Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
The CTMU is intended to constitute absolute truth. This is required for it to be a true Theory of Everything; if it did not constitute absolute truth, then its truth could be relativized to a partial context within reality at large, in which case it would not be a theory of everything.
Langan contends that a kind of absolute truth or knowledge is a requisite of our ability to sustain a perceptually consistent universe:
To perceive one and the same reality, human beings need a kind of "absolute knowledge" wired into their minds and nervous systems. The structure and physiology of their brains, nerves and sense organs provide them, at least in part, with elementary cognitive and perceptual categories and relationships in terms of which to apprehend the world. This "absolute" kind of knowledge is what compels the perceptions and logical inferences of any number of percipients to be mutually consistent, and to remain consistent over time and space. Without the absoluteness of such knowledge - without its universality and invariance - we could not share a common reality.
The task, then, is to construct a theory of this absolute knowledge. To do this, Langan argues, it is necessary to formulate the theory as a certain kind of tautology. This is because, he contends, (1) tautologies constitute absolute truth, and (2) any reasonable definition of "absolute truth" amounts to tautology.
In logic, a tautology is a sentence which is true under every assignment of true or false to its variables. For example, "A or not-A" (the law of the excluded middle) is a tautology because it is true regardless of whether A is true or false. That tautologies constitute absolute truth, says Langan, follows from their status in 2-valued logic:
Indeed, tautologies comprise the axioms and theorems of 2-valued logic itself, and because all meaningful theories necessarily conform to 2-valued logic, define the truth concept for all of the sciences. From mathematics and physics to biology and psychology, logical tautologies reign supreme and inviolable.
Further, continues Langan, tautologies are "absolute truth" not only with respect to logic, but with respect to the system of reality at large, where true (T) and false (F) correspond to systemic inclusion and exclusion:
Because a tautology is an axiom of 2-valued logic, violating it disrupts the T/F distinction and results in the corruption of informational boundaries between perceptual and cognitive predicates recognized or applied in the system, as well as between each predicate and its negation. Thus, the observable fact that perceptual boundaries are intact across reality at large implies that no tautology within its syntax, or set of structural and functional rules, has been violated; indeed, if such a tautology ever were violated, then reality would disintegrate due to corruption of the informational boundaries which define it.
Conversely, to show that any reasonable definition of "absolute truth" amounts to tautology, Langan reverses this reasoning:
Since absolute truth must be universal, it is always true regardless of the truth values of its variables (where the variables actually represent objects and systems for which specific state-descriptions vary in space and time with respect to truth value). Moreover, it falls within its own scope and is thus self-referential. By virtue of its universality and self-reference, it is a universal element of reality syntax, the set of structural and functional rules governing the spatial structure and temporal evolution of reality. As such, it must be unfalsifiable, any supposition of its falsehood leading directly to a reductio ad absurdum. And to ice the cake, it is unavoidably implicated in its own justification; were it ever to be violated, the T/F boundary would be disrupted, and this would prevent it (or anything else) from being proven. Therefore, it is an active constraint in its own proof, and thus possesses all the characteristics of a tautology.
The specific kind of tautology as which the CTMU is formulated Langan calls a supertautology, denoting the reality-theoretic counterpart of a logical tautology.
- Langan, Christopher M. On Absolute Truth and Knowledge.