Science Declares Our Universe IS Intelligently Designed

Typographical Variations Followed By Further Explanations

The e-mail address for this website is and is for general and significant questions or comments about GID (i.e. general intelligent design) or other aspects of the information on this Web site. Please be specific in the subject heading as to the content of your e-mail. If the subject heading does not convey the intent of the e-mail, then no further e-mails will be accepted from your account. Since my time and others at I. M. P. is very limited, it is necessary that I determine whether an e-mail question or constructive comment is of enough significance that I personally reply via e-mail.

The original version is 99.89% grammatically correct and is no longer published. There may be a few original versions still available. Noting that on page 5 in the last line the word is "mathematicians" can identify the original version. If you have this version, it's important that you consider the Original Version Typographical Variations.

In order to sustain my record of never having published anything without, at the least, a few typographical errors, here are such errors that appear in the 99.98% grammatically correct first revision. First revision

Further Explanations, Additional Refinements and Important Material
Major revision 1/23/2009. Last revision 18 FEB 2016.

If needed, a GGU-model glossary of terms can be found at Glossary.

I consider it as impossible for me to write a "complete" or "perfected" book in any aspect of science. All such material is partial in character since scientific models are either self-correcting or, at the least, can be descriptively refined. I could have spent the remainder of my life changing and altering the material in the book manuscript and, hence, it would never have been published. Indeed, the fact that it is published and not a complete incomprehensible "mess" is somewhat of a miracle since there were many attempts, external to Xulon Press, to scuttle the project.

(New research has actually altered what I now personally accept. However, the results in this book still hold for the reductionist, the philosophy that our universe is constructed from elementary entities. The new approach is detailed in the article on GGU-model processes.) The purpose of this article is to present refinements and, if necessary, specific technical corrections as they become necessary. This will be done in page number order. What may not be as clearly indicated, as I would have liked, is the use of the expression GGU-model. This is technically a mathematical model, a mathematical theory, which models logic-system generated consequence operators for its development. It has a technical vocabulary. This model is then interpreted in terms of the idea of intelligent design and other interpretations. At particular points within this book, the actually GGU-model interpretation being considered may only be recognized by examining the immediate context.

Important Aids to Comprehension.

(Note: The phrase General Intelligent Design Model (GID-model) is not used in this book. However, it is obvious to what this phrase applies.) In this book, I discuss the notion of the mathematical modeling of "abstract" objects by examples. The term "abstract" is used. But, rather than define it, the notion is illustrated in a particular context. Pure mathematics is a rational symbol-manipulation game that follows specific rules. Abstract mathematics is pure mathematics and the term "abstract" has various meanings understood from the context. I often term the symbols as "abstract objects." Also the term "abstract model" has different meanings. In this book, it means a mathematic theory about symbol-manipulation itself. That is, one investigates the notion of what constitutes the meaning of the term "rational" when one states that the symbols are being "rationally combined." Then conclusions are referred back to the original physical meanings for the symbols.

Most often, the rules for the symbol-manipulation come from two sources. The symbols can "represent" specifically defined physical objects or processes. Then the manipulation rules are obtained by considering what appears as basic physical behavior or objects that lead to more complex behavior or objects. Often this basic physical feature is common to more than one natural-system and this is the scientific process of "abstraction." After the rules are rationally applied, using mathematical reasoning that can be specifically defined, the results are then applied to the physical world using the original physical objects or processes the symbols represent. But, pure mathematics itself can be "abstracted." There can be manipulation rules that are common to other sets of manipulation rules. One then rationally applies these common rules to develop a more general theory, a generalization that applies to a collection of mathematical theories. For the Newton notion of "force and direction" (p. 34- ), an actual abstract (non-specific) entity is employed. Specified directed line segments are used as a model. Why are they "abstract" in this sense? Since they can be used to model other physical entities and, actually, they need only satisfy a specific set of axioms. (One might consider these as "variables" in mathematics, but a variable is actually a "symbol" that represents members of a "specific" set. Variables can be considered as "representing" abstract objects. However, an abstract object can be unique.) Then there are the axioms for the abstract nitts, elins and the rail relation (p. 43 -). These meaningless strings of symbols can be used to represent many different real entities and one simply studies relations determined by the axioms. They are used to model the common behavior of many different specific real objects. The process of abstraction in mathematics is often defined as expressing the common features of a vast array of physical entities but, in general, it's meaning is much broader than this.

For the nitts, elins and rall relation, I am trying to show how pure mathematics can be applied to concrete real problems. For four names {1,2,3,4}, the grouping {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4} satisfies the axioms and all the theorems deduced. Consider the therapist problem. He has 9 patients and he wishes to test his minimal contact theory. He wants them to meet in groups of 3, each patient to meet every other patient only once. This will occur if no two patients, as a couple, meet in a group more than once. The numbers fit the theorems stated and many others and axiom 3 and 5 seem to be his requirements. We give each patient a number from 1 - 9, the nitts. In general, there are 84 different 3-element subsets of {1,2,3,4,5,6,7,8,9} and, if the theorems hold, we are looking for 12 of these. This might just be a challenge to determine. After some effort one might consider the collection {1,2,3}, {1,4,5}, {1,6,7}, {1,8,9}, {2,4,9}, {2,5,7}, {2,6,8}, {3,4,6}, {3,5,8}, {3,7,9}, {4,7,8}, {5,6,9}. Obviously, axioms 1, 2, 4, hold. The 36 different two member subsets appear once and only once in these elin and axiom 3 holds. You can check that axiom 5 holds as do the theorems, which helped me to find these 12 groupings.

What is a "consequence operator"? (p. 70 -) It should be self-evident that it is an abstract entity having no specifically defined constituents in that the internal structure is composed of abstract entities. I specifically mention that consequence operators are relations between members of ANY object language. I give many examples of different object languages. The language used for the GGU-model is constructed in a specific manner. But, even then, there are infinitely different object languages that can be constructed in this manner. Hence, the mathematical objects, under my present usage, that are related by a consequence operator are abstract entities. A consequence operator is a mathematical object that is axiomized to behavior in a specific manner. The axioms form an abstraction of basic aspects of the human thought machine (i.e. information into the mental "black-box" and information out). For the formal "logic" models, the X, Y and Z (p. 77 -), although they start as representations for actual real strings of symbols, become abstract symbols since they also can be used to model other notions, say, images, that are not necessary considered as finite strings of symbols. Constructions with abstract entities are introduced by considering "expressions" such that (X -> Y). So, I have illustrated how one models with abstract entities.

A natural-system (also called a physical-system) as defined contains related and specific constituents. But, the notion is abstracted relative to behavior. The VCR or DVD behavior discussed is a perfect illustration of the abstraction process (p. 93 -). First, you have specific entities. [Note: In this article "altered" behavior of a natural-system includes the production of a natural-system.] Many individuals are trained to consider alterations in natural-system behavior or characteristics by applying specific natural (i.e. physical) laws, specific processes and the like. Of course, they can also "evolve" in a so-called "random" manner. But, the notion of non-specific "change" is introduced as an ingredient and generally modeled. This "abstracts" the notion of the time-development for abstract natural-systems. Abstracting physical notions such as this is not usually part of ones basic training in scientific discourse. This non-specific abstract approach is necessary since the GGU-model is a cosmogony. It is not a cosmology. Indeed, the GGU-model can be considered as a "larger" more complex physical environment in which universes are embedded. A cosmology would be where each natural-system is specifically defined in terms of its "physical" constituents and relations.

Then all of these developing abstract natural-systems are "glued" together by an "ultimate ultraword" to form an (abstract) universe. Although I state that specific information is used for a specific universe, comprehension may be hindered due to the lack of actual specificity for an abstraction. I have not started at a "low enough" level, so to speak, and I have not introduced "specific" entities for the construction, as yet. The result of all of this yields a "master universe." (I note that the actual generation of the time developing natural-system is considerably more difficult to comprehend. I have used a slightly unacceptable simple approach in the book.)

One major aspect of science is that it often leads to improvements over the original ideas. This has happened with the material in this book. I have purposely not included all of the processes that lead to a universe being formed due to future research considerations. This book remains very useful, however. Although there now exists the best possible unification of the collection of all physical laws and theories and the first ultimate ultraword need not be used except for reductionists, the idea of how ultimate ultrawords are employed to form collections of universes, and collections of these collections is still significant.

