The Concepts and Methods I Employ.

Robert A. Herrmann, Ph. D.
17 JULY 1999. Last revision 1 FEB 2016.

The Mathematical Methods
I am a member of a large community of mathematicians M, where the constituents employ their imagination. The concepts, where some may not even be fully expressible by a language, are mentally "comprehended" by members of M. Other communities that consist of entities that do not possess the necessary imagination or such mental comprehension can perform mathematical manipulation and apply the mathematics created by members of M to other disciplines. Such manipulations and applications are also performable by members of M.

Among other accepted methods, members of M employ classical logic to deduce conclusions. They accept informal set theory and extend the notion of the counting numbers to include basic properties termed as those of the informal natural numbers. When used by certain members of M to investigate symbolic forms, these methods are termed as metamathematics. A complete list of the methods employed cannot be fully expressed since from time-to-time additional methods are adjoined to this list. The methods used are expressed within the pages of the papers published by members of this community. Often one becomes a member of this community by presenting a vast collection of written statements that are judged to be "correctly" expressed using the language and methods accepted by the other members of M.

The GGU-model Methods.

The method I use differs from the Bacon method of pure experimental science and the pure assumed hypothesis-deduction approach of theoretic science. It incorporates the best of both approaches. If you wish to have any true comprehension as to the method employed it might be necessary to suppress any contradictory presuppositions.

[The specific mathematics used is a combination of the standard methods of analysis and methods from mathematical logic. The in-depth development of the mathematics began in 1966.] Although not first presented in this form, intuitively, this is how the methods can be conceived.

(1) Actual observed behavior (the data) is mathematically modeled. All of the real behavior and actual observable physical entities that yield this behavior form, in a technical sense, the physical “axioms (hypotheses)” used for the model. Replication is used to verify that such behavior remains valid.

(2) The linguistic structure of the theorems that are established is the customary structure. (However, the statements are written in various equivalent forms and even, at times, statements are not included that are to be "understood" by the reader. For example, a statement such as "There exists an A such that B" has the hypothesis(es) may be missing. In which case, these are to be understood by the reader relative to the material being discussed.) For the GGU and GID models, certain hypotheses that correspond to the observed behavior are considered and the conclusions rationally deduced. These conclusions are also termed as rational "predictions." This is especially so since the mathematical statements are to be "interpreted." They predict the behavior of predicted entities.

For example, a theorem might state after the hypotheses are stated or assumed known by the reader that "there exists a set A such that . . . ." This means that the mathematical object A is a member of the set-theoretic structure being used and it has certain properties. This statement is obtained via rational deduction. Hence, the rationally predicted A "exists." Then the A and its properties can be further "interpreted."

(3) The "interpreted" predicted entities and their behavior patterns are not observable via any machine or human sensor. This fact parallels that of the methods used in modern physics except that the fundamental entities and behavior that lead to these predictions are not invisible to observation. Hence, there is a major difference between the methods I employ and those employed for early history cosmology and quantum physics.

(4) The terminology used is a modified version of the original terminology used to describe the observed behavior. This is done so that the predicted behavior can be compared with the observed behavior of the original observations being modeled. Hence, this new terminology is formed so that it retains the original intuitive meaning that has led to the predicted behavior. [A math. model has two sets of “axioms” – the mathematical ones and the non-mathematical, which are, in this case, the ones describing such behavior.]

(5) The concept of a mathematical model includes that of the "interpretations." An interpretation is a consistent substitution of terms taken from a specific disciple for the mathematical terms employed. For example, such terms as "ultrawords," "ultra-logic-systems," "hyperfinite," "hyper-algorithm" and the like may be replaced with terms taken from another discipline. For the GID-model interpretation, such substitutions employ terms such as "higher-intelligence" and "higher-language." Then, for comprehension, results that compare the technical terms with the original ones employed are interpreted. For example, since many members of the standard language L are comprehensible via our intelligence, then many members of the hyper-language *L are comprehensible via an higher-intelligence. Thus, one has a rationally obtained behavioral statement relative to the higher-intelligence.

The mathematical structure has various special properties and certain conventions are employed. For example, when one writes AB (⊂ means subset), then this has the usual set-theoretic meaning. However, one often needs to state or understand additional characterizations for A or B. Indeed, *A and *B are generated by different sets A and B that are subsets of a standard language L. One may need to either state, or it needs to be understood by the reader, that *A and *B are "internal" subsets of *L. Then the statement σA ⊂ *A is a correct symbol string to write. But if AL, then using a special convention and the finite nature of the objects employed, this is often written as (I) A ⊂ *A ⊂ *L. To complicate this even more, by convention, some may also express this as (II) A ⊂ *A ⊂ *L. Both (I) and (II) can be interpreted in the exact same manner. But technically the objects in (I) include an additional structure that models "how" we actually construct words in L.

