Modeling Divine Attributes or the Biblical God is a Scientifically Rational Concept

Robert A. Herrmann, Ph.D.

In 1978 (Herrmann 1979, 93), a method to model God's Biblically described attributes as they are compared with human attributes was discovered. The modeling technique is based upon Genesis 1:26, which allows for such a comparison. As discussed in below, collections of such attributes may also be used to model other theological concepts. The basic results were first publicly presented in Herrmann (1982). In this article, I present the significant modeling methods used for the "attribute-model."

In 1979, using the 1978 methods, the foundations for the General Grand Unification (GGU) Model and the General Intelligent Design (GID) Model were developed. The mathematical portion of these models is rather complex and is not presented in the article. However, their significance is discussed. Are these mathematical models valuable?

For hundreds of years, atheistic philosophers and scientists have claimed that a supernatural God, as Biblically described, is an "irrational" notion. Indeed, this belief is particularly paramount today. But, if the basic attributes of the Biblical God can be modeled mathematically, then, since such a model uses scientific logic, this atheistic mind-set is falsified. Moreover, if it can be shown that every physical-system and alterations in the behavior of such systems follow God's creationary attributes, then this would give a vast amount of indirect evidence for the existence of the Biblically described God. Obviously, the existence of such models would be a valuable theological contribution.

What does it mean to state that Jesus is the Son of God? This statement occurs over forty times in the New Testament. In the Greek language, the term "son" need not correspond to a biological son or an adopted son. If an individual A had nearly the same characteristics as an individual B, then B could refer to A as his "son" and A could refer to B as his "father." Apparently, this is how "Son" should be interpreted in these many cases, but in the strongest possible sense.

Using Herrmann (1979, 93, pp-23-24), first, consider B as a list of God's Biblical attributes written in a form that can be qualified by the word "very." For comprehension, only consider the attributes that are similar to human attributes. Each member of the set "represented" by the symbol B can be specially expressed in a word-form. For example, in this list are words such as "intelligent, wise, creative, just, loving, etc." When the foundations for a mathematical model are specified, they are often straightforward. But, from such a simple basis, a highly complex mathematical theory can emerge. Such a theory can then be used to "model," via terminology changes, other discipline notions. What follows is an example of this process.

The basic intuitive idea is that the attribute being described by the phrase "very intelligent" is "stronger than" or "better than" or "greater than" or a similar phrase than the attribute described by the word "intelligent." Further, we would have that "intelligent" is "weaker than" the attribute "very intelligent." One continues with this intuitive notion and considers the attribute being described by the phrase "very, very intelligent" as stronger than the attribute described by the phrase "very intelligent." One uses the informal idea of "mathematical induction" and obtains a set BP that contains each member of B and all of the strings of arbitrary length of the qualified members of B, the "very, very, . . . very b" strings of symbols, where b denotes a member of B.

A special form of simple logic is also identified. Due to the forms involved and not due to the rules of grammar, this special form of logic is called "adjective reasoning." Intuitively, this form of reasoning takes any member c of BP and logically yields that member of BP and all of the other members that are "weaker than" c. For example, let b = "very, very intelligent." Taking b and applying the specified rules for this logical process yields the set {"very, very intelligent," "very intelligent," "intelligent"}. Adjective reasoning can also be viewed as a very simple restriction of one of the most basic forms of human thought - propositional deduction. Propositional deduction is a basic part of the classical logic used throughout scientific discourse.

Now comes the somewhat more difficult part. All of these intuitive notions are turned into standard mathematical objects by a coding process and they are embedded into the mathematical theory of natural or real numbers. I note that this is just what happens in modern digital communication and what is done to communicate with a computer. Each of these word-forms is considered as coded by a binary representation for a natural number - a string of 1s and 0s like 1001 = 9. In what follows, the standard coded results are denoted by bold fact type. Thus, BP denotes the coded and embedded set BP. Then BP is further embedded into a rather complex mathematical object called the Grundlegend structure (Herrmann, 1979, 93).

A mathematical theory, in form, is most simply understood as a collection of symbols that technically have no non-mathematical meanings. When one, in a consistent manner, substitutes for various mathematical symbols meaningful words or phrases from another discipline or a different portion of mathematics itself, an "interpretation" is produced. The entire substitution process yields a "mathematical model." Scientifically such interpretations yield the must highly consistent, rational and predictive collection of statements obtainable by a human mind using portions of classical logic. We certainly hope this is the case anyway. This is exactly what is done in the case of BP when it is viewed from the Grundlegend structure. The theory automatically generates the mathematical object *BP. The set *BP is predicted. It is not part of the hypotheses used. Significantly, there are additional mathematical objects in *BP that are not in BP.

