@U238: I at least agree with you in this: that most claims made about anything can be reduced to series of assumptions, the foundations of which may not be understood or knowable by us; and therefore most knowledge as we have it may not be objectively substantial, by any standard or method we devise. What we're left with, then, is likelihood or other products of memory - which may be more substantial to us, insofar that it's at least more practical to us, than truth. So some mode of skepticism or nihilism may be appropriate; and meaning may only be a subjective ascription.
I'm not sure that I agree with you, however, that 'Everything [!] is inherently meaningless'. If we believe meaning to be a subjective phenomenon, which doesn't exist without the subject; and if we believe meaning to be something that only occurs when a subject is congruous or otherwise aware of something other than himself (which may be objects); and if we believe that the conception of meaning is at least an occurrence in something, which may be the human mind, and which mayn't be anything or everything else, and which is at least existent insofar that that is the case - then we may infer at least that meaning exists, and that it exists where there is congruousness between the perceiving subject and the objects of his perception (which may even be the subject himself). We may believe further that meaning may exist in proportion to the number of subjects who perceive meaning; and that, therefore, meaning compasses everything applicable within human perception (including but not exclusive to the subject himself), insofar that meaning is therein ascribed. We may even believe this: that if there aren't subjects as such, but only intersubjects; if difference is false, and everything is unified, including humans and their perception of meaning; and, in this way, if humans are therefore innately congruous with what is unified, while being a part of a unity, and are even thereby variably aware of what is unified - then, if a person believed that everything as such had meaning, everything may well have meaning.
But this is a line of reasoning, like any other line of reasoning, that is founded on something that may not be knowable, and it may even be formed as a falsehood by the void of our knowledge. One of the difficulties of nihilism, is that it's somewhat self-defeating: if everything is subjective, and difference and whatever else is only discernible by the subject, then the claim 'everything is subjective' only may or may not be true. There are no claims that may be known in a strict way; nor is there any possible way to verify claims to show whether they are or aren't true - including claims about itself. This may, however, be the most honest thing to say about anything, which may be taken from nihilism: that what is true may not be discernible through human experience (that being the sum of its perception and its critical faculties, and so on).
I don't, however, know what to make or take from this kind of problem. It seems to me that there is a deficit of knowledge with which to properly decide it, and so it may not be soluble from any angle; logic itself is only a relevant means of knowledge insofar that it makes inferences from the world that are decidedly true. I'm too much a skeptic at the moment to say what claims are true or are not true. Meaning may be an innate part of existence, or it may not be an innate part of existence; to what degree it may be part or may not be part, I don't know, nor do I believe that we could begin to say.
The problem with skepticism, or the belief that everything is doubtable, is that it produces nothing: it makes no claims, besides itself, but only reduces claims. Knowledge thereafter is only inferred by our knowledge-producing edifices; knowledge in this way may be thought to be prejudiced, and maybe positively, toward what produced it. And so I'm in a muddle. In an important way, the only things that may be spoken of are the things that we perceive; and we may only claim things about what we perceive insofar that we're able to. What is at least useful to us, we may believe, is to discover utility: what may not be true may at least be good for or useful to us.
This reminds me of Nietzsche: 'Happiness and virtue are no arguments. But people like to forget... that making unhappy and evil are no counterarguments. Something might be true while being harmful and dangerous in the highest degree [!]. Indeed, it might be a characteristic of existence that those who would know it completely would perish, in which case the strength of a spirit should be measured according to how much of the "truth" one could still barely endure - or, to put it more clearly, to what degree one would require it to be thinned down, shrouded, sweetened, blunted, falsified' (Beyond Good and Evil, s 39, pg 239, BW).
But I'm reminded elsewise that everything known is at least the product of our prejudices, more than that everything is subjective. This makes the most sense to me.