If one looks at a paused VCR or DVD image, then rather than pushing a bottom to move to the next frame, one might decide that the next frame should be altered from the original. This process is what is modeled abstractly and discussed at length (p .110 -), but again the possible different alterations from the original are non-specific. The natural-systems obtained are still but abstract in character. This leads to a possibly new development for a natural-system and the combination of all such developments is a possible different universe. Now these are all analogue models for behavior (they represent behavior and properties where the objects presented need be the actual objects used). One does not need to assume that this is actually how it is done. Indeed, I mention how these universes can be obtained by applying the "randomness" notion and, in the minimal physical case (p. 183), all of these universe constructions can be eliminated.

It's remarkable that when I write the symbols "GGU-model" or say General Grand Unification, some individuals drop the word "General." They minds jump to the other end of the spectrum and look for a "Grand Unification Theory" using specific entities. Not seeing one immediately discussed they put the book aside, or worst. The same is so with the General Intelligent Design interpretation. Their minds seem to jump to the local and restricted theory (RID) of Behe and Dambski, and RID's application to specific natural-system levels many, many orders below the natural-system we term as our universe.

And "after" all of this, the model does reveal, all on its own, actual entities that are the fundamental somewhat specific ones from which everything can be constructed using to some degree the specificity mindset (p. 125). These fundamental entities are not part of our physical universe unless you extend the term "physical" to include all of the universes, the substratum and other aspects of the NSP-world.

It is very important to realized that the "physical" GGU-model is just that a model. This model can be interpreted in many intermediate ways where only a few such interpretations appear in this book. One need never assume that the external universe processes or objects, when described in detail, need to exist as specified. One can accept such general statements as: "There are processes that when applied to objects produce, in a step-by-step manner, universes with all of their levels of complexities. Further, the processes allow for variations in natural-system behavior initiated by participator actions." I do not contend that the detailed descriptions for the processes or objects correspond to a form of reality. I only contend that the GGU-model's technical apparatus models a form of reality beyond our physically sensed universe. I contend that the fact that the physical GGU-model is testable and falsifiable and predicts all sensed natural-system behavior within our physical universe implies that all such predicted behavior is indirect evidence for its acceptance as a viable "model."

****For the GGU-model, these operators, when physically interpreted, are separated into three categories depending upon their construction. These are the N-processes, UN-processes and the IUN-processes. They represent collections of processes that produce natural-systems or ultranatural-events or alter natural-systems or characteristics, or yield other defined objects. The behavior of these operators is determined by strict mathematical means. They are all modeled from describable human behavior and the properties of the UN of IUN-processes are predicted. In the physical interpretation, all notions relative to the intelligent design signatures are considered as extraneous and are ignored.****


In this book, I give a list of operators used (see third line page 166) for both the GGU-model secular, intelligent design and theological interpretations. These can still be used as examples of operator usage. However, after this book was published new research findings have resulted in a change to this list. The *S_N and S_W have been replaced. For simplicity, I did not give all of the operators used. In this book, the order in which the operators are applied is also not given. The basic operators used and how these are applied to the maximum secular and intelligent design scenarios I discuss next. Obviously, if possible, I would write a new version of this book to incorporate all of the alterations mentioned in this present article.

After constructing a pre-designed universe d in a step-by-step sequential manner, it is shown that an ultraword W exists such that, when a describable logic-system, denote by *S, is applied unordered members of a d are produced. The original members of d are members of d. However in this approach, the result *S({W}) is not in proper sequential form although members carry the necessary information to do this. Hence, based upon the human ability to order specifically indicated objects, a ordering operator O is defined that puts the entire d in its proper sequential order.

As a technical writer would do, each member of d is assigned a *-instruction which details how subparticles (now called propertons) are to be combined in order to yield the physical or physical-like event E. This set of *instructions is equivalent to a covirtual universe. To form any universe-wide frozen-frame, the coupled operator (StG) is applied. The G is modeled after how a work force can follow instructions and group together the necessary raw construction materials in order to form a specific physical object. The last operator St applied to each group of raw materials and forms them into a finished object E, an event. (The new approach eliminates the O operator and gives a much stronger ID signature than the ones used for this original approach. It has more convincing modeling definitions.)

The notion of indirect evidence is highly significant in physical model construction. Evidence "indirectly" indicates the existence of the behavior of hypothesized entities if the assumptions used to construct the model lead to events that can be observed either by human or machine sensors. However, one can never assume, with complete confidence, that such hypothesized entities or processes actually exist in object reality. In general, the model can only be considered as analogue modeling various entities or processes. This is especially the case where you have more than one model that yields descriptions for the same observed events. This is what often determines different science-communities, science-communities that accept different models that yield the same descriptions for the behavior of observed entities.

Relative to the GID-model interpretation, the basic hypotheses are verified billions of times a day. Further, this model is so highly scientific in character that whenever an individual conducts a scientific experiment and the experiment verifies an inductive or deductive statement, then this also verifies the GID interpreted GGU-model.

Please notice that there are various forms of "intelligent design" discussed in the book. They are the "metalogic intelligent design" represented by H and H and those that are represented by the designed standard or nonstandard consequence operators and other designed processes. Application of each specific consequence operator requires that intelligence be applied to a corresponding standard or nonstandard general logic-system. If the consequence operator is not first defined by a general logic-system, then the general "intelligence aspects" of the interpreted consequence operator axioms, model the mental processes that yield specific and fixed systematized collections of images. Additionally, specific images correspond to other specific images via a fixed relation. This requires a form of intelligent finite-choice. That is, for every image in the language, the specific finite-choice of a unique image from a collection of images. However, this selection requirement is the major part of scientific deduction. Thus, in both cases, the application of a standard or nonstandard consequence operator, models aspects of "deduction."

For a more in-depth discussion as to how the GGU-model operators mimic the behavior of a higher-intelligence, please see the section "A Higher-Intelligence and The GID-Model" contained in the article Introduction.

(Part of the following is taken from that article.)

****The General Intelligent Design interpretation is that the specific operators that produce the previously stated GGU-model results are each intelligently designed by H or H. In all cases, for the GID-model interpretation, the complete way that a higher-intelligence actually yields all physical behavior is not observable. For a higher-intelligence model, the algorithm is informally interpreted in terms of what would occur if the algorithm were formally characterized. It is applied to an extension of the original general rules of inference. These higher-intelligence processes yield a operator called a "hyper-operator." When each hyper-operator is applied and the collection of results examined, then this collection contains the original operator's results and many more. The ID-signatures that characterize the higher-intelligence yield an analogue model for what is not observed. The basic method is that indirect evidence verifies the hypothesized existence of a higher-intelligence. Considering hypothesized behavior that is mimicked by other comprehensible behavior is a basic method used within particle-physics. An example is Quantum Electrodynamics where Feynman diagrams are often employed and physical behavior is mimicked by the diagrams. The higher-intelligence ID-signatures for physical-like behavior is based upon similar but weaker processes that we can comprehend and apply. The fact that similar behavior is used yields a stronger modeling correspondence than occurs in many other accepted physical theories. Indeed, similar mental-processes are used whenever a computer simulation for physical-system behavior is constructed. Under GID interpretation, such operators are often called "intelligent agents." The term "agency or agent," when applicable, can be replaced by the term "action."****

In general, for the GID interpretation, I show how the intelligent agent H and, more significantly the higher-intelligence H, intelligently design every aspect of universe construction and also the behavior of each natural-system contained therein. This includes the pre-designs and the designs of all controlling intelligent actions. Why do I interpret H in the form H as a higher-intelligence? A material universe is described using a specific language. Although the logic-system used by H is the standard classical-system, the language is not. All of the names given to substratum entities, entities that, for GID-model interpretation, are not consided as members of a material universe, are considered as terms used only by a higher-intelligence. For example, ultralogic, an ultraword, ultranatural event, subparticle, etc. are such terms. If intelligent agency terminology is removed, a pure physical model emerges. In this case, the substratum becomes part of the a physical-like world.

Since I use models for human mental behavior as the basis for the GGU-model and human beings can use numerously many different logic-systems for different purposes, the same holds if one considers a theological interpretation where a single entity can exhibit such intelligence at various levels. [Note: The abbreviation GID is now being used for the general intelligent design interpretation of the GGU-model.]

