With the (important) proviso that "knowledge", "trustworthy", and "are true" need to be qualified with something like "approximately, kinda-sorta, most of the time", I think these premises should be assumed as working hypotheses on the grounds that if they are badly wrong then we're completely screwed anyway, we have no hope of engaging in any sort of rational thought, and all bets are off.

Having adopted those working hypotheses, we look at the available evidence and it seems like it fits them pretty well (note: this isn't a trivial consequence of having taken those things as working hypotheses; e.g., if we'd assumed that our perception, reasoning and memory are perfectly accurate then we'd have arrived quickly at a contradiction). Those propositions now play two roles in our thinking: as underlying working assumptions that are mostly assumed implicitly, and as conclusions based on thinking about things as clearly as we know how.

There's some circularity here, but how could there not be? One can always keep asking "why?", like a small child, and sooner or later one must either refuse to answer or repeat oneself.

Somewhat-relevant old LW post: The lens that sees its flaws. My memory was of it being more relevant than it appears on rereading; I wonder whether there's another post from the "Sequences" that I was thinking of instead.

With such skepticism, how are you even able to write anything, or understand the replies? Or do anything at all?

I think you misspelled "skepticism" in the title.

Also, your argument (including what you have said in the comments) is something like this:

Every argument is based on premises. There may be additional arguments for the premises, but those are arguments will themselves have premises. Therefore either 1) you have an infinite regress of premises; or 2) you have premises that you do not have arguments for; or 3) your arguments are circular.

Assuming (as you seem to) that we do not have an infinite regress of premises, that means either that some premises do not have arguments for them, or that the arguments are circular. Either way, you say, that means we have unjustified beliefs which are not known to be true.

This may be true, given a particular arbitrary definition of knowledge that there is no reason for anyone to accept. But if knowledge is defined in such a way as to be a contradiction, who would want it anyway? It would be like wanting a round square.

Memories can be collapsed under percepts.

In answer to your broader question - yup: you've hit upon epistemic nihilism, and there is no real way around it. Reason is Dead, and we have killed it. Despair.

...Or, just shrug and decide that you are probably right but you can't prove it. There's plenty of academic philosophy addressing this (See: Problem of Criterion) and Lesswrong covers it fairly extensively as well.

http://lesswrong.com/lw/t9/no_license_to_be_human/ and related posts.

http://lesswrong.com/lw/iza/no_universally_compelling_arguments_in_math_or/

Rather than going on a reading binge I recommend to just continue mulling it over until it clicks into place, because, similar to the whole "dissolve free will" thing, it feels clear in hindsight yet it is not easy to explain or understand explanations others provide.

I'll give it a shot anyway: The essential point is that ultimately you are a brain and you gonna do things the way your brain is designed to do them. Assuming you've satisfactorily resolved the whole moral nihilism thing (even though there is no divine justification for morality, we can still talk about what is moral and what isn't because morality is inside us), resolving epistemic nihilism follows an analogous chain of thought: There is not and cannot be any justification for human methods of inference[morality], but it still is our method of inference[morality] and we're gonna use it regardless.

Assume they're approximately true because if you don't you won't be able to function. If you notice flaws, by all means fix them, but you're not going to be able to prove modus ponens without using modus ponens.

I would agree if you can't trust your reasoning then you are in a bad spot. Even Descartes 'Cogito ergo sum' doesn't get you anywhere if you think the 'therefore' is using reasoning. Even that small assumption won't get you too far but I would start with him.

gjm has mentioned most of what I think is relevant to the discussion. However, see also the discussion on Boltzmann brains.

Obviously, if you say you are absolutely certain that everything we think is either false or unknown, including your own certainty of this, no one will ever be able to "prove" anything to you, since you just said you would not admit any premise that might be used in such a proof.

But in the first place, such a certainty is not useful for living, and you do not use it, but rather assume that many things are true, and in the second place, this is not really relevant to Less Wrong, since someone with this certainty already supposes that he knows that he can never be less wrong, and therefore will not try.

Standard methods of inferring knowledge about the world are based off premises that I don’t know the justifications for.

How do you come to that conclusion?

What the Tortoise Said to Achilles.