General Intelligent Design (GID) Evidence
Not Classified as Restricted Intelligent Design (RID) Evidence
And Other Significant Facts about GID

Robert A. Herrmann, Ph. D.
12 MAY 2006. Latest revision 5 AUG 2016.

The following is an in-depth article that does not include the specialized mathematics or the required theorems that establish the presented results. Actual physical evidence is described that verifies the GID-model when it is restricted to a material universe, evidence that is employed to predict the behavior of a "higher-intelligence." (In this article, the actual technical term "hyper" is not employed. The term "higher" has been substituted. What the term "hyper" signifies depends upon whether the entity so named can be compared with the entity denoted by the unmodified term. In all cases mentioned within this article, the term can be so compared.) The GID-model is a mathematical model based upon certain specific aspects of human linguistic experiences.

Unless otherwise indicated, whenever the term "intelligence" or "intelligent agency" (actions) is employed it refers to GID-intelligence as defined below.

Description. The term "description" means a collection (a set) of statements taken from a language L, where L contains written symbols, images or diagrams in the usual sense, and human or machine duplicating sensory impressions. (For various articles, the term "natural" always means "physical" as physical is defined by a specific science-community.) Descriptions first represent tangible objects that can be observed and that provide the specific information that characterizes a physical-system. (The term "observe" is more fully defined below.) This includes all observed values taken from measuring instruments. (It can also be assumed that such information is digitized in the sense of virtual reality.) The collection of objects that yield the set of all descriptions is termed a "general language." When the term "language" is used it refers to a general language. When descriptions correspond to science-community defined physical reality, then they are often called "physical events" since such descriptions should faithfully represent reality as reality is defined by science-communities. The modifier "physical" is often understood. Although not significant for this article, modern science also describes assumed but not observable entities and processes.

Finite Consequence Operator. In this article, such an operator is applied to a specific language L. When it is applied to a collection of L members, it produces a single collection of L members. This operator also has a set of characteristics that model the most basic aspects of human deductive thought. Hence, as interpreted in the GID-model, these characteristics signify that the operator represents intelligent actions.

General logic-system. As in formal logic, a logic-system is intuitively collection of sets composed of members from L. Such a set can contain but one or two members, indeed, any finite number of members of L. In a logical argument we can choose one or more of the one member sets and choose the single member it contains. (Our choices are always finite in number.) We then can choose members from a set of hypotheses. In a systematic way, these sets are searched. If all but one of the members of a set have been previously chosen, them the remaining one is chosen. This search and choice process is repeated. All classical and everyday deductive thought is equivalent to this process. Each consequence operator is generated by a general logic-system and conversely. The "systematic" part is more accurately defined mathematically.

Directly Observed. Perceived. In a general sense, the term "observed" means detection by means of human sensory impressions. Depending upon what is stated, observed also includes human sensory observations of diagrams and images. However, accept for the "machine recordable data," this is need not be considered a particularly trusted method within a "hard" physical science such as physics. Thus, a strict scientific definition is that directly observed data correspond to machine recordable information. Today, this includes methods that reproduce our major sensory impressions.

The "meanings" for human and machine sensory information are filtered through mental biases. If a machine is allowed to faithfully reproduce and record human sensory information and additional information only the machine can record, then the "interpretation" of such data is also related to an individual's training and biases. Of course, even a machine is subject to human biases relative to what it is actually "allowed" to record. In all cases, the interpretations of pure human and machine sensory data is controlled by the language, theories and biases of a particular group of individuals.

For modern predictive science, the language used to interpret data requires that it be restricted to that which is considered as unambiguous for the group members. The language must allow for classical deduction. Each group member needs to have the same "intuitive" comprehension as to the meanings mentally assigned to the expressions employed. In what follows, when the term perceived is used, one may substitute the more conservative term observed. Observation does not include imagined entities of any type.

Indirect Observation. This is a term that has been used to indicate that evidence is for something that "can be" directly observed. Observation within physical science and concepts within the Philosophy of Science should, but often do not, differentiate between these two types of observations - observations that "can be" or "have been" made. The problem is with the definition of "can be." This is often merely a rather unjustified hypothesis and tends to be a matter of opinion. Under various described scenarios, it was stated that the farside of the Moon, the surface of Venus and the details of the surface of Pluto are indirectly observable. Well after such pronouncements, these three surfaces were directly observed justifying the claims. Unless otherwise indicated, in this article, the term "observation" means direct observation.

Evidence. In this article, "evidence" comprises interpreted observations that satisfy a statement. This means that when the interpreted data is logically inserted into a statement, then that statement is "true" (is satisfied) for the interpreted data. Thus, evidence is related to something else to which it refers. It is evidence "for something." However, it is important to note that this is also a group concept. Accepted observations can have different interpretations and satisfy different statements. Technically, future interpretations cannot be linguistically ruled out. Thus, from a linguistic viewpoint, evidence need not indicate an absolute truth. There are other less strict notions that are termed as "evidence." These forms of evidence are indirect in character and as such are much less convincing.

GID-DESIGN. A design is a general language meaningful description. Specifically, each sequential slice of a universe, a universal-wide frozen-frame (UWFF), is composed of physical-systems. Via the developmental paradigm, each such physical-system configuration is considered as meaningfully described by a general language. Such design includes the described intertwining of a vast number, or even infinitely many, of such physical-systems. Design also refers to any described alterations in the designed configurations that may occur from one UWFF to another sequentially occurring UWFF. That is, by comparison, the alterations are considered as designed. There are other "designed" entities that are external to the design notion as applied to a UWFF. Such designs are based upon methods of describing physical processes and physical laws. For example, various "substratum processes."

For GID, a second form of design means the arrangements of the physical entities that yield the various patterns being described, the natural patterns, or the patterns that satisfy physical laws or processes. It is this "design" concept that is being general language described.

GID-INTELLIGENCE. GID intelligence relative to the UWFFs, referees specifically to defined algorithms that deductively yield the described sequentially intertwined physical-systems for each UWFF and the sequentially presented collection of UWFFs. Other described entities that apply such deduction, such as physical laws and the production of physical-systems, also satisfy this intelligence definition." Such deduction is modeled by defined logic-systems or corresponding consequence operators. However, GID-intelligence is not dependent upon the content of a physical law and no descriptive physical law need actually exist that satisfies such descriptive behavior. Intelligence so defined has a comparative numerical measure. GID-intelligent design corresponds to the deductive generation of designs and does not refer to other aspects of the designs.