New Signature Results

In general, when a general logic-system is used or a consequence operator applied, a great many extraneous results are obtained. The actual observations being predicted most then be chosen from among this extraneous information by an intelligent being. However, there are general logic-systems and corresponding consequence operators that eliminate all of this information and present only the actual real or assumed images. These operators are called "behavior-signatures" or "theory-signatures." They are discussed and defined in this paper. (This may not be the most recent revision.)

When considering the material in chapter 4, pay particular attention to my (corrected) statements in the first full paragraph on page 130. All of the previous constructions and the ones that follow in this chapter are needed. Independent from my theological belief, none of these constructions for physical-like behavior needs to be considered as objectively real in order to apply the pure intelligent design interpretation. These constructions are used so that statements of the following type are rational. "The behavior of each natural-system is intelligently pre-designed by a higher-intelligence. All natural-system behavior governed by probabilistic models is designed by a higher-intelligence and all such behavior is produced by intelligent agencies. All behavior classified as random is intelligently designed and produced by intelligent agency. Intelligently designed processes allow all biological entities to alter natural-system behavior. . . ." Of course, you can also consider combinations of these interpretations. You can consider part or all of the physical interpretations as comprising objective reality. The choice is yours.

In the GID interpretation, various consequence operators represent "intelligent actions" and they have appropriate "intelligent design signatures." For any universe, the operator *S is the general operator that yields, in primitive time (sequence), each universe-wide frozen-frame. [Below, in the "Technical" heading, I give the most recent technical explanation as to how this can actually be accomplished.] It signifies that this primitive time process is produced, and sustained by actions of a higher-intelligence - a nonstandard intelligent action. This process also produces the ultranatural events. The other operators discussed are relative to our universe and demonstrate how the universe-wide frozen-frames coalesce in primitive time to produce natural-system time developments.

There are various unifications for all natural laws and predictive physical theories such as the one I mention on page 169. The unification depends upon a choice of a collection of finite consequence operators or their, recently established, equivalent general logic-systems. (See theorems 2.1 and 2.2.) Each natural law can be written in general logic-system form and, as such, generates a physical-science "theory" as displayed by a finite consequence operator.

If V_w is the standard unification of all natural laws and predictive physical theories as it appears in Cor. 2.10.1 of the paper The best possible unification for any collection of physical theories, then *V_w is the higher-intelligence form for this unification. However, this unification yields a vast amount of subsidiary information distinct from the actual predicted physical behavior. Using Definition 4.1 in this paper all of the subsidiary information can be removed. This yields a theory-signature RI(L)_s. A theory-signature produces, from observed (or if one wishes assumed) objects or natural-systems, observed natural-systems or an alteration in natural-system behavior respectively. Hence, although to obtain a physical-theory scientists often use mathematics or unobserved assumptions, the collection of all theory-signatures also generates a best possible unification U and its higher-intelligence form *U. The *U unification can be chosen as the actual one employed by a higher-intelligence.

From the GID interpretation, intelligent actions are but restrictions of the actions taken by a higher-intelligence that controls such coalescence. The operator *S can be considered as displaying a general intelligent design signature, where some other operators yield more specific intelligent design signatures. The general intelligent design signature increases in strength as other operators are adjoined to produce specific natural-system behavior.

The General Theological Interpretation

The ultranatural (Natural) world is a subset of the nonstandard physical world. Theologically, is the ultranatural the same as the supernatural? The real notion of "supernatural" first requires a list be accepted as to what constitutes the "natural." For the GGU-model, only standard mathematical models are considered as representing behavior taking place within a "natural" physical universe. This is the GGU-model's definition of the "natural." The model, as first conceived and used to solve the General Grand Unification Problem, requires all of the ultranatural to be considered as but a new "Natural" environment in which our universe is embedded.

For the theological interpretation, the ultranatural can be considered as consisting of both the supernatural and new "natural" processes. For a Biblical theological interpretation, I consider almost all of the ultranatural, at least, as an interface between the supernatural and the physical world in which we dwell. Recently, I have used the term "preternatural" for portions of the ultranatural world when interpreted theologically. This alters the standard meaning of "preternatural." Clearly, the higher-intelligence H signifies a supernatural intelligence. I repeat what I previously wrote. Although the logical methods used by H are the same as used by H, they represent those used by a higher-intelligence due to the language employed. Such terms as ultralogic, ultranatural, ultraword and similar ones, if they refer to nonstandard entities, they have no direct meaning, for this interpretation, for a physical world. This is why the mental processes applied by H are interpreted, in this case, as those of a higher-intelligence H. But, depending upon the interpretation, the process *S may or may not be considered as supernatural. On the other hand, the ultranatural-world can be considered as "physical" for a pure secular GGU-model interpretation.

The GGU-model rationally verifies the Biblical descriptions for a supernatural God's creationary activities as well as how He can intervene and alter all physical behavior or characteristics. Except relative to certain very general statements such as those related to a higher language and the like, the model gives no direct information about the workings of God's supernatural world. Rules for the application of these operators and the intelligent actions that activate the various interface operators are, at least, considered as supernatural in character and in-depth details can only be known via a supernatural higher language.

There is a Biblical correspondence between how we describe and employ natural laws and predictive physical theories. Using languages, we have developed techniques that allow us to determine natural law behavior and construct predictive physical theories. This allows us to build a "man made" universe in order to rule and subdue the "earth." (Genesis 1:26, 28.)

[1] Entire Book. I have used the term specific information 97 times in this book. I have done so in various contexts so that the reader can gain an intuitive idea as to what this primitive notion entails. You can only comprehend a primitive entity by describing its properties rather than considering its composition. To aid comprehension,you will find a definition for specific information and two illustrations given in this paper.

Additionally, it may help comprehension to consider quantum physics. With respect to quantum particle or field physics, there is assumed to be primitive (i.e. fundamental) entities that follow patterns of behavior dictated by collections of symbols or images called the "laws of nature." The question relative to such patterns of behavior is what compels the primitive entities to follow or obey, so to speak, these laws of nature rather than behave in radically different ways? The same question can be posed at each level of the configured hierarchies that lead to macroscopic and large-scale behavior. Whatever this immaterial mysterious "stuff" is it may be "specific information." However, as indicated, such behavior can be further described from the viewpoint of subparticle theory, primitive time and the physical GGU-model. In this case, specific information could be the immaterial stuff that produces all of the subparticle combinations with specific configurations and yields every level of a universe-wide frozen-frame that is then realized. From a pure physical point of view, the statement that specific information is a primitive means that one cannot describe it as composed of other entities.

[1a] Page 7. Natural-system "behavior" also includes the notion of various "characteristics" that may need to be measured or that are but assumed. For example, energy, velocity, spin, momentum, etc.

[2] Page 68. The logic-systems being considered here are now called finite logic-systems in that the set of rules of reference is a finite set of n-ary relations. I have recently extended logic systems to include the case with the set of n-ary relations is not finite. For a given language, both types of logic-systems are called general logic-systems. I have shown in the paper "General Logic-systems and Consequence Operators" that there are non-finite logic-systems that correspond to finite consequence operators and such operators, looked at in the most general way, are finite consequence operators if and only if they are generated (defined) by a general logic-system. Importantly, there are other ways to describe deduction from premises and a fix set or members from the language (i.e. a 1-ary relation). Indeed, although it is equivalent to a general logic-system with the general rules of reference, one way is the usual way that appears when an individual reads a claimed deduction from premises. The actual rules of inferences are not stated in this method. Simply consider a set of fixed finite lists (steps) that use the premises or members of the 1-ary set to from a deduction using members from the same language as steps and the last step in the list is declared a deduction from the premises or 1-ary set. Within this collection of lists are all of the one-step lists that model the allowed insertion process as stated at the bottom of page 67. Using just this collection of allowed finite lists that lead to the allowed deductions, a finite consequence operator exists that will generate the same deductive results.

[3] Pages 71-74. First notice that as stated (1) does not include the additional requirement for (I) (page 69), that P be a subset of C(P). Although this requirement is stated, it should be include in (1). As implied at the top of p. 71, of considerable significance is the fact that, for application to actual real physical events, the natural laws, as here defined, and scientific theories need only give general predictions that can occur at any moment in observer time.

