I've only expressed skepticism against people who say "The math proves that wormholes are possible". "The math" can't prove anything. I think that's the same point you're making about logic in general, right? In any case, you can take any logically consistent statement, stick absolute garbage in its variables, and get any result you want. It's a classic stupid logic trick that you can prove anything, given both A and !A.
If you have garbage variables than you already have garbage variables and logic won't change that. Logic, by itself, is always accurate, mistakes happen due to pilot error or mistakes that existed independently of it. If you agree with the assumed facts, and as far as I am aware we don't currently have any relevant, absolute certainties, so you are going to be assuming something, and you don't find any flaws in the argument, then logic will always result in an accurate extrapolation of your understanding of the world.
I agree, I don't like using absolute terms, there IS always reasonable doubt, but many things are sufficiently well established that operating under any other known assumption will result in apparent mistakes. If you are unwilling to respect someone's ability to argue, then you probably shouldn't argue with them...
I have two gumballs spinning on my coffee table. Dust and papers are flying off it at random. It must be the work of black holes!
So... you have a coffee table, there are gumballs on it, paper and dust may also be on it. The gumballs are spinning without apparent cause. Dust and papers are flying off it without known cause. Assuming that you can actually detect physical objects, such as tables, gumballs, papers, and people, machines, or whatever might be spinning things and throwing things around. Then you have a situation that clearly does not conform to the familiar. It may be a practical joke, record it and wait a while, practical jokes will usually become apparent over time. If it isn't, then it could be black holes... There is no apparent cause, but there is no apparent cause for anything involved. It might be a quirk in a magnetic field, it might be a poltergeist, it could be an unknown intelligence, but even if it is gods or aliens or whatever then it is still probably a practical joke, in which case its demise will likely be triggered by the your imminent ability to verify the events. Maybe it is the convergence point of the earths rotation, the moons orbit, and the gravity of a passing black hole, whatever it is, it certainly doesn't conform to my understanding of 'what happens if I leave gumballs and papers on a table'...
How do you know that you think? You perceive thought, but that doesn't prove thought, a perception could perceive anything, that only proves the perception. A perception doesn't need evidence, but to be generous I will give it chaos to perceive, it interprets this chaos in any way it pleases. This perception perceives memories, and activities, and expectations, time doesn't actually exist, nothing changes, but it perceives change in it's static state so there is perceived time. Thus far I haven't been able to justify the pseudo-existence of the question of existence without a perception, but there really isn't any hard evidence to support that you, I, or anything for that matter has any measure of existence as you understand it...