Operator. Within much of physical science, an operator is, usually, a symbolic representation for physical processes - a physical process operator. Such operators have additional properties that are represented by rules for symbol manipulation. For the GGU-model, the term operator has a much broader definition. It includes operators that represent substratum processes. When applicable, an operator is also a mathematical object represented by a set of ordered pairs {(a,b)}, where the set does not contain distinct ordered pairs of the form (a,b) and (a,c). What this means is that a specific "a" corresponds to one and only one "b."

Physical-like. Physical entities and behaviors are characterized via language elements. Similar language elements are used to characterized physical-like entities and behavior. However, these entities and behavior, although similar to the physical, also have properties that the physical cannot have, or have some property or entity that, at the least, is not part of a defined physical environment.

A Signature A signature is a collection of described characteristics that indicates that an entity has produced an event even if that entity is no longer present or cannot be directly observed.

After constructing the major part of the GGU-model and the GID interpretation, I discovered the following two remarks. Hermann Weyl wrote

Is it conceivable that immaterial factors having the nature of images, ideas, (or) "building plans" also intervene in the evolution of the world as a whole?

Then Noble Laurent Louis deBroglie wrote

[T]he structure of the universe has something in common with the workings of the human mind.

The answer to Weyl's question is yes and the deBroglie statement can be fully justified. Physical science substitutes language descriptions for physical events (the actual material or behavior being depicted). Language descriptions can be further represented by images, and drawings. Today, language descriptions or images are translated into computer languages and the computer displays corresponding images that represent the language descriptions, and, hence, the physical world. The GGU-model uses mathematically defined operators that represent processes that produce physical entities and behavior. These operators are defined on an abstraction of the notion of a general language.

When "logical" arguments are analyzed, each member of a science-community is required to display their deductions using the science-community's specified logical-patterns. The basic GID-model idea is that each operator has a specific signature that characterizes the intelligence of the designer of the corresponding processes as well as a signature that implies that when an operator is applied a specific process is used that corresponds exactly to the intelligence necessary to infer behavior.

It should be self-evident, that assigning intellect agency to the GGU-model operators is an hypothesis that needs verification. Thus, one needs to show that each known physical process exhibits an "intelligent design" signature. Explicitly stating this signature would be direct evidence for the acceptance of this hypothesis. Displaying this human-like common feature satisfies the deBroglie statement and incorporates how we use building plans to construct. The existence of a high-intelligence is predicted and this prediction is verified by indirect evidence. Indirect evidence is used throughout physical science for objects that cannot be directly observed.

Indirect evidence for "something" (indirectly verified) means that neither a human nor machine sensor can, often by definition, detect the actual "something." The "something" is hypothesized. The concept is entirely based upon logical deduction that yields observable predictions. Due to the possibility of other hypothesized "somethings" leading to the same observable predictions, indirect evidence is never absolute.

The "existence" of almost all assumed subatomic objects and processes comes from indirect evidence. One can accept their existence based upon how they are predicted to affect observable gross material. The same philosophy of science holds and, hence, most be allowed for the notion of an higher-intelligence.

An additional discussion on indirect evidence can be found in section G.

It is important to realize that the direct evidence for intelligent design and indirect evidence for design by an higher-intelligence presented here is independent from whether one accepts any GGU-model physically generated cosmology. This evidence is independent from any cosmogony or cosmology. However, for our universe, the intelligent design satisfies the perceived physical regulations that are often predicted by scientific theories.

The basic requirements for the GGU-model is that a specific set of defined operators are applied and these produce and continually sustain the development of a universe. These operators satisfy empirical evidence. For this article, the GID-model interpretation is analyzed relative to such evidence. As discussed here, this is not a complete analysis. Aspects not discussed here appear elsewhere on this website.

The empirical evidence, for intelligent design, is (1) each of the GGU-model operators is intelligently described. That is, in restricted form, they specifically describe observable modes of human behavior that exhibit deductive thought. Then a mathematical model for these rationally predicts corresponding descriptions that give additional comparative information as to the behavior of an higher-form of intelligent agency. This higher-form of intelligent action need only refer to the rationally of various substratum concepts. (2) Each physical-system, its behavioral patterns, at each moment in a development and the ordered moment-to-moment developmental of a universe are intelligently designed. For (1) and (2), the originally described "intelligence" being displayed predicts the existence of an higher-intelligence that satisfies such characterizing statements.

Statement (1) is satisfied since each of the defined operators is modeled after processes that mimic a fixed set of human actions, where each action requires human intelligence to perform. The operators are designed by an intelligent being denoted by H as described in Herrmann (2002). Each of the operators used for all aspects of the GGU-model universe generating behavior have specific describable characteristics that mostly mimic human modes of deduction. The remaining operators mimic other mental processes and modes of human activity. These operators are discussed elsewhere. Hence, (1) is satisfied.

Empirical evidence supports the use of mathematics and the classical logic it employs as a valid predictor for future physical behavior. However, in general, the mathematics tends to produce what is classified as extraneous results and, in other cases, for example General Relativity, results that are not accepted as applicable to our physical universe. Thus, although mathematics is the most rational form of predictor used throughout physical science, it need not be considered as an absolute mode by which factual predictions are made.

The major purpose of this article is to establish the circumstances under which (2) is fact and it is composed of the following sections, (A) Physical-systems, (B) Physical Laws, (C) Scientific Theories, (D) General Applications of physical Law Statements and Scientific Theories, (E) More about Evidence, (F) Illusion, (G) Direct or Indirect Evidence and Nature, (H) (A link to) The Fundamental Universe-Generating Processes.

(A) Physical-systems. A science-community names a collection of observable entities as "physical-systems." Via a technical language, a physical-system is described. Such general language descriptions are meaningful to members of the community and produce mental imagery and possible other sensory information. The following simple logic-system will yield the description and seems to be the exact way humans impart such a description to others. A logic-system is formally composed of a fixed set of n-ary (n-placed) relations RI(L) = {R(1),R(2), . . . }. Each R(i) is composed of n-tuples that are denoted by symbols such as (a(1),a(2),...,(a(n)), with "n" coordinates a(i) and each a(i) is a member of the language L. This concept should be familiar to those who have had any instruction in two or three dimensional coordinate geometry.