On the other hand, "if" observer time is increasing, they can describe the "time" development of a natural-system. In this case, they are specified so as to include a specific moment in observer time. Hence, for this case, the logic-systems that generate such consequence operator and that are applied to a specific natural-system must contain statements that identify the natural-system relative to a "time" notion. This requirement is usually implicitly known but would need to be explicitly contained within any logic-system that produces or alters natural-system behavior, or produces or alters natural-system characteristics. If such an identification is not included, then it is possible that the theory would contradict axiom (2) and, hence, it would not be a properly constructed scientific theory. It is rather self-evident that to apply natural laws and scientific theories to the events sequences this requirement must also be met. Hence, technically, applicable logic-systems and their corresponding consequence operators differ from others in, at least, this one respect for each moment in increasing observer time.

Certain science-community logic-systems do not follow the same patters as those presented within (internal to) a mathematical theory. They can be modeled mathematically, where the arguments are rather dialectic in character, and this can lead to binary logic-systems formed by simply making pronouncements. In this regard, I note that the type of unification that is modeled by J yields a logic-system that forces the hypotheses {a,b} to be J-inconsistent, where they are A and B-consistent. A({a,b}) = {a,b,c}, B({a,b}) = {a,b,d}. However, J({a,b}} = {a,b,c,d,e}.

Is there a rule that a science-community would need to use or exclude for their K mode of logical deduction? Using logic-system rules, the reason why K is not a consequence operator is that one is allowed to use the previously obtained value "d" in the (d,e) relation to obtain the value "e." The operation that has defined K does not allow this. This shows that, for this example, what a science-community must exclude in their deductive processes that would lead to K (partially) falsifying GID. Note that consequence operators can be defined without first defining a logic-system. [See math.LO/9911204 Definition 2.4.]

However, every consequence operator defined on a finite language L determines a logic-system, as I have defined it, which will yield the same consequence operator. If L is infinite, then to make such a correspondence the definition of a logic-system can be extended easily to the general logic-system and this will always correspond to a finite consequence operator and conversely. [See this URL math/0512559.] Because the "inserting" rule is being used, one of the simplest methods to generator a corresponding logic-system is easily described.

Let L = {a,b,c,d, . . .} and C be a consequence operator defined on L. For the empty subset E of L, use C(E) as a 1-ary (unary) relation. For singleton subsets, (i.e. {y}}, define the binary relations {(a,x)| x in C({a}) }, {(b,x)| x in C({b}) }, . . . . For doubleton subsets define relations {(a,b,x)| x in C({a,b}) }, {(a,c,x)| x in C({a,c}) }, . . . {(b,c,x)| x in C({b,c}) }, {(b,d,x)| x in C({b,d}) }, . . . {(a,b,c,x)| x in C({a,b,c}) }, . . . . The logic-system you get need not be the same as the original one. For example, the original logic-system for L may not include any binary relations and, as is usual, no n-ary relations (n >2) with any repeated members in the first n-1 coordinates. Then the binary relations this method generates are {(a,a)}, {(b,b)}, {(c,c}), {(d,d)}, {(e,e)} which simply models the inserting process. Also notice that due to our choice method, it isn't necessary to consider such relations as (b,a,x).

More specifically, let L = {a,b,c} and your logic-system is {(b,c)}. Let C' be the corresponding consequence operator. We need only consider the values of C' that cannot be obtained merely by inserting hypotheses and these are C'({b}) = {b,c}, C'({a,b}) = {a,b,c}, C'({b,d}) = {b,c,d}, C'({a,b,d}) {a,b,c,d}. Now apply the above process. Then for the relations we have {(a,a),(b,b),(b,c),(c,c),(d,d)}, {(a,b,c),(b,d,c)}, {(a,b,d,c)}. Even if we eliminate those relations that model inserting, we have a different logic-system {(b,c),(a,b,c),(b,d,c),(a,b,d,c)}. This extended logic-system appears be one where we do not need to apply the procedure where we use previously "deduced" members of L to obtain other "deduced" members. Does this fact contradict the above reason as to why K is not a consequence operator?

The facts are that the above example is too simplistic to make such a generalization. This generation method can be used for any set function such as K and gives the needed additional insight as to why K is not a consequence operator. All we need to consider for K are the values K({d}) = {d,e}, K({a,b}) = {a,b,c,d}, K({a,d}) = {a,d,e}, K({b,d}) = {b,d,e}, K({c,d}} = {c,d,e}, K({a,b,c}) = {a,b,c,d}, K({b,c,d}) = {b,c,d,e}, K({a,b,d}) = {a,b,c,d,e}, K({a,c,d}) = {a,c,d,e}, K({a,b,e}) = {a,b,c,d,e}, K({b,c,d}) = {b,c,d,e}, K({a,b,c,d}) = {a,b,c,d,e}, K({a,b,c,e}) = {a,b,c,d,e}, K({a,b,d,e}) = {a,b,c,d,e}. The non-trivial portion of the logic-system corresponding to these values is {(d,e)}, {(a,b,c),(a,b,d),(a,d,e),(b,d,e),(c,d,e)}, {(a,b,c,d),(a,b,d,c), (a,b,d,e),(a,b,e,c),(a,b,e,d),(a,c,d,e),(b,c,d,e)}, {(a,b,c,d,e),(a,b,c,e,d),(a,b,d,e,c)}. Notice that using this rule, we have that C'({a,b}) = {a,b,c,d,e} since once we obtain from {a,b} the "d" we can use the rule with {a,d} to obtain "e," which is not equal to K({a,b}) since we cannot apply this rule to the K operator.

Finally, I mention that consequence operators can be generated by set-theoretic definition. For example, see Definition 2.4 operator C'(X,Y) in this archived paper. The operator K would falsify the general GGU-model hypotheses if one demonstrates that natural-system behavior follows the pattern predicted by the K operator. But, this is not the only way to falsify the general GGU-model hypotheses. If one can demonstrate that natural-system behavior as predicted by the consequence operator C'(X,Y), where Y is an infinite subset of a scientific language, then since C'(X,Y) is not a finite consequence operator it would also falsify the general GGU-model hypotheses.

Universe Construction Difficulties

[I assume for this section that you are familiar with the books contents and language.] Why are the illustrations on the pages for universe construction somewhat difficult to comprehend? The necessity to have alterations in the basic constructions and that any detailed instructions are contained in the incomprehensible ultranatural theories and ultranatural laws are the basic reasons why our comprehension must remain extremely partial and vague. I have done the best that I can, at this time, in illustrating what can be known. [The type of pre-design depends upon the interpretation. These constructions can yield the same results as discussed on page 172, the pure random subparticle combinations. On the other hand, the "or allowed" statement (page 122) can be interpreted as an intelligently guided more purposeful construction. Hence, there is a choice as to the type of pre-design that you're willing to accept philosophically. Among all of the libraries that generate the universes, there is a library where the basic describable natural processes that coalesce the universe-wide frozen-frames remain unchanged after realization. This seems to be the type of universe in which we dwell. The operators that model this coalescence of "natural-system" behavior do not change and still have intelligent action signatures. 3/1/06] (I have not shown in this book how to use subevent sequences (i.e. subdevelopment paradigms) to generate the members of the library {w_j}.

[4] Pages 80-81. For this book, the actual hypotheses for the GGU-model can be stated in technical terms. The major hypothesis is that the formation and behavior of each real natural-system is controlled or sustained by a specific set of significant general ultralogical processes as mathematically model. Mathematically, general ultralogical processes are (1) objects that satisfy the standard and nonstandard consequence operator axioms, the ultralogics. (2) The finite, hyperfinite, and general standard and nonstandard choice operators. In particular, order choice. (3) The process of combining finitely or hyperfinitely many objects into a single configuration. (4) The standard part realization operator st. These are considered as physical processes that are modeled by mathematical "operators." But, (1), (2) and (3) have characteristics that model human or higher forms of mental process. Also, (4) satisfies the same set of characteristics. The human or higher mental process characteristics for any GGU-model operator or process is termed as its ID-signature. The GID-model interprets these ID-signatures in terms of "intelligent agency." (For an intuitive discussion of what the hyperfinite means relative to a higher-intelligence, see hyperfinite.htm.)

