Ultralogics for the GGU-model and
the GID-model's Higher-Intelligence.

Robert A. Herrmann, Ph.D.

A "logic" is a set of rules for rational deduction. For the GID-model case, these rules are applied to a set of "hypotheses" and the results are called (rational) "deductions." For the GGU-model, the rules are equivalent to a substratum process used in the formation of a universe. As described next, this process directly corresponds to the "rationality" of Nature and is considered as having an intelligent agency signature. For the Complete GGU-model, these specific GGU-model rules directly correspond to the basic concept of GID-intelligence. [Additional mathematically related statements appear between the [ and ].]

We are told, from a human mental viewpoint, that "nature is rational." When we linguistically describe behavior of physical entities, we are able to predict their behavior by following certain linguistic rules - the rules for rational deduction. Look at a physics science-community textbook-derivation for the highly discussed galactic redshift. You can, as I have done, specifically trace out the step-by-step logical steps used to obtain the redshift expression. Any such derivation uses a "logic-system," which contains the "rules of inference" R and a set of mentally applied procedures, AG, the "algorithm," in order to obtain the deduced result. Recall certain applied mathematical notation. If you are given the measure, F, for the force of motion, and the mass, M, then you can calculate the acceleration, a, of a moving body as a = F/M. The force and mass can be considered as changeable. This yields an expression in "two variables," a(F,M) =F/M. Hence we have "a" applied to "F" and "M." In some areas of algebra, the symbolism is reversed to maintain a left-to-right operational notation in that F and M are first obtained and then "a" is applied. This is written as (F,M)a.

The general AG algorithm (operator) is applied to the R coupled with a set of hypotheses H, that is AG is applied to (R,H). Since the AG rules are fixed, this can be written as P(R,H) = AG((R,H)) [or ((R,H))AG in one of my articles]. This particular "redshift" physics logic-system R is part of the much larger physics science-community logic-system that may by mostly implicit in character until one explicitly argues for a prediction. For the GID and GGU-models, this entire procedure is equivalent to results obtained by successive modus ponens (i.e. the rule of detachment) deductions relative to a specially constructed "word." The R, H and AG are abstracted and mathematically modeled.

For the GID and GGU-models, the R coupled AG mental processes are equivalent to ordered modus ponens deductions applied to the hypotheses H. Hence, P(R(n),H) = AG((R(n),H)), for these models, is a logic applied to H, where the R(n) corresponds to finite sequence of "n," "If A, then B." forms and H is the "first" A in the "first" form. These are members of the language L. Indeed, any finite sequence of such forms is a "word" in L. (The notion of what constitutes a language is extended for the GID and GGU-models to include all digitized sensory human-impressions and specific unobservable behavior and entities.) The characterizing aspects displayed by P(R(n),H) are embedded into a mathematical theory. This yields the representation P(R(n),H) and, further, the mathematical object *P(*R(λ), *H) = *P(*R(λ), H) is predicted. [In the technical papers, the AG is denoted as an underlined script A. Further, mathematically the P alone is used as a representation for the collection, in ordered triple form, composed of R(n), H and value the P(R(n),H) as the R(n) and H vary.]

The "bold" notation indicates that this is an entity within the mathematical structure being employed. Note that the terminology being used is an "interpretation" for these symbolic forms. *P(*R(λ), X) is called an ultralogic, when applied to X, and it is defined on special subsets of *L, the internal subsets, and has predicted properties that can be compared to those of P via the interpreted representation P. When a single hypothesis H is considered, in this formate, it is considered as a singleton set {H}. [Note the actual formate uses the order pair concept and the reason for the * on P is relative to the single symbols representation for P. This yields the highly significant form *(P(R(n),H)) = *P(*R(n),*H.]

The logic-system approach is equivalent to a consequence operator C that takes sets of words in L and yields words in L. The operator C also has special properties but C does not display the R being employed. The set of words it uses is called a set of premises. If one takes a set of premises X ⊂ L, then the set of all deductions Y obtain is the result of this operator. This is denoted by C(X) = Y. It has been shown that, in general, each such C also determines a logic-system from which the C can be obtained. Hence, in general, the deductive results obtained by application of C are equivalent to the deductive results obtained by applying AG to a logic-system.