Yet, a more difficult part is investigating the properties of those members of *BP that are not in BP. The major result for this application is Theorem 4.4.1 (Herrmann, 1979, 93, p. 46). This is what has been discovered. Take any member b of B. Then there is an object d in *BP, which is not in BP, with the following "interpreted" properties. One cannot actually write down the complete form the object d takes, although we can write down portions of it. What we know, in general, is that it mathematically exists and some of its properties. For example, d's behavior with respect to the "better than" ordering can be expressed. Consider any finite string of symbols "very, very, . . . b." Then d is "better than" "very, very, . . . b." When adjective reason A is coded and viewed mathematically, a "higher form" of adjective reasoning *A is predicted that contains the original idea of adjective reasoning. Using *A, each "very, very, . . . b," no matter how many "very"s are placed next to the b, is obtained. What this means is that if d is interpreted as a Divine attribute, then the collection of all the weaker attributes are also used, in a comparative means, to define the Divine attribute. "God is good. God is very good. God is very, very good. God is very, very, very good. etc. " Indeed, the model explicitly shows that such a more complete collection of modified attributes is a logical consequence associated with a "higher intelligence."

Adjective reasoning, *A, as viewed from the Grundlegend structure, reveals a higher form of reasoning that when restricted to members of BP models human adjective reasoning. This verifies one aspect of Genesis 1: 27. God has given us some of His reasoning power. Since b is arbitrary, then these characteristics hold for any member of B. Note that in all cases of which I am aware, this human form of reasoning is equivalent to a portion of "scientific" reasoning. Further, these results have been rationally established by means of scientific deduction

[Note: The A and *A will yield extraneous results (i.e. forms). However, using the recently discovered notion of the general logic-system (Herrmann, 2001, 2006, 2006a), the A and, necessarily, the *A can be restricted so as to remove all of the extraneous results.]

Within physical science, and especially quantum physics and early history cosmology, the actual objects discussed cannot be directly observed. These objects are defined by their measurable and describable characteristics. Their existence is "indirectly" surmised by their observable predictions. Thus, using this acceptable indirect approach, aspects of human behavior and human reasoning yield indirect evidence that there rationally exists an object characterized by those members of *BP that are not contained in BP. (Symbolically this set of attributes is denoted by *BP - BP.)

The Scriptures state that "Christ is the image of ('the invisible' in the Sinaiticus Codex) God," 1 Cor. 4:4, and "He is the image of the invisible God," Col. 3:10. For these two Biblical statements, Vine states, that Christ is "essentially and absolutely the perfect expression and representation of the Archetype, God the Father," and that "Christ is the visible representation and manifestation of God to created beings" [Vol. II, p. 247]. Hence, for a set of God's attributes that are restricted to the created universe, let the restricted Father attributes be FA, let the restricted Son attributes be RS, and let HS denote the restricted Holy Spirit attributes. The Spirit attribute of God and the immortal spirit of a human being are considered as a type of restricted attribute. Notice that in John 14: 15-20, Jesus states explicitly that the Holy Spirit will display His attributes. Further, Jesus also displayed a restricted form of the "creation" attributes. (The man "Jesus" has attributes that are not Father attributes, such as various human characteristics. Further, when Jesus "speaks" one needs to determine whether He is displaying His physical and human attributes only, or His restricted Father attributes.) An important first step is taken when it is realized, using John 10:30, John 14:9-11 and the notion of "image," that, at least, in the physical-world

RS = FA. . . (1).

But, is there more that can be done using this mathematical approach? Consider the Biblical notion of "being perfect" or "being complete" or "mature." The Scriptures state in Matthew 5:48 that one of the Father attributes is being perfect. Also in Hebrews 2:10, 5:9, 7:28, we find that the supernatural Jesus is perfected and, indeed, perfected for the eon. Consequently, being perfect is an attribute of The Father and, in general, an attribute of God. This Biblical notion can be modeled by adjoining to the set BP additional word-forms that include the simplest logical implication associated with "completeness." This yields the coded set of comprehensible word-forms BPC. For this investigation, a set is "complete" if it can be logically demonstrated that it contains all objects that satisfy a specific requirement. A special logical process P, strong reasoning from the perfect, is defined (Herrmann, 1979, 93, p. 38). (This P is obtained by using a restricted form of propositional deduction.)