[5] Page 91. On this page, I mention that a complete and detailed logic-system need not, yet, exist. The logic-system is a technical device that may or may not exist in its entirety as "images". If it is not entirely expressed, then if one is seeking any new conclusion from a set of premises, whatever they may be, one "assumes" it exists. The reason for this that technically we do not usually have at the start of most investigations a complete set of rules of inference generated by the so-called natural laws along with the rules for acceptance of empirical evidence, the rules for experimental inquiry etc. We actually are constructing a more complete and "specific" logic-system from assumed previous logic-system rules of inference. (In mathematics, one often assumes that something exists and then, if possible, you construct or give specific examples.) The facts are that we usually are concerned with only a small portion of these other assumed rules of inference. One accepts a conclusion based upon various factors one of which is verification or that the "logical" argument mirrors previously accepted logical arguments. As I point out in the book, in a practical sense, logic-systems correspond to consequence operators and conversely.

Here is an example that shows how general the notion of logic-systems is and why this notion has such a wide range of application. Suppose that you state that "images" that are numbered from 1 to 500 when taken together yield image 501, 502, ..., 510. Then this previous sentence generates a logic-system composed of ten 501-tuple elements. In order to avoid any further discussion as to why this may be the case, you state that this is but an empirical statement based upon your observation. If you don't wish to be a one-member science-community, it's hoped that others would observe the same result. However, if no one else makes such an observation, then this does not erase the logic-system "images" generated. It may still be very significant to you. I will not argue for this notion since I consider, from examples, the assumed existence of logic-systems as self-evident.

[6a] Page 93. The developmental paradigm as here defined does not include any "subsidiary information" that may be included in those that appear in some of my older papers such as in Herrmann (1886b). The present restriction allows the developmental paradigms to be more closely associated with the event sequence notion. Statements involving these previous types of developmental paradigms can often be modified so as to include only the properties of these restricted developmental paradigms.

[6] Pages 100- . Relative to the general intelligent design interpretation (GID), the actual rules of logic used by H and H need not be explicitly stated. On the other hand, they are often the informally classical rules of logic. The H "metalogical" rules need not be explicitly stated as long as the "arguments" for certain conclusions are accepted by science-communities. The conclusions can come from both inductive processes through observation or other means or by pure deduction using an explicit set of rules. This yields an informal "scientific theory" that is intelligently designed by an H. As viewed from the nonstandard physical world, the theory can also be considered as intelligently designed by H via the restriction notion. However, such arguments lead to a formal definition of a general logic-system and the general rules of inference, which is a slight generalization of the logic-system notion as discussed in this book. The finite consequence operate is equivalent to the notion of the general logic-system. Hence, there is a finite consequence operator that corresponds to the informal theory and it represents intelligent action that is intelligently designed. [I also note that the term "Nonstandard Physical World" as stated on page 106 and defined in the glossary is a restriction of the actual NSP-world. Further, from a view point of a physical universe, the actual NSP-world, this restriction and the background universe are all omnipresent.]

The vast majority of physical-scientists consider descriptions as not mere models for behavior, but descriptions for how nature actually behaves. One quotation is all that is necessary. Richard Feynman states relative to QED, "I am describing to you how nature works. . . ." (Feynman, Richard P., "QED: The Strange Theory of Light and Matter," Princeton University Press, 1985, p. 10.) From this viewpoint, the behavior predicted by the intelligently designed natural laws and scientific theories is intelligently designed since such behavior is the result of application of consequence operators. [Note: The signatures used for GID and that indicate intelligent design always include, by definition, the results of consequence operator application. The only necessary additional requirement is that the described results correspond to reality.] This also includes the behavior of individual events that follow probabilistic models where each individual event is considered "random." There exist intelligently designed intelligent actions that control the realization of each such event. [See, Ultralogics and Probability Models. There are articles on this website relative to the notion of "randomness." For one discussion of this notion, you may wish to consider randomness.

[7] Pages 113-115. I thought it was self-evident that the presented line segment diagrams are very partial in character. It is obvious to me, anyway, that an alteration in the master tape takes place at tag T + s (i.e. the segment from T to T + s) and an alteration or duplication of the master tap can continue to occur on the right of the diagram where there appears to be a blank space. I might have indicated this by dashed line segments. For the first line segment diagram on page 114 (and for all the others), this could be indicated as follows:

[7a] As indicated by this and the other constructions, alterations in natural-system behavior include the "null" (i.e. no) alteration. Indeed, one can consider alterations in characteristics being the next image.

[8] Page 117. In the original version, as indicated under typographical variations, what I thought was self-evident can be better understood by inserting the indicated phrase although this addition is technically unnecessary when the next sentence is adjoined. From the windows point of view, one simply needs software that allows for a "clipboard" to retain an image. The image that is inserted is simply copied to the clipboard, the original image in the W file being altered is deleted at a position T + s and the clipboard image is then copied to the T + s position. But there is an additional step performed by the software. I state that the "same" image can be inserted. There appears to be no reason for inserting the same image and indeed this gives you redundant file names. So, assume that only images that are different are inserted and then the altered file is accorded a new file name. [In the original version, remove the phrase "the same or" from line 6.] Remember that these methods for displaying alterations in the master file are algorithms and they apply to each and every altered file, as it's often stated, "in like manner." The three methods (algorithms) I've presented for "universe construction" are only intended to indicate that such pre-design can be intelligently designed. Due to the ultranatural theories, ultranatural laws and ultranatural events, the actual method for such a construction is probably beyond our capacity to describe or comprehend.

****Of course, the three modes that allow for a pre-design and that include participator alterations are intended to serve a specific purpose. The modes are selected in the hopes that, at the least, one will be understandable. They are not intended to represent the exact way that a library of branches (i.e. universes) is pre-designed. They are intended to model only basic behavior. But, each one verifies the following "bold" statements as fact. Please note that in the simplest cases, the images actually exist in one form or another. Inductive generalization can be applied and many statements made. It is scientifically rational to assume that the natural and ultranatural behavior of every natural-system within a universe is pre-designed by a higher-intelligence. Further, as done by many science-communities, a positive language can be employed. This means that the "scientifically rational to assume" is deleted. Then one can alter this statement and be less specific. For example, for the GID-model interpretation, such rationally constructed statements can be (1) Event sequences are intelligently designed. (2) Event sequences are intelligently pre-designed. (3) Event sequences are intelligently designed by a higher-intelligence. (4) Event sequence are intelligently pre-designed by a higher-intelligence.****

There are various aspects of the GGU-model cosmogony that must generally remain vague as to their details. One of these is the notion of a basic universe. This is pre-designed collection of natural and ultranatural events (images) that, in a vague manner, might be considered as satisfying the general requirements of a specific ultranatural theory as comprehended by a higher-intelligence. In the same manner, allowable alterations of the basic universe form the branches of a specific library. Once again, in a vague manner, one might consider these alterations as satisfying the general requirements of a specific ultranatural theory as comprehended by a higher-intelligence.

There can, of course, be many basic universes and many corresponding libraries. The information that generates each universe and its allowable alterations is contained in various ultrawords. At present, I don't consider it useful to speculate as to the images that comprise these other basic universes since they are governed by ultranatural theories. However, as has been established, there are standard and ultralogic unifications for all of the knowable scientific theories that appear to govern the workings of our specific universe. For our universe, these unifications can be stated in terms of certain fixed parameters and the ultralogic unification is an example of an ultranatural theory, an ultranatural theory that generates a basic universe with all of its allowable alterations. Clearly, from experience within our universes, not all alterations appear to be allowed although as Wheeler claims under extreme enough circumstances many more alterations than presently accepted could prove viable.

I mention that there are "hierarchy" or "phase difference" multi-universe models. Let each universe (i.e. library) be governed by the same ultralogic unification that governs our universe with allowable parameter variations and suppose you choose such a hierarchy multi-universe model. Then in this case, it is easily deduced that if enough such universes are formed then it is highly probable that one would form having the exact appearance as the one in which we dwell. However, this does not invalidate any general aspect of the GGU-model's physical or intelligent designed interpretations. It simply gives you another choice from many different choices, where all satisfy the exact same physical evidence.

