Logic should not be trusted.

I bet most cautious readers are sensing a sort of peculiarity in MouthWash’s reasoning. That is to say, upon first reading (or second or third depending upon one's caliber) it seems obvious that something is off in the argument proper, even if it cannot be immediately identified. So let’s break it down (hopefully judiciously), and see what the argument is and where it founders. Let’s start with what I discern to be the first premise:(1) “First of all, I assert that even the most basic axiom could be false, since there could be some massive hole in it that our potentially defective brains cannot realize. ”Secondly, we’re supplied with the premise:(2) “Attempts to render logic relevant (such as Occam's Razor) fail because they are presupposed on the validity of axioms. ”So let’s summarize this argument in a more deductively accessible manner:(3) All axioms could be false(4) Anything that presupposes these axioms could be false(5) Logic presupposes these axioms(6) Logic could be falseAs you’ll see in the succinctly summarized version, (6) follows necessarily from the joint assertion of the previous premises (3,4 and 5). What you’ll find conspicuously absent from the deductive arrangement of the premises is the matter of trust. From the premises provided by my opponent, all we can legitimately deduce is that logic could possibly be false. So we have at least one problem to begin with, namely that this argument does not address the matter of trust at all. Thus, being the non sequitur, that it is, the argument never really begins. We’ll get into that in a minute. There still is a second matter to be addressed, namely the problem of begging the question. That is to say, the truth of the premises depends fully upon the truth of the very axioms in question. There are quite a few more problems, of course, like the problem of presumably supplying equaprobable value to the truth or falsity of axioms. Or the problem of axiomatic consistency being the only thing we experience and thus cannot be expected to act outside our realm of experience. We run even further into many epistemic problems that simply cannot in brevity be broached in this venue. So let’s address the two matters I mentioned. The Problem of TrustTrust: Firm belief in the reliability, truth, ability, or strength of someone or something. As you’ll notice, there is nothing inherent in the definition of trust that requires certainty in the Cartesian sense. For instance, I trust that gravity travels at a rate of 9.8 m/s2, even though I have not measured it myself. In fact, there is nothing inherently contradictory with jointly asserting that I trust that the rate of gravity is 9.8 m/s2, whilst also asserting that I believe the rate of gravity could be false. So I can believe that logic is possibility false while still trusting that it is not. Sense I have only ever experienced the reliability and consistency of axioms, I have very good epistemic reasons for believing that they are, in fact, accurate representations of reality. Even further, if I suspected that they were, in fact, false, I would still have to live my life as if they were true, given that everything we currently know about reality is bound, ineffably and with ruthless precision, by these axioms. The Problem of Question-BeggingThis is a brief criticism. The premises as outlined by my opponent and further summarized by me require the truth of axioms. Inasmuch as deductive rules of reason, such like those employed by my opponent, require the truth of certain metaphysical principles, like the law of non-contradiction and the law of identity. For instance, assuming that axioms are either true or false requires that the axioms governing the law of excluded middle and the law of non-contradiction be true. Therefore, the only way for the first premise to be operable is for at least some axioms to be true.