One can consider a general language description as separated into a finite set of ordered general language sentences, diagrams, images etc. A = {bi}, i = 1, . . . , n. You consider the follows binary logic-system, {(a,bi)}, where a = the name of the physical-system. The logic-system algorithm states that you consider the expression a and that, where the "a" appears as the first-coordinate in this binary logic-system, you "deduce" the bi. Further, an ordered logic-system requires that the bi step have the same order as the natural numbers 1, . . . , n. This is actually equivalent to the most basic of all deductive processes, the "rule of detachment (modus ponens)," as it is termed in elementary textbooks.

One can contend that if one starts with the name for a physical-system, then describes, from memory the physical-system, the logic-system employed mimics the mental selection process we use to express the description.

By definition, evidence for logical-deduction is a written step-by-step display using a specific language as its elements. The GID-model is not dependent upon physical laws. The general intelligence is dependent upon but one aspect of intelligence used by the human being. It is an ordered form of "modus ponens" deduction as illustration by a logic-system and the application of the logic-system algorithm. In particular, the binary logic-system is of the following form.

{A,(A,B),(B,C),(C,D), . . . },

where each member of the logic-system u-ary and binary relations has a distinct identified.

The letters denote descriptions or symbols for the progressive ordered names for the natural number. That is {1,(1,2),(2,3),(3,4), . . .}. We then apply the rules for the algorithm and obtain, in these cases, the linguistically ordered expression A,B,C,D, . . . and 1,2,3,4, . . . . These two forms represent the standard evidence that is mathematically modeled and that predicts a (hyper) "higher" form of deduction. These two forms are used to produce each physical-system within our universe and the step-by-step development of the physical-system known as our universe.

(B) Physical Laws (Laws of Nature). First note again that in GID-intelligent design is NOT dependent upon any descriptive physical law. This section is relative to those cases where physical law statements exist that predict observed physical entities or behavior.

How does the dictionary define a law of nature - a physical law? My dictionary states that a "law of nature" is "(a) a cause and effect sequence of events in nature or human activities that has been observed to occur with unvarying uniformity under the same conditions or (b) the formation in words of such a sequence." For the GID-model, using a physical law statement (b), rational processes are applied to obtain representations for the (a) cause and effect(s). These rational processes are the same as those used to deduce conclusions from an hypothesis (b). As demonstrated below, a physical law statement (b) is an intelligently designed aspect of the GGU-model and rational processes lead to (a) and to data verification. For our, universe it satisfies the designed sequential alterations, if any, in the UWFFs. Hypothesized physical law statements that do not allow one to test the required unvarying uniformity may or may not be accepted as physical laws. Even if testing is possible over a specific interval of observer time, there is no scientific way that absolutely determines that the physical law will remain unvarying and uniform during a "future" time period. Moreover, some science-communities may require a physical law statement to be tested in a specific way. It is not relevant to this article how one obtains verifying physical law data and whether data exist prior to or after the physical law statement is discovered.

(I) The existence of the collection of all described physical law statements indicates that our universe is externally designed in a special manner. This is, human intelligence can devise physical law statements using languages and other devices that mimic processes that appear to produce or alter physical-system behavior, or produce or alter physical-system characteristics. For science, these yield comprehensible "cause and effect" statements. These regulations are used to build our man-made universe or to predict behavior.

(II) (a) A physical law statement is construction in such a manner that basic logical processes can be applied. In order to verify experimental data or predict experimental data, a physical law statement requires application of a logic-system. The statement itself most be designed in a form applicable to the logic-system employed. As demonstrated below, there are different ways to do this. (b) If some pure data is used to determine directly physical behavior without requiring additional assumptions, then such data need not be modeled by GID. Such data can falsify aspects of the GID-model. There are mathematical examples of data that do falsify these aspects.

(III) (a) The production of or alterations in the behavior of a physical-system, or the production of or alterations in a physical-system's characteristics produced by application of a physical law statement are modeled by the GID-model. When any operator discussed here is applied, the operator's characteristics imply that the application is an intelligent action. There are examples where describable mental processes applied to descriptions for physical-system behavior falsify the GID-model (Herrmann (2002, p. 73)).

(IV) The GGU-model is a cosmogony. It is capable of producing every described cosmology and infinite many other ones. The production of or alterations in the behavior of a comprehensible physical-system is not the result of application of a physical law or physical theory. The construction of the GGU-model shows that these regulations satisfy or verify the law or theory predictions.

The following illustration of (IV) is presented in various articles. Consider a DVD, which when played depicts a rubber ball dropped from the tall table to the ground. There is a measuring rod affixed to the table that "measures" the ball's distance from the top of the table to the ground as it falls under the influence of gravity. As it begins its fall, pause the DVD player. The image displayed on the monitor appears fixed. Now forward the display one frame at a time. From our observation, the ball appears in slightly different places in each frame. Correspond the lapsed "time" to the number of frames observed. There is no law of gravity, there is no gravitational force "pulling down" on the rock. But for this locally observed experiment, we know that the distance moved, s, is proportional to the lapsed time squared. So, this allows us to calculate the distance, s, if we only know the frame number. This calculation is in good agreement with the numbers on the measuring rod. (Of course, the law is actually rather more complex than this.)

So, this illustration implies that this behavior is produced in such a manner that we can deduce such an expression and made such a calculation. We have directly observed behavior that can, but need not, be attributable to an intelligent agent that is, apparently, hidden from view. For a small "time" interval, the number of frames is so vast that even if one assumes the behavior is "continuous," the values for any comprehensible measure could not detect that the behavior is actually sequential.

The term "physical law" (law of nature) can also refer to human activities. These include such things as economic laws, among others, that are not usually considered as physical laws. Physical laws tend to have the most concrete defining properties. In this section, the term "physical law" refers explicitly to a physical regulation and possibly other accepted types of "physical laws" that fit the physical circumstances.

Although a (humanly) comprehensible physical law starts as a "statement" that can be logically applied more than once to physical situations, this does not mean that such a law is actually applied more than once. The statement comes from a language as defined in this article. The statement is considered as rather "simple" and is often used within more complex scientific theories. Such a law predicts, via application of a general logic-system, a science-community's experimental data. Such a law can be represented by language elements other than written strings of symbols.

Recall that a science-community is any individual or organization that, at least, uses an implicit or explicit fixed general logic-system. Hence, a meaning for the term "science" can be rather broad in character. "Science" can refer to any branch of systemize knowledge that includes a fixed general logic-system. Whether an investigation is "scientific" in character is also irrelevant for this article. If one uses terminology contained in Herrmann (2002), then physical law statements can include descriptions for how we comprehend the combining of various "simple" levels of the universe-wide frozen-frames (UWFF), the sequential slices.

