You're right, Sunni: the ultimate arbiter is reality. If you run enough laps around this mulberry-bush, you will occasionally have a good laugh at various commie types who equate the fact of existence with religion for the purpose of sneering it off as an objective referent "out there" (beyond any individual's subjective estimation) grounding "the notion" of objective rights. In his book, "Achieving Our Country -- Leftist Thought In Twentietth Century America" (1997), Richard Rorty takes a slightly more elevated tone in establishing the pedigree of this whole line of thought, citing John Dewey (p. 29), which ought to chasten anyone who has ever uttered the word "pragmatic" in the least favorable connotation. Dewey was "antiauthoritarian", don'tchaknow, and Rorty (correctly) points out that Dewey rejected the idea that human beings had to pay any sort of attention to reality.

It routinely shocks people when I point out to them that philosophy has been teaching for over a hundred years that there is no such thing as reality, but it's really just that simple. It shouldn't take a PhD to point out the necessary implications. On the other hand, whole legions of PhD's are now failing to figure it out, so there you go. Go figger it.

It should be borne in mind that there is a categorical difference between axioms (like "existence" ) and principles. The latter can be analyzed to constituent concepts: the former cannot. This is why this is important:

The whole point of logic (the rules of thought) is integrity of thought: a valid continuity from axiom to implication. The "individual authority" to be respected is the ability to abstract from axiom (reality) to implications -- which can (but not necessarily) become "principles", depending on contextual applications. For example: the necessary ability of humans to use their minds in order to conduct their lives only assumes the character of a "principle" -- a truth upon which other truths stand or fall -- when it becomes important to underpin its implications in something like politics, when it's under threat. Otherwise, it's merely an interesting fact.

And this is why it is crucial to not merely "disagree", but to positively point out when someone is wrong in their thinking: when their logic is not integral.

Facts are facts. And there really is an ultimate standard against which to judge them. Nobody is doing anyone any favors to ignore this.