It's impossible to know or prove anything absolutely

My opponent seems to be in two minds about what he is trying to argue; on the one hand he is stating that he cannot prove that nothing is provable, but on the other hand is going out of his way to prove that it is; and so therefore isn't. Dancing around words and terminology like a drunk on a saturday night, however, does not move the argument forward. There are two counter arguments proposed here; both of which are based on false assumptions. Firstly, the argument that Logic is somehow based on experiment and experience is absolutely wrong, almost laughably so. We do not need to investigate that 2+2 = 4, nor do we have to raid cupboards of litmus paper to state that "A statement that is absolutely true, cannot be absolutely false." Logic itself is all about inference; about A necessarily following B because of C; You do not ever have to see a right handed triangle, or to use meter rulers to prove pythagarus's theorum, nor do you have to hijack telescopes to prove simple logical induction; with certain statements, we can infer, induct or dedeuce that other statements MUST be true. To paint logic itself as somehow subjective or falsifiable; that were you to repeat the phrase "A statement that is absolutely true, cannot be absolutely false," again and again, it will somehow be incorrect; does not follow as a result. Logical reasoning; provided the correct logical process is followed, always gives the same answer through simple steps showing that if one thing is true, then the other must be. This is not because of measurements made, or objective evidence gained, as if somehow the logical framework relies upon them; it is because the starting statements are such that the resulting conclusion MUST follow. The second counter argument, and one that somewhat baffles me as my oponent seems to be making my case for me, is that somehow logic cannot be trusted. To put the case forward that we cannot be sure of logic, a mathematical curiousity has been quoted; which to anyone who has not paid a great deal of attention to the problem in question or mathematics in general will see is mathematics killer. Unfortunatley for my oponent, but fortunatley for all the thousands of mathematical genius's that have ever lived; who I am sure now breath a sigh of relief from beyond the grave; the mathematical example is fundamentally and critically flawed: In the step: (a+b)(a-b) = b(a-b) to: a + b = b We are dividing both sides by (a-b), but as a = b; (a-b) = 0; we are dividing by zero and both sides are equal to infinity: [inf](a+b) = [inf](b) While I await my oponents proof of how to resolve such infinities, as does the rest of the mathematical community; as such a logically consistent proof would open doors to resolving all sorts of physical theories, including resolving the resulting terms of string theory; I suspect that this was a simple error on his part. Going deeper to this argument, however, and the reason that this argument seems to be one sided in that we are both argument the same point; is as I stated before; to be unsure about logic; to be uncertain about whether true=true; is to be uncertain about everything, and if we are uncertain about everything, there is one thing that can be proven absolutely; that we cannot be certain about everything.