On Absolute Truth and Knowledge

First, a word on the title of this essay. Absolute knowledge is absolutely true, and absolute truth is the definitive predicate of absolute knowledge. That is, if something is known with absolute certainty, then it can be subjected to tests affirming its truth, while if something can be affirmatively tested for truth, then it is known with certainty by the tester. This applies whether the tests in question are perceptual or inferential. Where knowledge can denote either direct embodiment or internal modeling by an arbitrary system, and test denotes a straightforward systemic efficacy criterion, knower and tester can refer to reality at large. In this generalization, truth and knowledge are identical. While it is possible to split, splice and braid countless philosophical hairs over the connotations respectively attached to truth and knowledge, this simple generalized relationship conveniently spares us the necessity. It is with this express understanding that these terms and phrases are employed herein.

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; our minds and senses would lie and bicker without respite, precipitating us into mental and sensory chaos. Time and space, mind and matter, would melt back into the haze of undifferentiated potential from which the universe is born.

Given the fact that absolute knowledge is a requisite of our collective ability to sustain a perceptually consistent universe, it is nothing short of astonishing that there are people who react with incredulity or derision at any mention of its possible existence. Their attitude seems to be that the very idea smacks of "hubris", being nothing but an empty pretense exceeding the capacity of the small and overly-challenged human mind. The truth, however, is that hubris is nowhere more evident than among those holding irrational opinions in contempt of logic, and denying the existence of absolute knowledge is a case in point. In fact, the entire history of philosophy and science can be characterized as an undying quest for absolute knowledge...a timeless attempt to comprehensively extend the a priori and analytical into the realm of the apparently a posteriori and synthetic. This quest includes the efforts of researchers from many fields, from physics and cosmology to philosophy and computer science.

The Holy Grail of this quest is known as the TOE, or Theory of Everything. A TOE purports to be absolute truth by an implicit reductio ad absurdum: if it does not constitute absolute truth, then its truth can be relativized to a partial context within reality at large, in which case it is not a theory of everything. Thus, if a TOE exists, it falls squarely under the heading of absolute knowledge. But unfortunately, the proper method for constructing such a theory has not been entirely obvious, particularly to theorists steeped in the ambiguities and paradoxes of four centuries of post-Cartesian science and philosophy. As science has advanced and philosophy has wearily tried to keep pace, their once-stentorian claims of absolute truth have been all but extinguished, and the mainstream search for a TOE has lately been pursued without a clear understanding of what is being sought.

The apparent absence of a TOE notwithstanding, has any kind of absolute knowledge ever been scientifically formulated? Yes, in the form of logical tautologies. A tautology is a sentential relation, i.e. a formula consisting of variables and logical connectives, with the property that it is true for all possible assignments of Boolean truth values (true or false) to its variables. For example, the statement "if x is a sentence, then either x or not-x (but not both) must be true" is a tautology because no matter which truth values are consistently applied to x and not-x, the statement is unequivocally true. 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.

That a tautology constitutes absolute truth can be proven as follows. First, logic is absolute within any system for which (a) the complementary truth values T (true) and F (false) correspond to systemic inclusion and exclusion, a semantic necessity without which meaningful reference is impossible; and (b) lesser predicates and their complements equal subsystemic 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. So a tautology is "absolute truth" not only with respect to logic, but with respect to reality at large.

What does this mean? Uncertainty or non-absoluteness of truth value always involves some kind of confusion or ambiguity regarding the distinction between the sentential predicates true and false. Where these predicates are applied to a more specific predicate and its negation - e.g., "it is true that the earth is round and false that the earth is not-round" - the confusion devolves to the contextual distinction between these lesser predicates, in this case round and not-round within the context of the earth. Because all of the ambiguity can be localized to a specific distinction in a particular context, it presents no general problem for reality at large; we can be uncertain about whether or not the earth is round without disrupting the logic of reality in general. However, where a statement is directly about reality in general, any disruption of or ambiguity regarding the T/F distinction disrupts the distinction between reality and not-reality. Were such a disruption to occur at the level of basic cognition or perception, reality would become impossible to perceive, recognize, or acknowledge as something that "exists".

By definition, this is the case with regard to our cognitive-perceptual syntax, the set of structural and inferential rules governing perception and cognition in general. Since a tautology is a necessary and universal element of this syntax, tautologies can under no circumstances be violated within reality. Thus, they are "absolute knowledge". We may not be able to specify every element of absolute knowledge, but we can be sure of two things about it: that it exists in reality to the full extent necessary to guarantee its non-violation, and that no part of it yet to be determined can violate absolute knowledge already in hand. Whether or not we can write up an exhaustive itemized list of absolute truths, we can be sure that such a list exists, and that its contents are sufficiently "recognizable" by reality at large to ensure their functionality. Absolute truth, being essential to the integrity of reality, must exist on the level of reference associated with the preservation of global consistency, and may thus be duly incorporated in a theory of reality.