In this model, the set *BPC is used as a representation for the *-comprehensible God. (A comprehensible attribute is also *-comprehensible. *-comprehensible is a comparative notion. In order to "understand" what all members of *BPC - BPC signify, a higher language and higher "thought" processes must be applied.) The attributive set BPC contains the three sets that model the Father, FAC, the Son, RSC and the Holy Spirit, HSC, attributes. Since RSC is a restriction, it does not immediately follow that FAC = BPC. Depending upon how the C is constructed, application of Theorem 4.3.5 (Herrmann, 1979, 93, p. 43) yields a rational derivation for equations

*P(*FAC) = *P(*RSC) =*P(*HSC) = *BPC. . . (2)

The equations in (2) can be difficult to interpret when one considers that *P represents a higher intelligence. However, they do have one significance interpretation when viewed from the Biblical "third-heaven," so to speak.

(***) Using the operator *P to obtain the third-heaven view, the supernatural entity being described by *P(*RSC) cannot be differentiated from the other two within this third-heaven. All three represent a perfect entity, which is represented by perfect *BPC. (***)

Equation (2) has been established via mathematically (scientific) reasoning. Although, equation (2) can be discussed and interpreted informally, humankind cannot actually mimic the logical process *P. Additionally, this equation satisfies, at the least, three different notions. Which of these notions one accepts requires additional sources of rational information if one wishes to make an intelligent and rational Biblical choice. The notion of "choice" is one way of to determine intelligent actions. The actual attributes that produce (2) are the three sets of restricted physical world and C extended attributive collections FAC, RSC, HSC.

(A) Using the modeling notion of Occam's Razor, it is rational to state that the three related attributive descriptions, FA, RS, HS, signify that the Spirit of God, "simply" manifests itself within the physical world in specific Biblically described ways and these manifestations can be grouped, at the least, into three categories as observed within the physical world. That the one inseparable Spirit of God is the medium used to actuate each manifestation. This is the tri-category model. One can conclude, using this tri-category model, that part of the Divine "plan" (logos) is that, if necessary, God will present Himself to His created physical universe via RS. In this case, RS is a restriction to the physical universe of the attributes described by *FAC, as indicated by equation (1). Note that, in this model, when Jesus is "perfected" in the sense of restricted C, then the glorified Jesus displays attributes that were not displayed prior to His perfection. Further, as the supernatural Father, God can refer to Himself in various ways, such as emphasizing the completed *RSC without it contradicting this rational model. Significantly, this emphasizes the personal relationship between God and each member of His church. (As discussed below, there are other aspects of this restriction that are not represented by members of *FAC, that give a restricted process by which Jesus can also display His purely supernatural aspects.)

(B) On the other hand, one can accept the non-biblical notion described by Justin Martyr and the 900 years of "progressive revelation" needed to modify his description and accept a distinctly different classical concept. In this case, all the Biblical statements that imply equation (1) and the relation between Jesus and the Holy Spirit are rejected. In this case, it would be accepted that in the third-heaven *FAC, *RSC and *HSC describe distinct supernatural objects that share the basic attributes that would classify them as God and they use the same medium to manifest themselves in the physical world. Then equation (2) would be interpreted as a unification statement. Historically, there have been seven different methods suggested to unify these three collections. Indeed, some theologians have stated that how these three are unified should be classified as a "mystery."

(C) Some theologians suggest a third possibility. For them, equation (2) does not apply at the moment that Jesus is perfected, but rather at a moment near the end of Revelations. At that moment, their interpretation states that the distinct entities of (B) are unified in such a manner that they can no longer be differentiated one from the other.

Of course, a selection of the appropriate possibility should be related to actual Biblical statements, wherever possible. The two basic interpretations, (A) and (B), for equation (2), although poorly stated, were published in Herrmann (1982). Interpretation (A) is rationally obtained from the rationally predicted equation (2). Interpretations (B) and (C) are hypotheses termed as revelations and they do not follow rationally from Biblical statements. Objects such as BPC are composed of specific members that are additionally characterized as being "finite." This notion is transferred to *BPC, part of the "language" that can be employed by members of God's glorified church. "Expressions" from this language are *-comprehensible and carry an additional mathematical characteristic. One can substitute for the *, when appropriate, the prefix "hyper." Only such objects are hyper-comprehensible within this third heaven (2 Cor. 12:2). In 1 Cor. 13:12, Paul states that we will comprehend more. But, in many places, such as Job 28: 13, Psa. 139: 6, Isa. 55: 8-9, Rom. 11:33, the statements imply that, in general, God has incomprehensible behavior partially represented by *BPC - BPC.

Within the third heaven, it is sufficient that His glorified church view *P(*RSC), *P(*FAC), *P(*HSC) as representing identical objects (eq. (2)). This helps to explain why God identifies, in a specific manner, the *P(*RSC) attributive collection (the perfected and risen Son - the Glorified Jesus) as the most significant and hyper-comprehensible representation since it includes all aspects of His personal relationship with His physical creation and His church. Since technically RS is contained in *RS which is contained in *P(*RSC), then *P(*RSC) also represents God's abilities to accomplish tasks - His power - as the Biblical term "dunamis" signifies. (He has "great power; very great power; very, very great power; etc.) It is significant that the collection *P(*RSC) represents all of the hyper-comprehensible knowledge of God's comparative behavior that any of His created beings, in any of their allowable forms, can ever "comprehended."

