hypothesis is worthy of testing does not involve altering our subjective likelihood that said hypothesis will turn out to be true, then I quite strongly disagree.

But if you mean that clever arguments can't change what's true even by a little bit, then of course I agree with you.

If you go about selecting a hypothesis by evaluating a space of hypotheses to see how they rate against your model of the world (whether you think they are true) and against each other (how much you stand to learn by testing them), you are essentially coming to reflective equilibrium regarding these hypothesis and your current beliefs. What I'm saying is that this shouldn't change your actual beliefs -- it will flush out some stale caching, or at best identify an inconsistent belief, including empirical data that you haven't fully updated on. But it does not, by itself, constitute evidence.

So a clever argument might reveal an inconsistency in your priors, which in turn might make you want seek out new evidence. But the argument itself is insufficient for drawing conclusions. Even if the hypothesis is itself hard to test.