It is important to understand that a mathematical model is not merely a haphazard collection of interpreted statements. The statements most be a especially selected collection from the many that can be rationally deduced. The selection of such a collection does not affect their rational production. For hundreds of years, the language of the "infinitesimals" and their known properties were employed to generate a vast collection of physical statements that do not include the infinitesimals or any of their properties among the statements. The same holds for the limit concept, where the entities cannot correspond to a local finite set of physical objects. Such auxiliary mathematical objects and procedures have been and remain today a major aspect of how mathematics is applied to obtain the actual behavioral descriptions that do not include any of the employed auxiliary features. Hence, it is unnecessary that I presently consider a philosophic discussion of this approach.

(6) In all respects, the basic GGU-model and GID-model interpretations have established the scientific rationality of various statements, which remains the major feature of the GGU and GID-models. One such statement is that "All observable physical objects and their observable behavior patterns are designed and sustained by an higher-intelligence. This higher-intelligence satisfies Biblically described characteristics." These mathematically obtained results do not establish the first statement as fact. Observation indirectly verifies this statement. This method is endorsed by Paul (Rom. 1:20). It is the physical evidence that we can "clearly see" that indirectly implies the power and divinity of the "invisible" higher-intelligence.

Now for a further discussion of this method. For the general intelligent design model, the unobserved behavior is shown to verify philosophic or theological descriptions. Recall that early history cosmology and quantum physics assume the existence of entities and processes that cannot be directly observed. They are used to predict behavior that is physically observed and the assumed entities and processes are accepted as "fact" based upon this indirect form of verification. In quantum field theory, there are numeriously many such invisible entities, the quantum fields, hypothized. They are assumed to exist throughout physical space.

There is also an invisible entity required by the GGU-model. It is called the "substratum" within which the mathematically modeled GGU processes take place. This medium includes the "covirtual" universes. The model predicts that it can include additional aspects that are not specifically comprehensible by humankind. However, the GGU-model processes have specific descriptions as to how they behave and produce universes. Although it has a more substantial foundation than various physical theories based upon invisible primitives, it is the fact that the processes can be interpreted via the language of intelligent agency and Biblical theology that makes it difficult for some to accept. However, as is done for many physical entities, these additional interpretations can be ignored.

My philosophy of science has certain aspects in common with the philosophy of instrumentalism. For the GGU-model, a gleaned physical law is not related to a physical "cause and effect." The cause and effect notion is but an aid when we predict physical behavior. The GGU-model is also based upon the notion of the physical-systems - a collection of entities. Properton collections allow for physical-systems to be those that are classified as observable. However, physical-systems may be composed of unobservable "particles" as proposed by quantum physics. These can also be referred to as physical-systems that comprise another physical-system's internal structure. These are all produced by properton formations. The "lack of knowledge" aspects of the model tends to limit speculation as to the possible unobservable constituents of a physical-system.

Relative to the GGU-model and propertons and physical-systems, there are unobservable aspects of modern physics that are unnecessary. Primitives such as the mentioned quantum fields, possibly "strings," "virtual" particles and processes, and unobservable hidden aspects of early history cosmology are entirely unnecessary. Therefore, I do not consider such systems or entities as physically necessary. As an example, excitations of quantum fields need not cause the fields to produce characteristics of "particles" since the fields need not physically exist. I emphasize this basic approach. It is not necessary to consider quantum fields and other such unobserved hypothesized entities as physically real. The observed behavior of an event sequence is pre-designed in an atemporal sense. These unobserved aspects of modern physics are "instruments" used by us to predict behavior, behavior that we may not be able to otherwise predict nor comprehend.

God has gifted us with an extraordinary mental capacity to construct theories for the sole purpose of predicting actual observed behavior. Such predictions are necessary so that we can follow His requirement that we "subdue" the earth and, in so doing, build our human made universe.

For the method I use, actual observable behavior predicts entities and processes that yield directly observable data as well as the unobservable. Hence, in a much stronger fashion than early history cosmology and quantum physics, the existence of physical-like and unobservable entities and processes as predicted by the GGU-model method can be accepted as fact more readily than predictions for behavior within an unobservable world that is based upon unobservable hypotheses.