[9] Page 130. In the statement that I have made in the first full paragraph that "I've absolutely no idea how . . . " it would be better to remove confusion that "anything" be replaced by "many things." As previously indicated, my "scientific" pure positivistic approach is related only to the notion of what "forces" natural-systems to behave in a specific manner and to aspects of the subatomic region. It is a much "deeper" how than usually considered within scientific discourse. It's the illustrations of how universes can be pre-designed, how probabilistic behavior is obtained by intelligent actions, how participator alterations are controlled, how I technically describe subparticles, how "natural laws" that others and I consider as human inventions come into being, etc. What is absolute fact is that the GGU-model predicts rational behavior and rationally generates general statements about such "hows." But, the "actual" mechanisms most certainly need not be those presented.

[10] Pages 135-140. As mention, the unification presented on these pages in both versions is not the only ultralogic unification. Rather then use the unification mentioned on pages 167-168 in the second version, the ones mention previously,*V_w or *U, appear to be the most appropriate ones to select.

These are the basic operators that can be interpreted as displaying intelligent design features. S, *S, P_p, PI_Pp, the ordered choice operators O, *O, a hyperfinite informational instruction operator, the various forms of the hyperfinite summation operator, the st and, if philosophically necessary, which it is probably isn't, the special general random operator D' discussed below. (The standard part operator st can be considered as the extended st' consequence operator followed by the realism relation.) These are all designed and applied by the special external operators H and H. For each science-community logic-system, there are the individual S_N (or similar ones) and their extensions *S_N. The standard logic-systems are the ones unified by *V_w or *U.

However, I have not made it clear that the unification operators that relate conjoined frozen-frames need not be considered as actually applied. Our universe is so constructed that these operators are satisfied. A theological purpose for this is so the we can "subdue the earth" and build our man made world. On the other hand, the P_p and PI_Pp are applied to maintain the predictions for the probability models. For a great deal more about these operators, see processes.htm

[11] Page 139. A logic-system generated by an ultralogic is, in general, not the same as a logic-system used in this book to generate a consequence operator. Any consequence operator generates a set of rules R of inference that can be used to generate the same consequence operator. These rules are often expressed in a manner different from the original set of rules. Consequently, if a consequence operator is obtained originally by a finite set of rules R', then R need not be the same as R'.

The first discussed unifying ultralogic, unifies all physical theories in a special manner. This is a "general" unification. Although this unification does require that descriptions for natural laws and logical axioms be present to generate changes in natural-system behavior, the final result is a "relativized" unification. If no natural laws are included in the image X, then the difference between the image S_N^V(X) and the image X can be considered as an image that represents only the original natural-system, including any changes, and nothing more nor less. As mentioned, the set of rules of inference that generates this relativized operator are probably different from the original set of rules of inference.

[12] Page 142, 147. I point out that subparticles yield an absolute "realism" philosophy of science in that all of the characterizing properties for elementary particles and combinations thereof are "real" characteristics and are covirtually present prior to the application of the standard part operator. This helps to eliminate an absurd quantum measure theory interpretation as to how such characteristics come into being. As a primitive, specific information may be "something" associated with an image that "forces" subparticles to form various configurations. It's these configurations that we eventually experience.

However, there is ultranatural specific information. It is not possible to know which came first ultranatural specific information that would yield associated ultranatural physical theories and ultranatural events, or whether a type of "higher" language, as stated here, yields ultranatural physical theories and these are what "force" ultranatural and natural events to be configured (i.e. yields the quality I term as specific information). But, this does not change this ordering at the level of human experience. I still accept that the primitive quality termed as specific information configures what we first experience in the natural world and the regularities we call natural laws are then a product of these experiences. 6/12/02 (p. 147) The finite consequence operator denoted here by P_p, and used for distributions has a special intuitive property, among others. From the proof of theorem 2.1 in Probability Models and Ultralogics, the P_p is equivalent to applying, one at a time so to speak, the event or not event consequence repeatedly. This is what would be observed in the natural world. The theorem actually shows that it is rational to argue for a result that only involves a hyperfinite choice operator. Once the actual form of P_p is established, then it can be generated by application of hyperfinite choice.

[12a] Page 148-149. There is no question about it that my use of the word "tosses" is very confusing. Indeed, I do not mean what it appears to state. In the first example, the "8 tosses" means "8 experiments of three tosses each." An "experiment" is the tossing of the coin a specific number of times and recording the appearance of the H and T. The "10 tosses" statement that follows this example means how many tosses ones makes for an experiment. Thus, in this case, you toss the coin 10 times and record the H and T. Also the probability is not finding an ordered collection of Hs but just that exact number and only that number of them in the ordered collection. A probability cell such as [9,10] yields the probability that as you continue the experiments with 10 tosses each, the probability of getting exactly 9 or 10 Hs is 0.01. The probability of getting a distinct ordered collection is 1/512. The 100,000,000 means a total number of tosses, a specific number of tosses, times the number of experiments. Also, using the discrete binomial distribution, each cell size can be reduced to one unit in length.

[13] Pages 153-154. The C' operator discussed in this section is the C operator defined in reference Herrmann, R. A. 1987, Definition 2.4 (i) and used in Herrmann, R. A. 1999(b) (page 10, second paragraph), and elsewhere. In the most general case where no other probabilistic model is known, one may be able to calculate the probability that an event will occur if the number of all possible events is known and it is believed that each event is equally likely to occur. Using such specified knowledge, this equally likely probabilistic model can be considered as produce by a C' type operator. But, one most have the specified knowledge and accept the below defined notion of general randomness. However, in all cases, independent of any other behavioral model, there is an underlying consequence operator that can be rationally assumed to represent a physical process or an intelligent action that guides such behavior. This operator also satisfies the hypotheses of Theorem 1 on page 14 of Herrmann, R. A. 1999(b).

Consider any appropriate language L (including images). Let M be a member of L and be a statement (this is to be conceived of as an informational image) that gives various physical characteristics for a physical entity. Suppose that X is a member of L that is not equivalent to M and also lists a set of physical characteristics for some entity. Consider the consequence operators generated by the logic-systems {(M,X)}. Consider any nonempty finite set of these logic-systems {(M,X_i)}, i = 1,...,n. Then consider the consequence operator D defined by the logic-system {(M,X_i)|i=1,...,n}. D is a consequence operator and is the same as the union operator required to satisfy Theorem 1. To see this, let A be any subset of L such that M is a member of A and C_i be the consequence operator generated by each {(M,X_i)}. Then D(A)= A U {X_1,...,X_n}= (A U {X_1}) U . . . U (A U {X_n}) = C_1(A) U . . . U C_n(A). Now if M is not a member of A, then D(A) = A = C_1(A) U . . . U C_n(A), since each C_i(A)= A. If you now consider a non-empty finite collection of M type descriptions and the set of simple consequence operators, C_j, generated by the logic-systems that contain but the single ordered pair, then defining D' in the same manner but allowing the M to vary, it follows by a simple induction proof that D' is a union consequence operator generated by the collection {C_j}. This is one of the signatures for general random behavior. [It is also possible to extend D' to a hyperfinite ultralogic if required.] Hence, since M can be fixed and X vary, we can use these consequence operators in place of the C' and they too have the discussed significant hidden signature.

These results are related to all natural-system behavior that is altered in primitive time. One can rationally assume that H intelligently designs natural-systems that suffer time dependent alterations in characteristics. And, there are underlying special intelligent actions that mediate these alterations and logically unite universe-wide frozen-frames. These special intelligent actions are only revealed when there are no other comprehensible intelligent actions that control and unite primitive time dependent alterations in specific natural-system behavior or characteristics. All intelligent actions are designed and applied by H. This is revealed by their ID-signatures.

