I always find it amusing when people who get their views thrashed over them containing some particular kind of fallacy tend towards accusing others of engaging in the fallacy, almost as if they don't understand fallacies or logical reasoning at all.
The modal error which occurs most frequently is that which happens when a person imagines something as being possibly the case but the person asserts that something as being actually the case.
This error most commonly occurs when a person has not sufficiently imagined other possibilities which could be the case and/or when a person has not sufficiently dispensed with other possibilities that could be the case.
You have nailed it once again.
It is a modal error to identify one of many possibilities and then draw logical conclusions from that possibility as if the possibility were a fact. Before that, it is simple arrogance, hubris, or ignorance to believe that the identified possibility is a fact in the first instance.
Jarhyn's posts contain multiple assertions of fact, which deny contrary possibilities that he lacks any basis to deny. Because Jarhyn does not qualify his statements with terms such as "I believe" or "If" or "Accepting ___ to be true," etc., his statements are asserted as facts that must be accepted as true for purposes of engaging with him. Moreover, this is not simply a matter of linguistics. Rather, it is plain from Jarhyn's multiple posts that he is, in fact, wedded to paradigm that he accepts, axiomatically, as true and denies contrary possibilities.
I believe (and do not profess to know as a fact) that humans do not know, and are incapable of knowing, anything to a certainty. Within that belief, I necessarily accept that my belief may be wrong. Without regard to whether humans are capable of knowing anything to a certainty, however, I am relatively confident that Jarhyn is not the extraordinary human being (who I doubt to yet exist) who has such access to the secrets of the universe that he can accurately claim to know anything with certainty -- including the asserted facts that no two objects can concurrently occupy the same point (without regard to the number of possible dimensions), that "A" cannot equal "Not A", and/or that 1+1=2. Like most others, I live "as if" the foregoing propositions (and many others like them) are true. Unlike Jarhyn, however, I hold open the possibility that such propositions are false -- though I lack the mental capacity to wrap my brain around how that can be so, because my hardware, software, both or something else, seem to preclude me from doing so.
It is plain from Jarhyn's multiple posts that he is wedded to a paradigm (which also is the underpinning of science) that (i) there is a reality, (ii) humans are capable of discerning that reality, and (iii) math and physics are the tools by which humans are capable of doing so. Jarhyn seems to add computer science to the toolkit he trusts to be capable of being sued to discerning reality, and he also appears to believe that he has a sufficiently understanding of math, physics and computer science that he can use these tools to discern reality and root out false constructs. Within Jarhyn's paradigm, he rejects as preposterous any proposition that conflicts with his perception of reality based on his application of math, physics and/or computer science.
If Jarhead is the most extraordinary human ever to walk the earth, then his posts would would be entirely true and all contrary posts equally false. I very much doubt that is the case, but I am open to that possibility. If, however, Jarhyn's paradigm is simply one or many possibilities, then Jarhyn repeatedly commits the modal error of reasoning from his possible paradigm to necessary conclusions that reject all contrary possibilities.
So long as Jarhyn remains wedded to his paradigm to the exclusion of all others, the only rational conversation that can be had with Jarhyn must assume the truth of his paradigm and reason within it. That, however, is a conversation that belongs in a Forum on Math, Physics or Computer Science, and not one that belongs in a Forum on Philosophy, which is what I understand this Forum to be.