The history of how physical law statements are obtained clearly indicates that all have developed through human mental procedures that, for recent history, include the notion of mathematical abstraction. Consider observed data, where intuition is a first step. Materially, intuition is based upon human mental processes that yield directly an hypothesis that states that there is a correlation between observed physical events. Once the hypothesis is stated, then this correlation is tested. "It is a perception of relations and not subject to any rules of validity, and represents the gropings and tentative guessing of a mind aiming at knowledge." (Cohen and Nagel, "An Introduction to Logic and the Scientific Method, Harcourt, Brace, NY (1934, P. 275).) However, these "gropings" use mental processes and often use back-and-forth refinements that yield an improved correspondence between a physical law statement and data. The first step for such intuition does fit the "finite choice operator" as GID-model interpreted. When only empirical data are being considered, then an hypothesized physical law statement must satisfy the data. Verification establishes a correlation between data and the purposed law and requires a logic-system. (The logic-systems used in this article have a slightly more technical name. They are the general logic-systems.)

It is a fact that any data determined physical law statement must satisfy the requirements for a logic-system if that physical law statement is used within any science-community theory. This follows since such a theory must predict the original empirically obtained data from which the physical law statement is obtained when restricted to appropriate objects. Such empirical data often represent information that requires interpretation (i.e. translation). This yields a relation between descriptions by considering the "before" and the "after" effects for the physical state-of-affairs investigated.

What is actually accepted as a physical law statement depends upon the science-community. Consider Kepler's Second Law Planetary Motion. He used the orbit of Mars as his one example. He considered the numerical data obtained by observation from the earth and assumes the earth is in a circular orbit about the sun. This data allowed him to consider the Mars path of motion over fixed periods of time. He selected many different assumptions and tried to deduce the data. After much contemplation and calculation Kepler discovered principles that do predict the data. He showed that for any fixed period of time, the line segment from the planet to the sun will sweep out a constant space region area. And, this law satisfies the data. Technically, the geometric configuration predicted is mostly not related to observable physical entities but this numerical result is mentally perceivable. Notice that deduction is a required aspect for determining whether a statement is a candidate for been termed a physical law, even if the following PA form is not employed.

Consider experiments made in 1900 relative to the notion termed the "photoelectric effect." Light-"waves" fall on the surface of a certain piece of material. It is determined that an electric current can be produced and it is assumed this current is caused by the light. But, this "law" can be stated in different ways. One textbook states that when a high-frequency of radiation falls on a certain metal, it is found that electrons are ejected. In the first statement, the cause and effect are observable via human sensory impressions and a machine. The second statement has an observable cause, but the effect would probably not be considered as being observed since I know of no instance where the ejection of an electron was observed. Only the effect such an electron has on gross matter was observed. This second statement uses a defined "mentally perceived" entity.

(1) By applications of a science-community's general logic-system, an experimental set-up is constructed. (2) Then measurements are made. (3) Then a graph is drawn. (4) Cartesian geometry is applied and an energy equation is written down that relates the measured quantities. It is hypothesized that electrons with mass m cause this current and they can acquire kinetic energy of (1/2)mv2, where v is the electron's relative speed. An equation hf = (1/2)mv2 + hf(0) is deduced, where f and f(0) are two frequency measures and h is the slope of a linear graph. Notice how application of various general logic-systems yields this equation. This is yet another way to describe this law. The graph relates observable quantities and the equation is immediately apparent. The basic classical continuous wave-theory is applied. However, that theory implies that it would take considerable time for the current to flow. This wave-theory prediction does not correspond to the experimental data. Hence, for this scenario one might replace the wave-theory behavior with a new physical law statement.

Suppose the (1900-01) Planck general logic-system that uses "electromagnetic energy elements" is applied and this equation is re-interpreted using a different physical language. By finite choice, let h be Planck's constant and then let hf be imagined as a single "bundle" of energy, later called a photon, which corresponds to an electromagnetic energy element. Then when a photon interacts with an electron suppose that all of this energy hf is "immediately" given to the electron. The actual physical law statement can be expressed in general logic-system form in various ways. It can be stated in the general rules of inference when used for any physical theory. As with the deduction of a physical-system description, it can be deduced in an appropriate ordered form.

Let p = Light of a specific frequency falls on a photoelectric surface. (a) = Light energy (a photon) is absorbed by an electron; (b) = a photon is essentially absorbed instantaneously by an electron; (c) = all of the photon energy is absorbed by a single electron; (d) = a portion of the absorbed energy is used to free the electron from the surface; (e) = the current produced by the photoelectric surface is proportional to the number of photons. Then consider the following, PA, physical law statement, where for many scientists, the PA description is mentally comprehensible.

PA is the following logic-system.

Application of the logic-system algorithm yields the following ordered description.

"Light of a specific frequency falls on a photoelectric surface. Light energy (a photon) is absorbed by an electron; a photon is essentially absorbed instantaneously by an electron; all of the photon energy is absorbed by a single electron; a portion of the absorbed energy is used to free the electron from the surface; the current produced by the photoelectric surface is proportional to the number of photons."

Notice how application of the first three ordered pairs of PA models a physical process termed "photon absorption."

These logic-system forms a general rule of inference. To use this general rule of inference, the basic logic-system algorithm is applied, where the first step is to consider the one hypothesis p. Then the behavior pattern is predicted, in the case, in its appropriate physical order. (As previously stated, PA can be considered as a shortened version of a basic set of "if" and "then" statements or a single statement as described below.)

This binary relation, PA, does not give a description for a relation that exists between measured values. It is self-evident and implicitly assumed that such unobserved predictions are translated into a general rules of inference that yields observed numerical values. There are infinitely many general rules of inference that yield the same physical law operator. Of course, the equation is not displayed in PA. The "energy" being imparted is not displayed. Members (a) - (d) do not correspond to specific and observable objects, say a particle that is only a bundle of "energy" or another particle's "kinetic energy," an unobserved property associated with movement. Of course, (e) might, at least, be partially measured by a machine. The physical law statement is obtain by writing the (cause) p statement. Then the rules for deduction yield effects statement (a) - (e).