Originally, the logics considered for the "The Theory of Ultralogics" were of the consequence operator form and *C was called a "superlogic." I had to changed the name to "ultralogic" since the term superlogic was already in use. But, why use the prefix "super" or "ultra"? Are "mental" processes characterized by *AG really "super," or as now termed "ultra," when compared to AG? Why do I term the characteristics for *AG as those of a higher-intelligence?

Note that each member of L is directly related to a corresponding member of L. And, how words are formed using members of L is directly related to an operator defined on L. Each alphabet member of L is directly related to a member of L and the length of a word in L corresponds to the notion of length of a word in L. Thus, for our purposes, L behaves like a language. In terms of the higher-intelligence (HI) interpretation, it turns out that HI can use the *P(*R(λ), •) process on members of a language *L that are much larger than those in L, the set that represents our human language. But, our human language is contained in *L. If you restrict these particular HI activities to L, then you get P(R(n), •). So, mentally, human beings are associated with this HI "starred" process. But, basically, for this interpretation what can the HI do that human beings cannot?

Let X be an interpreted finite set of hypotheses that humans can use, and Y the (interpreted) set of all deductions. Consider a defined standard logic-system process G(R',X) = AG(R',X), where R' is the set of rules of inference and X is a set of premises to which the rules are applied. Then using the same interpreted X the HI *G deduces conclusions *Y. *Y can be the same as the deductions Y, but, although *Y contains Y, *Y is, usually, much, much larger than Y. This is the exact definition for a "stronger" process and indicates why *G represents an HI-designed action.

The reason for an increase in deductive power is that when *G is investigated it is discovered that members of *Y can be the result of applying hyperfinitely many *algorithm steps. This is the case for *P. The hyperfinite includes the finite, but, often, it is highly infinite in character. The G that humankind uses is restricted to finitely many steps. This also implies that to obtain any deduction, we can use only finitely many premises. This need not be the case for application of *G

If X is an infinite set of premises, and in science there are many of these since varying parameters are often used, then each deduction uses only a finite subset of X. But, for general *G, hyperfinitely many premises from an automatically expanded set of premises *X, which contain the X premises, and the predicted "rules of inference" *R, can be used to obtain deductions. Such an hyperfinite set can be infinite, and, in that case, it has a "size" "greater than" any infinite entity ever considered for any application of the infinite to standard physical science. Further, for the GID-model, it is predicted that, in a microsecond, the HI can deduce an infinite hyperfinite set of conclusions by application of *P(*R(λ), •) to H.

Another aspect of the HI processes is relative to the language *L. This language contains certain objects that behavior like ordinary language symbols, words, sentences and has a grammar. But, for these objects, no human being can have any direct knowledge as to what are the words, sentences or even the symbols. The HI can use hypotheses from this unknowable portion of its language and deduce meaningful members for our language L for which humans can have direct knowledge.

There are other rather unusual differences between the HI processes and what humans can do but it requires one to have a basic knowledge of the workings of the nonstandard model. Nevertheless, these intuitive notions, in my view, certainly should indicate, on a basic level, why I use the term ultralogics. BUT, now I come to the truly sensational difference between ultralogics and human mental activity.

One can characterize human mental processes in a general manner. Then it turns out that there are other HI processes called "pure" ultralogics. This type does not carry the "star" on the symbol used to identify it. They have all of the same characteristics as listed above but with a major difference. If you restrict their behavior to the language L, you do not get all of the properties being expressed by the pure ultralogic. Indeed, some described results that one would observe would appear to be unguided and chaotic from the human viewpoint. The ultralogics that model probabilistic behavior are of this type. In this case, this shows that HI has intelligently designed each finite sequence of the specific physical events, where it is often assumed that the behavior is random, AND maintains the probabilistic behavior as well.

For the GGU-model, ultralogics are also termed as intrinsic ultranatural processes, or IUN-processes. From a secular viewpoint, they can be considered as force-like processes. Using this terminology, they can be considered as producing physical-systems, and producing, staining, guiding or controlling physical-system behavior. Their relation to intelligent design by a higher-intelligence can be considered as an extraneous interpretation that is ignored as is done in quantum logic. For the GID-model, ultralogics have the same GGU-model "meanings" except their relation to intelligent design is not ignored and these IUN-processes are coupled with the intelligent agent characteristics that are considered a general signature for the intelligent design aspects. From the GID interpretation, ultralogics are designed by an HI, when applied they exhibit HI actions, and, necessarily, the structural and behavioral patterns produced are intelligently designed.

Last revision 14 FEB 2018.