Application of this general D' type underlying operator is relative to the notion of general randomness. This philosophic concept can be defined as done by Bohm (Causality and Chance in Modern Physics, Harper & Sons (1957)), where he discusses limited context randomness. He states ". . . it is not considered as being arbitrary and lawless relative to a certain limited and definite context, but rather as something that is so in all possible contexts." Relative to human comprehension and operationally, this means that there is no language, no theory, that will "ever" be able to predict the exact occurrence of an event. In the case discussed in the book, if you have one event, then this would apply to any other event in a finite sequence of events. However, the D' operator yields the same signature for this merging of any two universe-wide frozen-frames. Although it may seem unnecessary to many physical science-communities, I discuss on page 162-163 that fact that it is rational to assume that every member of a universe-wide frozen-frame, every natural-system, has a unique identifier, as does each universe-wide frozen-frame. If the above consequence operator D' is obtained by letting the M vary over all of the natural-systems in one universe-wide frozen frame, then the X can represent possible altered behavior or characteristics that appear in a different universe-wide frozen-frame at a different moment of primitive time. [As mentioned, if for various reasons there might be infinitely many different logic-systems {(M,X)}, then there is a much less trivial pure ultralogic that can take the place of the D' operator.]

Primitive time is defined technically on pages 65-66 of my book "The Theory of Ultralogics" found in this file. [resp. at the math. archives on pages 61-62. There is a refinement to this definition that can be found in this paper. There is always a nonzero finite primitive time interval between successive universe-wide frozen-frames. Although special methods can be applied in other cases, it is usually assumed that standard primitive time is a standard sequence. As mentioned on page 66 [resp. 62], you can even assume that there is a minimal positive primitive time interval between successive frozen-frames. If there are no other ultralogics that control the combining of successive universe-wide frozen-frames, then it is always the case that using the above consequence operator D', alterations in natural-system behavior or characteristics between successive universe-wide frozen-frames can be considered as produced, controlled, or guiding by intelligent actions. Of course, depending upon the theory used, other intelligent actions that are "stronger than" the above D' operators can also guide the behavior. This fact does not abrogate or in anyway contradict the results obtained by means of D' for other stronger intelligent actions would yield the same results. Consequently, from the view of the GGU-model, the notion of general randomness is false in that there is a context that allows one to rationally assume that such behavior is intelligently designed.

[13a] Page 162. Lines 1-2. It should be obvious, what the "identical" notion means. Every specifically described elementary particle has intrinsic characteristics or properties that distinguishes it from all other types of elementary particles. All members of the entire collection of specific particles when compared with each other are considered as quantum physically identical. For electrons, this can also be stated as "electrons are [physically] indistinguishable among themselves." [Pohl. H. A., Quantum Mechanics for Science and Engineering, Prentice-Hall, Inc, Englewood Cliffs, New Jersey, 1967, p. 74.] This does not preclude other characteristics or properties that do distinguish particles when they appear in other groupings involving other types of particles.

[13b] Page 164. Lines 3-4. The statement that the "DVD_2 has the exact same images at and before |_T as those contained in DVD_1" also holds in general, for the DVD illustration, for any change to another DVD. This algorithm means that for any moment in primitive time the DVD being realized contains all of the previously realized images. Hence, the activated DVD also acts as a "history" file.

[13c] Page 169. In this book, I generally discuss the operator *S. Other information can be obtained from investigating the operator *S_N. In particular, it is from such scientific theory generating consequence operators and the logic-systems that generate them, that it has been shown that there can exist objects that behavior like natural laws, but do not just apply to the substratum but also indirectly affect a physical universe. Such objects are members of the set of "ultranatural" laws. Other investigations also lead to objects that behave like physical objects but again are within the substratum. The model automatically generates some of the properties of these predicted objects. These properties have led to the theory of subparticles.

[14] Page 183. For the minimum physical scenario, I have only mentioned two standard types of consequence operators (logic-systems) that indicate an intelligent design, at least, on the level of human intelligence. However, there are more. Indeed, in note [13], I defined a logic-system and associated consequence operators that yield an underlying logical pattern that would indicate that an intelligent agent designs "random" behavior. If it is assumed that in actual practice only a finite number of events can occur that would yield a partial sequence of relative frequencies, then, in Herrmann (2001(b), p. 323), a single standard consequence operator is displayed that yields such a sequence. The same holds for the case of distributions. Thus, such finite probabilistic behavior is also the product of "standard" intelligent actions. Finally, as mentioned, there is also a non-restricted standard unification for the set of all physical theories. Hence, for the minimum physical scenario, it is rational to assume that all "random" natural-system behavior, all probabilistic natural-system behavior and all such behavior predicted, in a general manner, by standard physical theories is produced, controlled or guided by intelligent actions. These actions display, at the least, the same level of intelligence as displayed by members of the various science-communities. In this minimum case, one can than determine from personal evidence whether this is but an apparent intelligence produced by some standard evolutionary process or the restriction of a "higher" intelligence. [For a further discussion of evidence, see [22a]].

[15] Pages 189-210. (My creationary model has been considerably altered from what appears here.) This refers to the "And God said" sequence. In Genesis 1, there are nine such phrases but only eight are followed by an operative phrase beginning with the notion of "Let . . ." or "to become. . . ." The complete sequence requires such an operative phrase, which is again something I thought was self-evident.

[15a] Page 196. For a theological interpretation, the standard part operator is a signature for the realized "For he spake, and it was done." This phrase signifies that only one application is necessary to obtain the exact required results. The standard part operator, when applied to any collection of subparticles SP needed to generate a realized image, satisfies axioms (1), (2) and, for our finite universe, (3) on page 71. In general, it satisfies (1) and (2) and it is also "monotone." As used, it does not satisfy the last requirement for a consequence operator, noted on page 69, that P subset of TH(P). However, when an ultralogic is applied and the "hypotheses" are removed, then the standard part operator properties do model this restricted consequence operator process. Hence, one can trivially turn this operator into a consequence operator by simply adjoining the original collection of subparticles to those obtained by its application. Recall, that the word used here for "spake" can apply to a "mental" type of command.

If one concludes that various physical laws for the original Earth and its local environment were different from those of today, then the statement about "natural laws" is not exactly correct. Let V_w denote the (join) operator defined in definition 2.5 of The best possible unification for any collection of physical theories or considerer the U previously. As mentioned, each physical law corresponds to a general logic-system and can be included within the unification V_w or U. The actual ultralogic that sustains the development by requiring each frozen-frame to coalesce in a special manner is *V_w or *U. Two such coalescing operators can be used, one for the original Earth and its local environment and one for the external universe.

[16] Page 194, 200. I mention on these pages the vacuum of particle physics and the ZPF and the fact that these invisible entities "can be realized." All "invisible" subatomic entities can be realized via ultimate subparticles combining into intermediate subparticles, which have the characteristics of these entities. However, one can also have only the theories realized and not all of the actual entities. Subparticles can "jump over" many of these assumed entities and combine directly into entities that reveal themselves as gross matter. In this case, the theories become bookkeeping devices that allow us to predict behavior of gross matter via imaginary processes or entities that need not actually exist. Of course, whether one considers such entities as objectively real is a philosophic stance.

[16a] Page 202-214. There has now been developed other types of "in-transit information" models. The one discussed in this section is type (I). Further, there is yet another model for what occurred during and after the Flood. The major type is the "rapid-formation" model that, depending upon choice, may or may not coupled with a "hot firmament" beginning. There is a new Flood model that satisfies each strictly interpreted Biblical statement related to Divine creation and the Flood as well as all present-day observable evidence for both a "young" and an "old" earth.

[17] Page 208. At the end of paragraph 1, I make the following statement: "This I interpret to mean that the entire physical universe present at that moment rather abruptly ceased to exist materially." The word "materially" is very significant since all of the pre-designed events sequences will always exist in covirtual form. When these Scriptural events occur there will be the usual conjoining of branches of a Genesis library.