The GID-model states that duplicating such physical law statements in such a form via general logic-systems is an ID-signature for intelligent action (agency). Additionally, mathematical models are now the major way to predict physical behavior. These employ a vast array of logic-system deductive schemes to achieve the observable predictions. Such schemes also yield GID-signatures that the behavior is produced by intelligent actions.

(C) Scientific Theories. For this article, a scientific theory is considered in the broadest sense. It can use more than one physical law as hypotheses or other working hypotheses, where the working hypotheses need not be considered as uncontested physical laws. It is not the purpose of this article to discuss the science-community conditions an hypothesis needs to satisfy before it is declared a physical law. It is self-evident that a scientific theory is intelligently designed by those who construct the theory since a science-community's logical-system is employed and portions are displayed.

For the GID-model, the notion of what constitutes a scientific theory is broad in character. A scientific theory has all the same properties as a physical law operator, where the term "scientific" requires that a specific logic-system be stated. With few exception, this refers to portions of classical logic. The GGU-model is an interpreted mathematical theory that uses this form of deduction. The standard GGU-model operators that correspond to deductive thought display classical deduction. Scientific theory operators SN as they appear in some of my older publications do not use the PA form but employ physical law statements in hypothesis form. For a specific purpose, the SN are used to define the operator SNV. This operator appears in Herrmann (2002) and elsewhere. However, it still generates extraneous results.

As demonstrated in this article, in modern scientific discourse, what is defined as a physical law or a physical theory need not be related to how these notions are defined by philosophers of science. What is a working hypothesis today, may be declared as a physical law tomorrow. When Newton first stated it, it was called the "Law of Gravity." But, we now have the Hilbert-Einstein theory of gravity. I suppose that most physicists consider it as a, not very simple, but inviolate physical law although stating that gravity is caused by the curvature of space has little physical meaning unless the term space is defined using a physical rather than geometric language. Do we still call the Kepler statements "laws" although they are predicted from the theory of gravity?

The actual rules of logic used by individuals to construct scientific theories may not be explicitly mentioned although, for scientific theories, classical logic is the usual approach. Such logical rules need not be explicitly stated as long as the "arguments" are accepted by a science-community. In general, the conclusions can come from either inductive processes through observation and generalization, or from pure general deduction. This can yield informal scientific theories that are intelligently designed by trained individuals. However, when challenged to specify the deductions used for the arguments, a general rules of inference must be constructed. It is shown in the articles listed in the Special References that the processes that yield a physical universe are the result of applications of (ultra) logic-systems. Hence, the specific physical processes that correspond to each informal scientific theory also correspond to intelligent actions produced by intelligently designed logic-systems. I point out that such logic-systems are not based upon the notion of logical "values" such as two-valued models for "True or False" or any other valuation notation.

(D) General Applications of Physical Law Statements and Scientific Theories. There are, at the least, two ways to show that such applications are, for the GID-model, intelligently designed, at least, from the viewpoint of human intelligence. One is my published method to obtain the best possible consequence operator or equivalent general logic-system unification for any set of consequence operators or equivalent general logic-systems, respectively. This result shows that any application, finite or infinite, of physical law statements and scientific theories is equivalent to a single unifying operator or equivalent general logic-system. (See Herrmann, R. A., "General Logic-Systems and Finite Consequence Operators," Logica Universalis, 1(2006):201-208 or General Logic-Systems . . . and Herrmann, R. A., "The best possible unification for any collection of physical theories," Internet. J. Math. and Math. Sci., 17(2004):861-721 Corollary 2.11 p. 864, or Best Possible . . . and Theorem 2.2. Then there is the example discussed in the chance.pdf file in Statements that describe emergent properties are also included within this unification. (Physical entities using informational ultrafast propertons with correlating ultranatural events are compelled to display this properties.)

There may be those who reject any physical law statement or scientific theory that postulates the existence of any unobserved object. This rejection will not eliminate the statement that our universe is intelligently designed.

A second approach is a rather trivial fact. Consider the language L used to represent descriptions. If one accepts that the description X in F(k) either produces description Y in F(k + 1) or is altered to yield the description Y in F(k + 1), then by using a single symbol not in L, say |, and attaching it to each X, say X|, then there exists the entire set of ordered pairs {(X|,Y)}. This general logic-system will generate each Y from the specific X|.

(E) More on Indirect Evidence and Nature. Although I have purposely not as yet stated how the "ultra" entities are interpreted, there is one application that answers one significant physical science question. How can individual random production of physical events lead to theory predicted probabilistic behavior. For the GID-model, there exist "pure" ultra-logic-systems that yield individual probabilistically described events. The ID-signatures for these pure ultralogic operators is that of an higher-intelligence and only an higher-intelligence. Thus, by similar rational choice, one can accept, via indirect evidence, that an higher-intelligence produces and controls or designs all such behavior. [See Probability Models.]

Nobel Laurent Richard Feynman stated during his public lectures on QED

. . . while I am describing to you how Nature works, you won't understand why Nature works that way (Feynman, p. 10)
But what does he mean by "Nature," which he often refers to as a She? Does he mean the usual dictionary definition or maybe something else?

Does the GID-model imply that there is "something" within "Nature" itself that corresponds to intelligent agency? Does this notion of intelligent design model the behavior of an actual object? Physical laws are not "stated by Nature." They are human constructs that remarkably predict observed physical-behavior. How is it possible that assumed impersonal Nature develops from moment-to-moment in such a manner that we can use material that Nature does not itself construct and predict its future behavior? From a viewpoint of the most fundamental aspects of modern science, the mathematical model, one easily concludes that the linguistic procedures we employ to describe physical-system behavior model "something" that, at the least, is related to human mental behavior. Or as deBroglie wrote "[T]he structure of the universe has something in common with the workings of the human mind." But, what might that "something" be?

Each standard GID-designed physical-system corresponds to actual material entities, the physical-events or simply events. Using the Feynman terminology and the GID-model as an analogue model, it is rational to state that Nature rationally combines material entities to produce physical-events. At each moment in the development of our universe Nature has rationally intertwined these physical-events and has rationally produced a step-by-step development of these intertwined physical-events. Further, Nature allows rational beings to alter, to various degrees, these physical-events.

The above expressed GID entities exist as actual linguistic constructions and how these constructions can be rationally obtained is a rather trivial fact. These are mathematically modeled by the standard mathematical structure. When this standard model is embedded into a nonstandard structure other entities are predicted that can be compared with the standard ones. These predicted entities are named with an additional prefix "ultra" such as ultranatural laws, ultra-logic-systems, ultrawords etc. and can be compared with the underlying entities, natural laws, logic-systems, words, etc. This is similar to quantum theory or early history cosmologies where physical objects or processes are accepted based only upon deduction and indirect evidence.