On the other hand, the fact that any reasonable definition of "absolute truth" amounts to tautology can be shown by reversing 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.

To recap, the characteristic attributes of a logical tautology are as follows: (1) it cannot be disobeyed, which implies that it has universal scope and thus accepts and truthfully predicates all closed sentential (predicative) structures, including itself and logic in its entirety, under assignment to its own variables; and (2) it is self-affirming or self-justifying and figures in its own definition or demonstration within the associated grammar. Obviously, (1) and (2) are not independent; (1) implies that a tautology is a universal, self-similar, metalogical element of syntax of the language and metalanguages of which it is a part, while (2) says that it is a critical element of syntax that cannot be eliminated without compromising the integrity of the syntax as a whole (thus, any supposition that it is false or eliminable reduces itself to absurdity by syntactic rules of inference, forcing the syntax to “protect itself” through reductio ad absurdum). Since any reasonable syntactic and/or semantic definition of absolute truth bestows upon it the properties of necessity and truthwise invariance with respect to content, it is unquestionably tautological in nature.

Accordingly, it is desirable to formulate reality theory as a tautology. To whatever extent this can be done, the theory constitutes "absolute knowledge" and is therefore eligible as a TOE. This suffices to show that if the form of absolute knowledge hopefully referred to as a TOE exists, it must be tautological. Next we will show that a TOE and its universe can be related in such a way that the theory is semantically tautological with respect to its universe, i.e. that (a) the theory is intrinsically tautological, and (b) its tautological structure is modeled by its universe. And in the course of doing so, we will show that it is indeed possible to ensure by the method of constructing this theory that its universe coincides with reality at large, and thus that it constitutes a valid theory of reality. Specifically, the construction will incorporate one or more attributes that are necessarily modeled by reality at large, and that simultaneously ensure the theory's tautological structure.

How can a TOE, or comprehensive theory of reality, be structured as a tautology? First, by definition, a TOE is universal; this is implied by the E, which stands for Everything. Thus, it is comprehensive. Second, it is self-referential; a theory of everything, being a part of the "everything" to which it refers, must refer to itself. More precisely, a TOE must be totally recursive in a manner analogous to logic, each atom referring exclusively to other parts of the theory, and be able to refer to itself in part and in whole in order to possess full logical closure. This can be arranged by incorporating one or more self-representative variables and their definitive relationships, up to and including a dynamic variable representing the theory as a whole (in fact, the theory can incorporate a “hology” predicate that goes considerably farther; instead of merely containing itself as a variable, a theory equipped with such a predicate can everywhere contain itself by virtue of self-similarity or self-distribution). Because it represents a theory of perceptual reality, this variable contains all elements of cognitive syntax and their perceptual contents; since variables can be defined in general terms without specifically enumerating their contents, we do not need to know exactly what it contains in order to use it. And third, because logic is the primary ingredient of cognitive-perceptual syntax, the self-referential TOE refers to logic in part and in whole and is therefore metalogical. Thus, it can incorporate a kind of ultimate truth predicate that asserts its own tautological structure and guarantees that no matter what (semantic and other) kinds of paradox may arise within the theory, they can always be resolved within the theory. A theory possessing all three of these properties is called a supertautology, denoting the reality-theoretic counterpart of a logical tautology.

Let us now attend to some of the details of constructing a supertautology. First, we repose the a priori and analytic knowledge that we are given in the form of cognitive syntax, including logic and all of its implications, in a variable to which we apply (a) the rules of logic itself; (b) three recursively-related metalogical axioms that are themselves true a priori and analytically implied by each other (in a word, self-evident). Note again that in creating and assigning content to this variable, we do not have to enumerate all of its contents; we can refer to them en masse by their joint characteristic, namely the "absoluteness" necessary to ensure perceptual and inferential consistency. Since a theory falls under the mathematical definition of a language, it is natural to refer to the contents in question as the "rules of syntax" of that language, or simply as its syntax; thus, the TOE recursively contains a variable representing its own syntax, permitting the manipulation of that variable and the grammatical extraction of its implications according to syntactic rules. This recursive construction makes the "absoluteness" of the variable (and theory) logically heritable, conferring absoluteness on whatever is inferred within the system. Together, the “implicate” variable and its “explicate” theoretic medium comprise a bootstrapped extension of the self-referential syntax of logic itself, letting that syntax be “mined” for a potential wealth of hidden analytic content.

The key to applying this knowledge scientifically is the semantic functionality of the three metalogical axioms adjoining the object-level syntax. Conveniently, these (recursively related) axioms can be thought of in terms of a trio of property-principle pairs, the "Three Cs" and the "Three Ms". The Cs are three properties that a TOE must inevitably possess, namely Comprehensiveness, Closure and Consistency, while the Ms are metalogical axioms respectively associated with those properties. These principles are the Mind Equals Reality Principle (associated with comprehensiveness), the Metaphysical Autology Principle (associated with closure), and the Multiplex Unity Principle (associated with consistency), respectively abbreviated M=R, MAP and MU. We have already been partially introduced to these principles in all but name, and in any case need only one of them to proceed farther: M=R. Concisely, M=R asserts that there exists a semantic (language-to-universe) correspondence between objective reality and the absolute subjective rules of perception and inference, i.e. cognitive and perceptual syntax. This correspondence defines a morphism, incoversion, predicating the assignment of a certain structural predicate, hology, to the universe-language/metalanguage system (see Introduction to the CTMU).