[18] Page 210. One thing is certain, research is a continuous process and new deductions often develop after a book is published. I have taken this present approach to make corrections or refinements to the original book so that a new edition would not be necessary. It seems that further considerations allow me to alter the notions discussed in the first full paragraph on this page. The change I purpose still verifies all associated Scripture. In the last line of that paragraph, the phrase "out of nothing" can be deleted. For further reasons for this slight alteration please see What Can Be Known

[19] Pages 210-213. (I now accept Eden Model.) For the theological interpretation mentioned, I have only briefly discussed the MA-model "aging" processes. I have been asked whether there is a simple explanation, based only upon event sequences, for the "hard evidence" for the existence of life-forms as represented by ancient artifacts and fossils found throughout our "local" environment. There is a possible MA-model styled explanation that appears here, I think, for the first time. It need not be the case that such evidence indicates the actual realization of ancient life-forms. There are covirtual event sequences that would yield such evidence but these sequences are only realized at the time of the Flood. This would be consistent with the in-transit information model and the hot firmament model with removal of any morphing boundary. There is a definite purpose for this as well. Such evidence indicates what "would have been" the case if our local environment had not been created originally to develop in a very special manner. There is Scriptural evidence for this aging process. God states in Genesis 6: 13 "I will destroy them (together) with the earth." The actual meaning of the term here translated as "destroy," relative to the earth, should be "ruin." There are pre-design branches of the Genesis sequence that do, indeed, "ruin" the originally created special aspects of the earth and original portions of the solar-system (the local environment). A shift to one of these branches would remove all the "obvious" evidence that such a special pre-flood local environment existed. This shift is made so that, after the Flood, the natural-system behavior within the local environment appears consistent with the designed evolutionary processes that govern the development of the exterior universe. This type of alteration in our local environment would be a one-time event as indicated in Genesis 8:22 and 9:11. The next such alteration will be to the entire universe as indicated in Revelations 20:11 and 21:1.

The branch chosen would contain certain anomalies within our local environment that cannot be entirely reconciled with any described standard evolutionary mechanism. This would be a signature, for those who can discern such anomalies, that God created our original local environment in a special form as indicated within the Scriptures and the development of certain entities within, at least, our local environment cannot be satisfactorily explained by means of any internally displayed and described "natural" mechanism. For many individuals, a selection of such a branch would form part of the "strong delusion" that God said He would "send." Such a deception is accorded those that "received not the love of the truth, that they might be saved."

[20] Page 214. I no longer believe that the formation of the external universe occurred during day-three. It seems more probable, to me anyway, that it occurred during day-four, the day that other objects external to the "earth" appeared. This does not alter the observer time notion of "sudden appearance" during day-four. As pointed out, for day-three "sudden" appearance may be greater than instantaneous in certain cases. There are various types of time involved including primitive, observer and Earth-time (or earth-time). Earth-time is time measured via any extremely periodic Earth-bound (or earth-bound) natural-system behavior. It is a restricted form of observer time. It's Earth-time that corresponds to the creation-day notion. I am not sure that for these Biblical models it really matters greatly whether stars and, possibly, all other solar system members (i.e. not the earth, sun and moon) where formed during day three or day-four. However, since "the stars also" statement appears in the day-four description, it is more consistent to assume that they did not just "appear" during day-four but were created during that day. The purposes stated for the created day-four objects are significant

[21] Page 216. I thought it was self-evident as to whom I am referring by the phrase "the deity is God as He is described by a literal Biblical interpretation." As an Apostolic, I firmly believe that the deity that has created all there was, all there is, and all there ever will be has a personal name. This name is clearly identified in the New Testament as "Jesus."

[21c Page 225 The Glossary. For refinements and changes to some of the definitions listed, please see this Glossary.

[22a] [Technical Additions]. For a discussion of actual direct and indirect scientific evidence for the GID-model interpretation see Evidence.

[22b] Since this book is written for an audience with some advanced technical training, I have styled the material as it would apply mostly to a simple universe (book p. 101) and a single final event sequence. The facts are that the actual "final" covirtual image that appears at time t and to which subparticle formation and the standard part operator is applied is obtained by means of a much more technical process where we can't have a detailed explanation for all that occurs. This is a rather technical explanation that uses my book The Theory of Ultralogics Part II referred to below as II. I use terminology taken from this mathematics book.

In section 7.1 of Part II, the event sequences are restrict to intervals of the form [t(j),t(j+1)). These sequences are composed of a strictly increasing sequence of primitive time identifiers that converge to t(j+1) (II p. 61). Each one of the frozen segments (i.e. frozen-frames) that correspond to each identifier is taken from a totality and the totalities are contained in a denumerable set of totalities denoted by (script)T. Since the entire collection of countably many such intervals forms a countable collection of denumerable sets, it can be viewed technically as an event sequence d. This is why the term sequence is used. The bijection that yields such a sequence is not used in my ultralogics book. However, the inverse of this map allows one to locate all of the sequentially denoted members of d that correspond to each member of [t(j),t(j+1)). Thus, the sequence-generating map is but a modeling artifact. [Hence, the d can always be viewed as being expressed in the original primitive time order.]

Each of these intervals generates an ultraword w_i.The ultraword for a specific natural-system that generates its event sequence d is actually an ultimate ultraword w '_ j obtained by application of Theorem 7.3.4 to this countable collect of ultrawords. In the book, I call these event sequence generators - ultrawords. To investigate what is occurring about a specific t(j+1), one simply applies Theorem, 10.1.1 (II p. 89). I point out that, in general, it is not necessary to consider the d as related to such time intervals. In this case, one simply applies Theorem 9.1.2. Also, note that the nonstandard event sequence generated by ultraword w_i is hyperfinite and, hence, from the viewpoint of a higher-intelligence has all of the formal behavior of a "finite" set.

As is well-known, there are members of the ultrawords w_i to which *S applies where the primitive time identifies correspond to infinite Robinson numbers with their usual ordering. Further, depending upon the exact members of the original d, the following holds. (i) If an original "converging" portion of d restricted to one of these intervals is composed of "repeated" images that converge in standard primitive time to a specific interval end-point, then the corresponding nonstandard members of *d only differ in that they now require a Robinson styled infinite number primitive time identifier. If this is not the case and the images for various reasons are considered as non-repeated, then these nonstandard members of *d not only have Robinson styled infinite number identifiers but the actual "images" themselves may be difficult or even impossible to "describe." These are the ultranatural events. Unless you can characterize in a special way each member of such a d interval in terms of our standard model, then there is no method that gives us any idea as to the content of these ultranatural events, these pure nonstandard frozen segments.

It's important to remember that these processes are for the generation of many distinct universes. Although within our universe the outcomes of the entire universe generating process may appear to some scientists to be discontinuous in character within certain subatomic regions, it has been shown (II p. 77) and Herrmann (1987) that within the substratum this can be the product of hypercontinuous behavior. There are particle field theories that also imply such sequences of altered behavior, at the least, as to "location." Then, of course, we have the hypothesized general behavior of the "vacuum" of particle physics. Hence, within our present universe the event sequence frozen-frames that generate certain w_i do display an infinite sequence of different frozen-frames. In all cases, the ultranatural events would be, within the substratum, (nonstandard) hyperprimitive time infinitesimally close to standard t(j+1). Under the definitions used in the physical interpretation, these events indirectly affect the frozen-fame image at t(j+1).

Herrmann, Robert A. 1987. Fractals and ultrasmooth microeffects Journal of Mathematical Physics 30(4):805-809.

[22c] When the final (book) ultimate ultraword composed of the above defined event sequence ultrawords is decompressed, you do not have just a single ultraword for a given natural-system but you have a countable collection that can be considered as partitioned. This yields at time t a countable collection of covirtual images, (information) for each specific natural-system. It is at this stage that other appropriate intelligent actions coalesce and yield the appropriate image from this collection that corresponds to the "previous" image. This is particular required so as to preserve the probabilistic outcomes and, where appropriate, the macroscopic and large scale regularities. This is followed by subparticle formation and realization via the standard part operator. However, other aspects of the coalescence cannot be described since they would be associated with the ultranatural events. This process yields an actual realized observer event sequence through and including the time t event. The way the actual model is constructed for a non-simple universe at time t, all natural-systems that exist at t have event sequences for the behavior prior to t.

The GGU-model can be used to obtain event sequences that yield increasing, suspended or decreasing observer time. However, accept for Divine intervention, I reject, for our universe, any notion that there may be realizations that reverse the forward arrow of observer time. I consider all such natural-system "backward in time" notions as but modeling artifacts. However, when realization occurs for such a observer time arrow, the next realization in primitive time sequence ordering, due to this time notion, must become the only realized image. The information that produces the "previous" realizations can be assumed to still exist as a covirtual objects. They can be considered as forming a type of natural-system history file. For the theological interpretation, these can be important objects. They can be retained in the form of compressed ultrawords that contain all of the "prior" information as to the actual real behavior of any natural-system. Biblically, the natural-system ultrawords, from any past, that comprise an individual's life and an "immediate" environment can be used to verify the rationality of Rev. 20:12 - 13. They can be considered as contained in a "book."

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