Using a nonstandard model, a hyper-language is predicted. The rational generation of a UWFF (a slice of our universe) can be replaced by an hyper-algorithm applied to an "ultraword." The generation of an entire universe can also be modeled by an ultraword. Propertons are described by members of this language. The secular instructions for the formation of physical-systems from propertons is composed of members of this hyper-language, members that we can comprehend. Hence, the nonstandard model is a necessary requirement for the secular GGU-model. And there is also the rationally predicted ultranatural systems. These are additional substratum "systems" that behave like physical-systems but are formed by x-tons. Our entire universe at any moment in its development is a physical-system. It is predicted that universe wide ultranatural systems occur as our universe develops. These could be but repetitions of UWFFs, empty systems or "something" entirely different from our physical world. Thus, the nonstandard model has some rather interesting additional features.

Although the GGU-model is falsifiable relative to the logical production of physical behavior, obviously the predicted entities or behavior cannot be employed within a physical laboratory setting to produced physical entities or behavior. This is the same property required of the standard cosmological model. But, all that has physically existed, now physically exists and will ever physically exist is indirect evidence for the existence of the GGU-model processes. It should be noted that this model also avoids the obvious infinite logical regress that occurs when one concludes, for a cosmology, that a physical entity or process is "self-produced." It has a stronger "scientific" bases than any known cosmology.

(F) Illusion. From observed human linguistic behavior, the GID-model rationally predicts behavior that, by comparison, would be that of a higher-intelligence. This fact does not imply that such an higher-intelligence exists. As with the accepted existence of entities within quantum physics, the existence of an higher-intelligence is accepted based upon indirect evidence. One can accept this hypothesis based only upon this rationally obtained prediction. Within particle physics, the hypothesis of photon absorption is accepted for the exact same reason. There are philosophic attempts to dissuade individuals from accepting this higher-intelligence hypothesis. The argument is that evidence implies only an apparent design; it is an illusion, which is not objectively real. Of course, the same can be said for many quantum physics entities. But, there are strong counter arguments to the claim that GID intelligent design is illusion.

In Herrmann (2002), I discuss, beginning on page 178, the notion of apparent design or illusion as stemming from a basic evolutionary explanation, where the claim is that the human brain evolved and displays an "evolution of conscientious." This presupposes that the natural-system behavior comes first. One then argues via the notion of the evolution of human consciousness and corresponding brain development, that human observations and the brain evolved in such a manner that the behavior patterns we observe within nature developed the mental machinery we now term as rational thinking. However, I show that this evolutionary argument fails for the notion of mathematical and other forms of abstraction and, hence, fails for the GID-model. The GGU-model is based entirely upon mathematical abstractions and abstract concepts.

Besides (I) and those mentioned in the referenced book, there are additional arguments that this interpretation is not illusion. For example, the logical generation of models that represent natural law statements and scientific theories that predict behavior is a recent development. The creative ability of the human brain to perform this activity is not restricted to specific regions or social environments. Indeed, there have been and there are today many individuals who engage in this creative activity. Individuals observe, and then describe or model physical regulations. Some of these are used to produce technical advancements.

Certain technical advancements are used to describe or model additional physical regulations. On the other hand, these regulations are used to produce technical advancements. It is self-evident that such a human aptitude is required prior to this process. This ability appears to be rather widespread in character and often a manifestation requires one "to be in the right place and at the right time." This ability is not attributable to a single source and this talent has been displayed over a rather historically short time period. A simple and rational explanation is that this mental ability is a pre-designed aspect of brain activity that displays itself in concert with technical advancements.

The actual indirect evidence for the higher-intelligence that probabilistically "produces" a natural-system or natural-system activities does not correspond exactly to any form of human intelligence. It cannot come from any form of material brain activity that predicts the observed natural-system patterns. This fact comes from the proof of the main theorem in the above-mentioned "Probability Models" paper. This higher-intelligence is NOT an "higher-extension" of any form of modeled human intelligence. No biological object within our universe can apply this general logic-system and obtain any of the stated results.

As pointed out in the first paragraph of my comparison article, all claimed direct or indirect RID evidence is also GID evidence. Finally, what follows is a detailed discussion of a remarkable fact - a fact that gives further evidence that the GID-model notion of intelligent design is not illusion.

Consider a known and well established set of physical laws, where each set is denote by N(j), and, for each fixed j, there is an i such that i ≠ j, N(i) ≠ N(j). Physical laws are described by ordinary languages, which can include diagrams. "Nature" neither displays such regulations in these forms nor states the physical characteristics that are needed to predict behavior. The N(j) are expressed in a language L(j). Let each N(j) be applied to an observed set of hypotheses X. Then for each j, using the human brain and a general logic-system, a science-community obtains the set of predictions Y(j). These predictions can be intuitively considered as contained in a "book." Of course, you will not find a logic-system explicitly displayed by "nature." Consider those members of Y(j) that are directly observable. It is a remarkable fact that, when properly restricted to behavior that appears only to be caused by the laws constituents, the observable predictions Y(j) can be verified. Such verification is a recent development. It first seems to begin with Galileo. Moreover, when the members of each Y(j) are compared, there are no contradictory statements. The vast majority of humanity use science-community predictions and they do not produce them via a logic-system. They "trust" the science-communities, which need only contain a single individual, where the community adheres to a scientific method and via deduction produce the predictions.

The sets of physical laws can be combined. They can be taken two at a time, three at a time, and so forth, and again predictions can be made. The same consistency should be maintained. This is not, however, the way it is done in practice.

(A') Usually, to obtain detailed descriptions for natural-system behavior based upon X, the entire combined collection of predictions {Y(j)} for X, as j varies, is considered. A collection of books is consulted and the predictions applied to the specific cases where the language corresponds.
Methods (A') and (A'') below are not only the usual approaches but are the exact way science-community results are combined when many individuals construct portions of our man-made universe or discuss physical predictions. Does the (A') approach follow the rules for logical deduction?

(B') NO, in general. Although each member of a set Y(j), can be considered as produced by a general logic-system and each separately yields rational predictions, the combined set {Y(i)} of the predictions need not be rationally produced. There are infinitely-many examples of this.

