Modeling Divine Attributes
Robert A. Herrmann Ph.D. In 1978 (Herrmann 1979, 93), I discovered a method to model God's Biblically described attributes as they are compared with human attributes. Collections of such attributes can also be used to model other theological notions such various Trinity concepts. The basic results were first publicly discussed in Herrmann (1982). In this article, I present the actual modeling methods used.
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 nor 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.
From 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." These are attributes that can be compared to those of His created. For example, in this list are words such as "intelligent, wise, creative, just, loving, etc." 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 is a member of B. It seems that BP, from a mathematical point of view, can also be considered as a collection of formula taken from a very simple propositional language.
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. It is shown that this yields an operator called a "consequence operator" (Herrmann, 1979, 93, p. 29-30). Mathematically adjective reasoning can also be viewed as a very simple restriction of propositional deduction.
Now comes the somewhat more difficult part. All of these intuitive notions are turned into standard mathematical objects by a codifying process and they are embedded into the mathematical theory of natural or real numbers. The standard embedding process is often 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 an "interpretation" is produced. The entire substitution process yields a "mathematical model." Scientifically such interpretations yield the must highly consistent and predictive collection of statements obtainable by the human mind. 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. 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 4.4.2 (Herrmann, 1979, 93, p. 45). This is what is discovered. Take any b, a member of B. Then there is an object d in *BP with the following interpreted properties. The object d takes the b and qualifies it with many, many "very"s. Further, when the "better than" ordering is embedded, one concludes that this d gives a meaningful attribute that is "better than" (stronger than) any of the "very, very, . . . b" attributes that are qualified by any finite number of "very" symbol strings. Moreover, *BP also contains the original weaker members of BP. Logically this is necessary since if d is interpreted as a Divine attribute, then the collection of all the weaker attributes are also used as a comparative means for defining 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, is a higher intelligence consequence operator. As easily shown by characterizing adjective reasoning defined on a single member of BP, when *A is applied to d, then d and all of its weak forms are "logically" produced. Since b is arbitrary, then these characteristics hold for any member of B.
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. Indeed, by the specific information associated with these characteristics. Thus, using this acceptable indirect approach, it is rational using mathematical reasoning to assume, at the least, that an object characterized by *BP exists.
The Scriptures state that "Christ is the image of ('the invisible' in the Sinaitcus Codex) God," 1 Cor. 4:4, and "He is the image of the invisible God," Col. 3:10. Relative to these two Biblical statements, Vine states, relative to such an image that it 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" [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 HG denote the restricted Holy Ghost attributes. The Spirit attribute of God, like the immortal spirit of a human being, is considered as a type of restricted attribute. Notice that in John 14: 15-20, Jesus states explicitly that the Holy Ghost will display His attributes. Further, Jesus also displayed a restricted form of the "creation" attribute. This form corresponds, at the least, to how God created Adam and Eve. (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 only human attributes, 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 "perfectness" or "completeness" or "mature." The Scriptures state in Matthew 5:48 that one of the Father attributes is perfectness. 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 as well as an attribute of the 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. The coded C models "perfectness" in the following sense. For some logical process H, where H is a consequence operator, H applied to some DC can yield an object that contains no, some or all members of BP. A special consequence operator P, strong reasoning from the perfect, is defined (Herrmann, 1979, 93, p. 38). In this model, the set *BPC is used as a representation for the *-comprehensible God's. [The notion of *-comprehensible is described below.] The attributive set BPC contains the three sets that model the Father, FAC, the Son, RSC and the Holy Ghost, HGC, 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(*HGC) = *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."
(***)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.(***)Although, equation (2) can be discussed and interpreted informally, humankind cannot actually mimic the logical process *P. Further, this equation satisfies two trinity notions. Which of these notions one accepts requires additional sources of rational information, if one wishes the choice to be rational. The actual attributes that produce (2) are the three sets of physical world restricted and C extended attributive collections FAC, RSC, HGC.
Using the modeling notion of Occam's Razor, it is rational to state that the three related attributive descriptions, FA, RS, HG, signify that the Spirit of God, "simply" manifests itself within the physical world in specific Biblically described ways and these manifestations can be grouped into, at least, 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. Note that, in this model, Jesus is "perfect" in the sense of restricted C. Using this tri-category model, part of the Divine "plan" is that, if necessary, God will present Himself in the restricted form of RS to His created universe. Further, God as the supernatural Father 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.
On the other hand, one can accept the notion of progressive revelation over about 900 years and accept the classical Trinity concept. In this case, all the Biblical statements that imply equation (1) and the relation between Jesus and the Holy Ghost are rejected. In this case, it would be accepted that in the third-heaven *FAC, *RSC and *HGC 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. Historically, there have been seven different methods suggested to unify these three collections. Indeed, some theologians have stated that how these three are unified can be classified as a "mystery." Some theologians allow for application of *P but not at the moment that Jesus is perfected, but rather near the end of Revelations. Of course, a selection of the appropriate possibility should be related to actual Biblical statements, wherever possible. These two possibilities, although poorly stated, were published in Herrmann (1982).
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 will be employed by members of God's glorified church. "Expressions" from this language are *-comprehensible and carry an additional mathematical characteristic termed as "hyperfinite." Indeed, one can substitute for the *, when appropriate, the prefix "hyper." Only such objects are hypercomprehensible within this third heaven (2 Cor. 12:2). In 1 Cor. 13:12, Paul states that we will comprehended more. But, in many places, such as Job 28: 13, Psa. 139: 6, Isa. 55: 8-9, Rom. 11:33, the statements mean that, in general, God has incomprehensible behavior and this would also transfer to the representations BPC and *BPC.
A compressible attribute is also *-comprehensible. These Scriptural statements imply that the representation *BPC cannot be assumed to identify all of God's attributes. There can be other attributes for God that are not hypercomprehensible and, hence, not expressible in any manner by any member of His glorified church. Within this third heaven, it is sufficient that His glorified church view *P(*RSC), *P(*FAC), *P(*HGC) and *EPC 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 hypercomprehensible 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 hypercomprehensible knowledge of God's behavior that any of His created beings, in any of their allowable forms, can ever possess.
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 deBroglie". . . 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 was not based upon any desire to model mathematically any additional Divine attributes. I postulated that a solution to this problem involves a collection of mathematical objects that model "thought processes." But, what thought processes and what mathematical objects? 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 consequence operators (Herrmann (1979, 93, pp 65-128). These operators are not well known and were introduced by Tarski in the 1930s. From the thought process viewpoint, these operators model the most basic aspects of deductive thought. The other operators that complete the solution are the choice operator, the ordered choice operator and the "hyperfinite sum" operator that conjoins "finitely" many simple objects to form a more complex object. These three operators model aspects of how the mind "intelligently" deals with the information that is contained in a meaningful language.
After the General Grand Unification Model (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 all physical-system behavior is pre-designed 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 every physical-system must display a signature of a higher intelligence. Of course, the GGU-model in its pure secular form need never be interpreted theologically. However, 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 General Grand Unification Model and General Intelligent Design Theory (Herrmann, 2002.
References Herrmann, R. A. 2002. Science Declares Our Universe IS Intelligently Designed, Xulon Press, Fairfax, VA.
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. However the version with the fewest typographical errors and a few additional refinements, for the present, appears only at this URL.
Vine, H. E. 1940. Expository Dictionary of New Testament Words, Fleming H. Revell Co., Mew York.