Oh don't worry, if you haven't broken it you'll break it soon in this thread.
I can't help but wonder WHAT is the wordcount record.
Easiest way would be setting a new one. 10^23 words schould do
Again, I'm a bit short on time, but if you reread your post, you'll find that you strayed quite far from axiomatic deduction. ("It is I1, but I1 that appears to be I2, depending on what level you're looking at.") What you say is fine by the standards of sane everyday reasoning, and a very valid concept of how the world works (I use something very similar, too) - it just isn't all clear from your first two axioms.
Hell, maybe tonight I'll do a tract on axiomatic moral philosophy and you can whale on me for a while, eh? I feel kind of bad for constantly critizising without doing stuff on my own...
That's the cool things about discussions in philosophy - if you have someone to criticize you, you can refine your argument to patch the problematic parts. And flipping the tables should be pretty fun, although my arsenal is not nearly as extensive as yours. I do know some things about philosophy, but my knowledge is fragmentary and unsystematic, since I never properly studied it outside of amateur-level reading here and there. I found your reference to Hume particularly difficuly to take on, since I had a hard time of finding good summaries of his beliefs in the matter we were discussing, due to that.
Also, a bit of self-critique, Axiom of Objectivity can be broken down further to a simpler, less specific, and less controversial axiom that, however, has similar implications. Namely: 'Contradictions don't exist'. It is a simple, basic prerequisite for logic to be useable, and does interesting things to solipsism. The formulation in the last post showed my bias against solipsism, since it was explicitly targeted against it (I count Berkeley's metaphysics or sci-fi 'AI in a box' and the like as a subtype of solipsism, just in case it's not clear).
Now, the current (Third? I think by now it's third) formulation does very interesting things to solipsism, since it technically allows it, with a caveat that the world created by a solipsist's mind is logically consistent. And the requirement of logical consistency means, among other things, that in a hypothetical solipsist universe the reality (a set of all objects everywhere) created by a solipsist's mind cannot be willed out of existence. So with that formulation, you can have solipsist metaphysics, but logic forces you to behave the same way as though you were using non-solipsist metaphysics. Meaning that even if I had only that single axiom, there is no essential difference between solipsist and non-solipsist metaphysics, as long as there is logic.
And the thing about logic is that it's undeniable. If you deny existence of logic, you've just performed a smash and grab of a concept of denial. And that has implications that I cannot even formulate without getting a headache, and I'm suspecting inspecting logic is like trying to divide by zero on a pocket calculator.
But, back to responding. The sentence you quoted was supposed to convey that while intuitively it appears to be I2, I2 behavior is a macro-level emergent behavior while at the object/atomos level, the only thing that changes is the dimensional configuration of I1-following objects/atomoi (I think that's how the plural would look).
I'm having a creeping suspicion that universe runs on math, but I resist it since it seems like a nasty, nasty reification.