The only point I was making is that Eli's comment was not, contrary to your claim, an argumentum ad consequentiam. That's an entirely separate question from (e.g.) whether it involves something you can call "faith".
But: If you define "faith" broadly enough then sure, everything with any element of belief to it involves "faith". Derive everything rigorously from axioms? That means having "faith" in your axioms! Do literally anything else at all? That means taking a step at some point that doesn't have a watertight logical justification, so it's "faith"! -- So, sure, Eli's argument (or at least my sketchy reconstruction of it) involves an element of "faith", just like literally every other argument anyone could ever possibly make.
I guess this is what you mean by denying "that truth is knowable". If by "knowable" you mean "... with literally no room for any sort of uncertainty" then I vigorously agree with you -- but I have the impression (perhaps wrongly) that you were offering this as some sort of correction or education for eli_gottlieb, and I see no reason to think he needs it. All he's said is that he believes in science because it works, and that is perfectly consistent with taking "believe" to mean "accept as our current best approximation, to the best of our knowledge, to the truth, with the understanding that later discoveries might change our opinions greatly" or something of the sort.
You're right. I conflated argumentum ad consequentiam and affirming the consequent. If X works, then I should believe X is true is not the same thing as if I don't believe in X then X won't work. I rushed my response to you because I was between meetings.
But my core argument here is that we have no starting point. If you want to call them axioms that's fine, but I'm not here to quibble about language. Even if we had no experience of senses and minds leading to erroneous perceptions and thoughts, we would still have no way to prove that our minds are reliable. At best we would have smaller priors. But quite the opposite, we routinely encounter evidence of erroneous perceptions and thoughts. In dreams, lunatics shouting on the street, or our seemingly invisible optic nerve.
The problem with saying:
> Faith is when one acts on a belief without having any rational reason for it. My rational reason for believing in science is simply: it works!
Is first defining faith incorrectly[0] and then second by appealing to its outcome as a measure for its justification. Theologians manipulate their mental state with their own methods. When they say they encounter manifestations of the divine and say they have a rational reason for their religious beliefs by saying "it works!" they're doing the same thing.
Only by humbly admitting that our starting point requires some first acceptance can we then make progress. If you want to take it as an axiom that your mind is reliable, that's fine for you, but it isn't something that's necessarily true. I love Russell, but when he tries to break out of this by calling solipsism a self-refuting idea he's being intellectually dishonest. He was more honest when he was younger and he said solipsism is boring. And there[1] we fully agree.
[0] Faith is about mental state, not action. From Google dictionary: "Complete trust or confidence in someone or something."
Faith and plausibility remain two different things, unless you really want to argue that "faith" is simply "any overcoming of radical skepticism or solipsism".
In the seems.