I'll have a shot at truth.
Within any system of logic a 'truth' is a theorem that doesn't contradict the other theorems or the axioms. Conceptions, perceptions, logical conclusions etc are all true or false in this sense, and only in this sense. (Hence Plato's allegory of the cave).
It isn't obvious that this is true in the case of perceptions, but it is a philosophical orthodoxy that all perceptions are 'theory-laden' thus subject to the same lack of certainty as any theory. 'Experience' escapes this limit since it is not possible to be wrong about what you are experiencing, only about the cause or meaning of the experience.
An 'ultimate' truth is presumably an assertion (or piece of knowledge etc) that is a completely true statement about reality.
Two questions come up. Can we ever know a 'truth', and is there any such thing as a true statement about 'ultimate' reality?
Aristotle, Plato, Russell and Popper (etc) doubt, for logical reasons, whether we can know for certain that any statement is true. For Aristotle (and Popper I think) certain knowledge (truth) is identical with the knower, thus can only be achieved through direct experience. The general suggestion is that no system of formal reasoning can produce certain knowledge, or knowably true statements. Goedel's proofs suggest this, and Quine argues much the same. It's hard to see how they can all be wrong given the strength and variety of their arguments.
Non-dual philosophers go a step further, perhaps explaining why the above is true. According to them there are no assertions that can be made about reality that are true or false. This sounds a bit mystical but it is really just a logical extension of the above argument. Not only can we not reason our way to the truth because of our human failings, but it isn't even possible to do it in principle, not in any possible universe. Hence the hint from Lao Tsu when he says "true words seem to be paradoxical".
However these folk also argue that it is possible to know truths about reality. This is because it is possible to know things that are true without being able to prove them systematically (as Goedel showed). This sounds self-contradictory but it isn't quite. Basically they are saying that it is possible to know some truths with certainty, but not possible to assert them since language is 'dual' and thus not up to the task. All one can do is assert half-truths.
This is to use 'truth' in two different ways. The first means roughly 'provably true within the system given that the axioms are true' and the second 'true of reality'.
The consequences of these two different approaches to truth can be seen in the fact that scientific or mathematical truths (inasmuch as they refer to reality) can be provable but must be uncertain, whereas by a 'non-dual' view truths about reality can be certain but cannot be provable.
Thus Buddhists never assert anything about reality without immediately contradicting themselves, (unless they're not concentrating), for there are always two ways looking at 'ultimate' reality, two aspects which contradict each other. Hence 'emptiness/fullness', the two meanings of 'Brahman' and so on).
I hope that makes some sense. All objections welcome.
Canute