The mathematics that appears in Herrmann (1979, 93, pp. 27-56) can be used to model other theological notions that some would consider less significant and, in some cases, highly speculative in character. Some of these are associated with C. S. Lewis descriptions. In this short article, I will not consider any other material that appeared in the original G-model book.

In Aug. 1979, I was challenged to solve the General Grand Unification problem. The problem is to find a collection of mathematical objects from a specific category that will unify all physical-system behavior. I recalled two statements:

"The structure of the material universe has something in common with the laws that govern the working of the human mind." Louis De Broglie

". . . events in the remotest parts of space appear to obey the laws of rational thought. . . . According to it what is behind the universe is more like a mind than it is anything else we know." C. S. Lewis.

My original solution to this problem began with the notion of a scientific theory. All such theories use human thought processes to predict physical behavior from a set of hypotheses. The solution was not based upon any desire to model mathematically any Divine attribute. I postulated that a solution to this problem involves a collection of mathematical objects that model "thought processes." The question then becomes, what thought processes and what mathematical objects would solve this problem. The actual mathematical structure used is not one of the usual standard structures, but the solution requires a "nonstandard" structure. General nonstandard structures were not discovered until 1961 and applying nonstandard analysis to thought processes had not been done.

The problem is solved, in the main, by applying standard and nonstandard analysis to certain operators (Herrmann (1979, 93, pp 65-128) that, at the least, represent the most basic aspects of human deductive thought. For this application, an "operator" models processes in a specific manner. When an operator is applied to a set of hypotheses X, it predicts all of the conclusions that can be rationally deduced from X. In the 1930s, Tarski introduced operators that accomplish this. They are not well known. Two other operators that complete that solution are also modeled by other aspects of human thought. One is the "finite ordered choice operator." This operator models the human ability to take a finite collection of objects and "order them" in a specified manner. Then there is the "finite sum" operator that conjoins "finitely" many simple objects to form a more complex object. These modeled processes are all needed to use scientific theories or physical laws to predict behavior. These operators are coded and their properties investigated using nonstandard analysis. The results are the GGU-model and the GID interpretation. I note that the term "nonstandard" does not mean there is anything wrong with the mathematics, it is a technical term.

After the secular GGU-model was constructed, it became obvious that this model can be interpreted in a manner that will model other Divine attributes. Among these attributes are the Biblically stated Divine creationary methods, the notion that God designs all physical-system behavior and entities and yet allows free choice, that God is a higher intelligence, that God sustains the behavior of all physical-systems within our universe and that physical-systems display signatures for God's higher intelligence. Two more operators have been discovered (Herrmann, 1994) that when theologically interpreted yield sudden alterations in our physical world that can be classified as miracle events. Moreover, they verify the Biblical statements that supernatural influences can affect human thought processes. Of course, the GGU-model in its pure secular form need never be interpreted theologically.

Thus, the rational existence of the Biblically described God is further strengthened by considering the Biblical creationary aspects of God as they are modeled by a theological interpretation of the GGU-model, the GID-model (Herrmann, 2002) as well as other rationally described processes.

References

Herrmann, R. A. 2002. Science Declares Our Universe IS Intelligently Designed, Xulon Press, Fairfax, VA.

Herrmann, R. A. 2001. Hyperfinite and standard unifications for physical theories, Internat. J. of Math. and Math. Sci., 28(2):93-102.

Herrmann, R. A. 2004. Nonstandard consequence operators generated by mixed logic-systems, http://arxiv.org/abs/math/0412562

Herrmann, R. A. 2006. General logic-systems and finite consequence operators, Logica Universalis, 1:201-208.

Herrmann, R. A. 2006a. General logic-systems that determine significant collections of consequence operators, http://arxiv.org/abs/math/0603573

Herrmann, R. A. 1982. "The reasonableness of metaphysical evidence," J. of the American Scientific Affiliation, 34(1):17-23.

Herrmann, R. A. 1979, 93. "The G-model Applied to C. S. Lewis. The Mathematics." This portion of this book is now contained in pages 1 - 64 of "The Theory of Ultralogics" (1993). "The Theory of Ultralogics" is available at the Mathematics and Physics Archives. http://arxiv.org/abs/math/9903081 http://arxiv.org/abs/math/9903082 However, updates may appear at this URL.

Vine, H. E. 1940. Expository Dictionary of New Testament Words, Fleming H. Revell Co., New York.