Hology, a special kind of self-similarity conferring supertautological status, equals the relationship of the TOE and its universe to the self-representative variable by which it is encapsulated. Hology means that the syntax by which reality configures, recognizes and processes itself is the image of a distributed endomorphism, the incoversion morphism, surjecting the objective self-intersect (distributed component) of reality onto every interior point and region of reality as transductive syntactic potential, i.e. as general rules of transduction to be variously expressed by objects at any location. Although real objects generally access and express only a small part of this syntax, combinations of interacting objects may express and access more of it by mutual input-to-output behavioral transduction; through this kind of behavioral transduction, the self-intersect, though generally composed of distributed rules applying everywhere in reality, resolves to a Distributed Conditional Form (DCF) explicitly containing all of the local systems and states generated by those rules. The self-intersect and its DCF resolution comprise the syntax and language of reality. Because hology maps the reality syntax to our cognitive syntax - because the self-intersect plays dual objective and subjective roles - perceptible objects and processes tautologically conform to our innate perceptual categories, making the TOE a supertautology comprising the purest and most universal kind of absolute truth.

The above reasoning subjects the absolute (a priori) knowledge in our minds to a kind of recursive "squaring" operation, causing it to self-explicate as its own medium and projecting it onto external reality. This repetitive operation resembles the mutual reflection of a pair of polymorphic mirrors, one labeled mind and the other labeled reality, that faithfully reflect each other's evolving image. Although one might suspect that the tautological nature of the construction renders it barren of interest, this would be akin to saying that a squaring operation never yields more than the original number. While that might be true for a featureless numeric identity (e.g. 1² = 1), the cognitive syntax of the human mind is far from "featureless". In recursive self-combination, it is capable of generating a universe, and a theory constructed according to this recursive relationship is capable of veridically capturing that universe. Indeed, there is a sense in which the TOE, and all of the absolute knowledge it holds, is identical to the universe it describes. But the meaning of this statement - and it is a statement that is pregnant with meaning - lies beyond the purpose at hand.

The CTMU is a theory of reality, or TOE, that has been constructed according to this blueprint. If, as a rationalist, one insists that absolute truth and knowledge are exclusively mathematical, then the CTMU is mathematics; if, as an empiricist, one insists that they reside exclusively in our direct perceptions of reality, then the CTMU is embodied in our direct perceptions of reality (including our direct perceptions of the comprehensiveness, closure and consistency of reality). The truth, of course, is that by the method of its construction, it is both. But in any case, would-be pundits who cling blindly to folk-epistemological "absolutes" like truth is never more than provisional, science is inherently without stability and there are no such things as absolute truth and knowledge are urgently in need of an intellectual awakening, and until it comes, should refrain from disseminating their irrational opinions to others who might gullibly mistake them for fact. Such truisms have their contexts, but these contexts do not include the highest levels of discourse regarding truth and knowledge, and they do not include the CTMU.

There is, of course, more to the CTMU than just its supertautological structure. For example, it incorporates a new conceptualization of spacetime, resolves numerous high level reality-theoretic paradoxes, and establishes a bridge between science and theology, all with considerably more detail than this brief monograph allows. But as regards "absolute truth and knowledge", its status as a supertautology is necessary and sufficient to explain why it is uniquely qualified for the title. If the simplicity and elegance of its design seems "too obvious", "too convenient" or "too good to be true", this is certainly no fault of the theory or its author; at best, it testifies to the opacity of certain formerly useful but outworn conceptual barriers erected in science and philosophy over the last several centuries, and to the inertia of the scientific and academic establishments which tend them.

One final note. The CTMU is neither intended nor presented as an encyclopedic compendium of absolute truth. It is meant only to provide a comprehensive, consistent and self-contained (and to that extent "absolute") logical framework for bridging the gaps between apparently unrelated fields of knowledge, helping to locate and correct fundamental inconsistencies within and among these fields, and developing new kinds of knowledge that might arise from the intersections of fields which already exist. Because the real universe is everywhere in the process of self-creation, human knowledge can and must continue to grow. The CTMU is intended not as a brittle, undersized pot that will root-bind and choke this growing knowledge, but as fertile and well-aerated soil through which it can spread. By its very design, the CTMU will continue to accommodate and accelerate our intellectual progress...and since there is no other theory that fully shares its design, it is irreplaceable for that purpose.

This completes our introduction to the topic of absolute truth and knowledge.