When a data-set exists, the Bacon empirical approach requires that an "educated" guess be made. However, my approach is not actually a mere guess. I knew some-how-or-other from my experience or otherwise that if I modeled the data-sets using a new mathematical approach, then most likely I would be able to solve the General Grand Unification problem and also secure the GID-interpretation. I have developed elsewhere a model that shows rationally that immaterial entities can influence human thought. Prior to 7 April 1977, I exhibited no great creative ability. This is not the case after that date. I always give credit to God for influencing my thoughts.

I use the same methods as those used by the scientific community relative to indirect (observational) verification. As stated previously, properly constituted creationary theories use the exact same rules and procedures as those used to construct properly constituted "standard" scientific theories. When I am concerned with creationary science, the procedures I practice do not alter, in any manner, the accepted methods but improve upon them. For a pure secular physical-like application, the "behavior" is interpreted as that of physical-like processes within a substratum world. Using these accepted methods, there tends to be two approaches to creationary science. One approach is to add to the hypotheses a "Divine intervention statement." The addition of this hypothesis during various aspects of theory building does not alter the methods utilized. The method I use is not of this type.

I emphasize, that all of the creationary science models I have discovered do not use as a fundamental hypothesis any such Divine intervention concept. This is why the GGU-model has purely secular interpretations. Relative to creationary science, I use the concept called re-interpretation. After a model is constructed, not before, the terminology is altered by replacing "ultra" or "hyper" prefixed terms with "higher-intelligence" mental-like terms. The terminology is again altered and these terms are replaced by theological expressions. All other aspects of the scientific method used remain unaltered.

There are assumed physical events employed by most of the theories produced today by secular theoretical methods. These events cannot be verified by an exact laboratory experiment using the hypothesized physical entities or processes. Hence, all such theories and the events they tend to explain should probably be categorized as a form of scientific speculation although many, who through great effort produce such theories, would probably categorize their work as but theoretical science. However, such theories cannot be characterized as scientific fact.

Notwithstanding such a categorization, the questions these theories attempt to answer are, however, highly interesting relative to an individual's personal philosophy. For this reason, knowledge as to the existence of the refined and improved theories - the standard theories - and the existence of the creationary theories that, relative to explanatory power, are equivalent to or better than standard theories is of considerable significance. It is self-evident that, in order to consider a choice between competing theories, individuals would need to have unbiased knowledge as to a theory's specific predictions as well as the hypothesized unobservable entities and processes. However, if an individual wishes to make an informed and appropriate choice from a collection of theories that are equivalent in explanatory power, then the choice would need to be based upon philosophic or other non-scientific considerations.

As a minimal requirement, I consider a properly constructed scientific theory or model as a (Biblical) "creationary" science theory or model if it, at the least, does not contradict a strict interpretation of the Bible's Genesis 1 creationary statements when so interpreted. The strength of any such theory or model depends upon whether it also predicts not only each Biblical creationary event, including the Genesis Flood, but whether it also predicts physical events as observed today. There is a theological interpretation of the GGU-model that yields every strictly interpreted physical event as described in Genesis through the Flood, as well as, all physical events that have been observed and recorded since the Flood. Of course, besides this minimal requirement, Biblical creationary theories can validate many other theological principles. The following is a major requirement for my Biblical interpretations.

The Bibles states that one should neither add to nor subtract from it. This does not just include words and phrases but concepts as well. I follow the Paul Rule of 1 Cor. 15:1-2 and throughout all of my creationary science and theological writings I adhere to the follow: As proposed by some philosophers beginning after the death of Apostle John and who apparently use forbidden methods of discourse (Col 2:8), I do not accept that, throughout Biblical times, God may have deceived His followers. Some claim that His ideas and concepts as originally presented within the Bible's pages are faulty. The claim is that the strict or obvious nuances in meanings for the Biblical terms used therein are incorrect and have other meanings that have been hidden until revealed after the death of Apostle John. This claim I reject. These other meanings even contradict the strict or obvious nuances. God notes when He sends a deception. For me, any such alterations in the strict meanings or obvious nuances for the words as understood during Biblical times would make the entire Bible untrustworthy and even contradictory and, hence, useless except for historical information.

The article Genesis 1 is my strict interpretation of Genesis 1 to which I apply the GGU-model. Of course, the GGU-model applies to other interpretations as well.

Reference

[1] A more in-depth discussion of what constitutes direct or indirect "physical" evidence. See section (F).

[2] Imagining the Infinite.


Click back button, or if you retrieved this file directly from the Internet, then return to top of home page. If you retrieved this file while on my website, then return to top of home page.