While I think this is fundamentally the right sort of answer, it does require a wholesale rethinking of the idea of rationality, and that might be a bitter pill to swallow.
What happens when we are persuaded by an argument? When we are convinced to change our minds? Those idioms leave us a bit passive, as if an argument pushes and pulls our beliefs like so much gravity. It's more decorous to say that we
find an argument persuasive or the evidence convincing; sounds like we've rendered a judgment, in keeping with our high station.
Neither of those is particularly attractive. I think it's easy to accept pragmatism in the abstract -- to think this must be the way we think -- but difficult to believe it in particular cases, where it seems to us we have closely examined the logic and the evidence and taken a position. When doing philosophy, in particular, this is what we tell ourselves, and each other.
We may claim to be comfortable distinguishing the logic of discovery and the logic of confirmation or justification, but I think mostly we aren't. Chess provides a clear example, as usual: there's a saying among masters that the move you want to play is the right move, even if it seems impossible. This is intuition, and the idea is that careful analysis will justify your inclination, so some part of your mind must have zipped through that analysis without bothering to keep you informed, which would only slow things down. That fits nicely with the two-systems model, because the fast system here is just the unconscious and efficient habits that used to be carried out laboriously and consciously. --- But that still suggests that the conscious analysis you do is properly modeled as reasoning of the most traditional sort. There's no difference in kind here, only a difference in implementation. (This algorithm is known to work, so we can run it on the fast but unconscious machine.)
What is difficult to accept is that reason is really and truly rationalization, that justification is always and only post-hoc, that we are simply incapable of relying on logic and evidence alone to form our beliefs even if we do so to justify them. We want to believe that the process by which we reach a conclusion is quite similar to the process we would use to justify reaching it, and we want to believe that includes a free act of judgment.
I don't believe we ever
choose what to believe, but only find that we do or we don't. And that applies here as well. It's what I find I believe, and others find they believe differently. What's worse, I find I cannot help but believe I have considered evidence and argument to reach this conclusion, but even if that is so, at no point did I weigh it all up and freely judge that it is so. All I can say is that argument and evidence seem to assail me like so much sensory input and the result is that I believe what I believe. I have to hope that what reason I have has done a good job filtering and weighing its inputs to reach a sound conclusion. If I try to justify my belief, I will surely succeed. It's one of my best things, as it is for everyone; rationalizing is our super power. Now I have to hope, as well, that my post-hoc justifications are everything they seem to be.
So, yes, I broadly agree with what you posted,
@Janus, but I reserve a bit of Humean horror that the foundations of my rationality are not themselves rational.