The fact is that it is not typical for the (A') or (A'') below to correspond to predictions that are rationally observed. There is a new significant result, in terms of general logic-systems, that substantiates the significance of (B') relative to intelligent design.

It has been established that, in general, to obtain rational combinations of all of deduced predictions {Y(j)} an immense amount of knowledge is required. [See General Logic-Systems Theorem 2.2.]

***(C') An individual would need to combine ALL the languages and all of the general rules of inference used by each science-community into one general rules of inference and apply the combined general logic-system to X, as well as all the other possible hypotheses, just to get a rational combined-theory and not simply apply the (A') method.***

Moreover, the (C') method yields the appropriate unification U for the logic-systems used by the science-communities to obtain each set Y(j). Even if each of the science-communities uses the same general rules of inference, say classical logic, then this does not mean that the (A') method is equivalent to the (C') method. Since much natural-system behavior comes about by application of numerous physical laws, then merely using members of Y(j) would not be sufficient to predict accurately much physical behavior. Hence, application of U is the appropriate approach. But, there is such a vast amount of knowledge required to do so, I know of no individual that can accomplish this task.

On page 73 of Herrmann (2002) is an example where the (A') method does not yield the same result as does the unification of the logic-systems. It is easy to describe the worst-case scenario where the (A') approach is not equivalent to the unification of all of the physical theories. Consider a language L and assume that two science-communities use classical logic. The first science-community uses its cosmology X(1) and predicts that our universe will continue to expand forever. The second science-community uses its cosmology X(2) and predicts that our universe will cease to expand at a future moment in observer time. Each science community shows that its cosmology is consistent by demonstrating that there are members from L that cannot be deduced from its cosmology. However, even though they both use classical logic when the (C') combination is considered, the combined cosmology {X(1), X(2)} will predict each member of L. This is what occurs when two theories yield contradictory statements. That is, the combination is logically inconsistent and cannot differentiate between fact or fiction.

(A'') In physical practice, the unification is not employed. A few Y(i) are selected based upon the assumed processes that appear to affect the behavior of a natural-system. These recognized combinations of physical laws are used to predict physical-behavior that is verified. This yields the actual Y' used by humankind. If these mental processes yield inconsistencies, then there is no meaningful correspondence between observations and a descriptive language. That is, no description could be trusted as specifying a physical fact since the negation of the description can also be rationally obtained.

Since for (A') or (A'') the unification is not employed and inconsistencies have not appeared, then this implies that the logic-systems that yield the Y(i) are rather special. One can conclude that "nature" or "something" has produced physical behavior in such a way that our formalizable modes of rational thought can describe laws that predict such behavior. And, significantly, this "something" has done so in such a manner that a unification of these laws is consistent and does not alter the predicted results. We are actually employing a small portion of this unification. And, it appears, as yet, no human being has obtained the necessary physical ability to apply the unified logic-system and deduce each member of Y(j) and other possible conclusions. The fact is that the combined sets of natural laws {N(i)} and predictions {Y(i)} we use for experiments, accepted observations and even our everyday activities has not led to inconsistent natural-system behavior. This is rather unusual.

Do our actual mental abilities correspond to our sensory experiences?

We have the habit of combining certain concepts and conceptual relations (propositions) so definitely with certain sensory experiences that we do not become conscious of the gulf - logically unbridgeable - which separates the world of sensory experiences from the world of concepts and propositions (Einstein, 1944, p. 287).

As noted above, one of the most significant concepts that does not come from sensory experiences is the ability to "abstract." That is, to find a common bases for a collection of mental or physical events. This ability is required when many physical laws and theories are obtained. It is strongly required when combinations of physical laws, theories or properties are considered. Although distinct physical laws, theories or properties tend to use distinct languages this is not why there exists a unification U of any such distinct collection. It is only through abstraction that any such unification exists. Further, the (abstract) concepts utilized are not defined material entities and they also are not related, in any manner, to sensory experience.

As mentioned, physical laws are not "stated by nature." They are human constructs that remarkably predict observed physical-behavior. Importantly, it is the consistency of U that yields the consistency of the Y' and not conversely. The languages we use to describe these laws do not appear as natural entities, but they are constructed by mankind. It is well after their construction that they are used to describe physical-behavior. I know of no adequate evolutionary mechanism that can explain this correlation between created language and its future application to predict logically observed physical-behavior.

Hence, due to special (A'') and the U properties, I cannot argue, using any proposed evolutionary mechanism, that the special design represented by the (A'') method and the unification U is illusion. The (A'') method serves a specific purpose shared only by one collection of known creatures. The purpose is that rather ordinary human beings can apply the predicted (A'') statements, correlate these to physical entities and build our man-made universe. It appears that our universe and human beings are designed in a special manner that maintains this correspondence between language, mental abilities and natural-system behavior. There is no other known biological entity that has, on its own, established this remarkable correspondence.

What has been presented here is the major piece of a vast mosaic that indirectly establishes that a "higher-intelligence" has purposefully designed "all there was, all there is and all there ever will be." Although these results satisfy all the physical science rules for indirect evidence and the conclusions cannot be eliminated, they can be ignored.

(G) Direct or Indirect Evidence.

Recall that "direct" means that the entities and relevant measures can be directly observed by human or recordable machine sensors, respectively. However, in general, there are various degrees as to what "direct" means. It first means "indirect" in that one can, but need not actually, make an observation. Relative to direct evidence not produced by a reliable machine, there are the usual problems that occur when only human observation is or was employed and the observation cannot be made again. This latter problem occurs with historical events or those "one-time" physical events that cannot or have not, as yet, been duplicated within a laboratory setting. The "first-reports" are the most reliable.

Documentary evidence has many degrees of reliability. The most significant first-reports are those attested to by the individual who has communicated the observations. The individual verifies that the statements are, indeed, those communicated. When such reports cannot be so verified they are, in general, less significant. In such cases, other verification methods may be acceptable. If an event being described cannot be repeated in a highly similar manner, then presuppositions are necessary. The most significant being that the communicated observation presents a factual description. Of course, there are numerous many reasons why an individual may not consider this a presupposition. On the other hand, other individuals do consider the belief in the factualness of a description as a presupposition.

Relative to documentary evidence one needs to have confidence in an individual's truthfulness and the actual unbiased ability to make a correct report of the events. Obviously, these traits do not guarantee that a report is accurate. The more first-reports of the same event that satisfy observer criteria yield additional strength to the observation being described as an observed "fact." First-reports are descriptions and the accuracy of such a report depends on applying a "language" that clearly conveys the observation to others. If not exactly duplicable by a machine, then the transmission of a report via translation into another language or, over long periods of time, and having it duplicated or restated by others can be rather problematic. In such cases, considerable documentary analysis may be necessary.

It has been shown that every natural law statement can be replaced by a general logic-system. But, in general usage, this representation is not necessary. What the replacement does, however, is to show that each physical regulation can be consider as intelligently designed.

Consider an hypothesis stated in a "scientific" language. If everything within the hypothesis is actually observable, then direct verification may be possible. Consider Galileo's law of fall, where Galileo specifically stated that his result contradicts Aristotle's. Indeed, Galileo gives one of the first, if not the first, description as to how his law can be (approximately) verified.

Taking his law of fall and using mathematical reasoning based upon a portion of the informal classical logic (i.e. ICL) the speed of a "falling" object and the distance it falls is predicted. The portion of ICL used can be replaced by a general logic-system, which yields the same prediction using his law. (Note that before and at this historical time such predictions were deduced by geometric means.) The prediction is verified by comparing observed results with the predicted results. Then one states that "the prediction holds" or is "verified." But, is there something else of significance being verified?

Basically, a general logic-system is being verified. It's the general logic-system that yields a prediction. The prediction is "rationally" obtained. For the GID-model, the prediction is intelligently designed. After trillions and trillions and . . . of applications, the ICL does directly verify predictions for natural law statements. (However, recall that there are infinitely many general rules of inference that produce the same results as those obtained via ICL.) Some scientists consider ICL as a "universal" logic-system although certain behavior within quantum measure theory does not directly correspond to some basic ICL rules. But, ICL is used to produce the underlying theory itself. Hence, even if some behavior is not following ICL patterns, the behavior is being controlled, in a certain manner, by ICL. This is the same type of control exhibited by the GGU-model and all known scientific cosmologies. In the GGU-model, the general logic-system being used to produce all GGU-model results is ICL.

Consider the photoelectric effect. Neither human nor machine sensors can observe the first four PA predictions. Hence, these PA conclusions cannot be verified directly. Any possible verification resulting from the natural law statement only indirectly verifies these predictions. Science-communities use additional hypotheses and, usually, portions of ICL to predict statements that are directly verified by human or machine sensors. This gives predicted and observable "evidence" that "indirectly verifies" the hypotheses. In this case, the claim is that photons behave in the described sense.

The GID-model evidence discussed above is not dependent upon one specific type of general logic-system. A logic-system such as PA can be included in the ICL logic-system. Moreover, any intelligent action associated with any general logic-system can, but need not, be interpreted as a restriction of an action that carries an higher-intelligence signature. Of course, for a specific physical hypothesis the assumption about ICL may not be correct in all cases. For two reasons, the hypotheses or even the logic employed need not be the correct. (A'') Other hypotheses, and ICL, may lead to the same predictions. (B'') Or, other or the same hypotheses, and a different general logic-system can lead to the same predictions.

There can be no absolute "scientific" knowledge that hypotheses, which cannot be observed, actually depict reality. This is especially due to (A'') since many of the modern natural law statements are only indirectly verifiable. (A'') forms the basis of many alternate theories. Importantly, for the GID-model interpretation, (B'') is rather significant. Although natural law statements and almost all scientific theories are based upon ICL, for a most perplexing aspect of physical-science, probabilistic behavior, the GID-model interpretation shows that an intelligent action, which is not characterized by ICL, guides and sustains the behavior. This intelligent action is a "higher" form of intelligence that cannot be "exactly" replicated by human actions.

(H) The Fundamental Universe-Generating Processes. For the general GGU-model mechanisms that indirectly imply that an higher-intelligence uses intelligently design processes to generate ANY universe, please see the article Fundamental Universe-Generating Processes.

Practical Applications of Logic-systems - the Practical Logic-systems. As applied to physical science, applications of logic-systems to deduction proceed as follows: A particular language is expressed in specific forms and these are used to generate the relations R(i) in RL(L). Usually, the hypotheses are the members of R(1). The set R(1) also includes all other auxiliary material such as the mathematical correspondences and procedures. These are part of the employed language. Further, what is not generally stated but rather "understood" is that a logic-system is expandable. This simply means that when deduction is applied it is relative to a particular logic-system and language and, hence, a continual deduction can occur relative to an expanded RI(L). Thus, at the conclusion of a set of derivations, the final logic-system is considered as the complete expanded logic-system that yields the entire collection of deductions. It is at this point that practical logic-systems are most often analyzed.

Within mathematical logic, the classical logic-system is based upon specific "forms" of expression. The forms are expressed symbolically and carry no additional content. The established results are then applied to create practical logic-systems, where the symbols within the forms are replaced by meaningful language elements. For example, if a form is P &Q => R, then a practical form is "If P = a photon and Q = an electron interact, then R = the photon will impart momentum to the electron." As shown in Herrmann, (2002), these elements can be images.

Special References.

All of the mathematical "proofs" and modeling results needed to justify the above remarks are contained in various books, published journal articles or they are stored at the or archives. They appear in the following stored versions and the references listed in each paper. Paper 1, Paper 2, Paper 3, Paper 4, Paper 5, Paper 6. These papers may also appear in the zip file, bookmath. The entire foundations for the mathematics is contained Herrmann, R. A. 1993 as listed below. It's best that you not concern yourself with the basic mathematics itself, due to its difficulty, until you grasp the intuitive basis for general intelligent design theory.

This e-mail address is for significant questions or comments only. E-mail is deleted based upon the subject heading. E-mail that has the subject heading GID and nothing more is the only e-mail considered. I. M. P. will determine whether an e-mail question or comment is significant enough to warrant an answer.


Einstein, A., 1944, Remarks on Russell's theory of knowledge, in, P. A. Schlipp (ed.) "The Philosophy of Bertrand Russell," Tudor, New York: 277-291.

Feynman, Richard, 1985. "QED The Strange Theory of Light and Matter," Princeton University Press, Princeton, NJ

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

Herrmann, Robert A., 1993, "The Theory of Ultralogics," book 3. (This book contains the last improvements and updates.) Or, the old version math/9903081 and math/9903082 The newest version is found at Book I of III, Book II of III, Book III of III

Herrmann, Robert A., 1986. D-world evidence, C. R. S. Quarterly 22(2):47-53

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