General Intelligent Design (GID) Evidence Not Classified as Restricted Intelligent Design (RID) Evidence And Other Significant Facts
The following is an in-depth article that does not include the specialized mathematics or the required theorems that establish the presented results.
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 this article, 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 natural-system. 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.) By personal choice, descriptions can also include the assumed physical objects that are not directly observable. 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. Descriptions are also termed as "events" since such descriptions should faithfully represent reality as reality is defined by science-communities.
Physical process operator (relation). A physical process operator (function, transformation, map, mapping, etc.) is equivalent to a physical process binary relation R. For a specific L, let the ordered pair (a,b) be any member of R. Reading left-to-right, the first member "a" (also called first coordinate) is an event and the second member "b" is an event that is associated with "a." There does NOT exist a member c in L, distinct from b, such that (a,c) is in R (i.e. there are no distinct members of R that have repeated first members). The first member varies over a "domain" of events. This relation represents an operator P. The operator P is applied to "a," written as P(a), and P(a) = b is the result. When the language L is restricted to what a science-community considers as perceived physical entities or characteristics, then P is a physical process operator.
General logic-system. This is 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 L. Let X denote a "set." As such, it can contain but one member of L and this member might be one of the coordinates a(i). Or, X can contain more than one member and various members of X can be coordinates of an n-tuple contained in some R(i). (Technically, X may contain no members.) There is a descriptive algorithm that employs RI(L) and generates a deduction, in a finite number of steps, from a set of hypotheses X contained in L. This generalizes the notion of a formal proof.
Finite Consequence Operator. In this article, such an operator is applied to a specific 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. Unless specifically modified, the term "operator" means a finite consequence operator.
The Standard General Intelligent Design (GID) Interpretation. The intelligent design conclusions presented in this article are obtained by interpreting mathematical statements. "H" intelligently designs different types of operators that produce or alter natural-system behavior, or produce or alter natural-system characteristics. (The H denotes the mental processes a mathematician uses to construct mathematical theories and the different types of operators used in the GGU-model. It is extended to a higher-intelligence.) For consequence operators, the descriptions obtained by applying each operator to a specific description are intelligently designed since the methods used to obtain the descriptions satisfy all of the rules and axioms that characterize standard scientific deduction.
Observed. Perceived. In this article the term "observed" means detected by means of human sensory impressions. Depending upon a what is stated, observed can also include human sensory observations of diagrams and machine behavior.
What is "perceived" is science-community defined and includes what can be observed as well as other imagined (hence, mental) constructs. In what follows, when the term perceived is used, one may substitute the more conservative term observed.
Each standard natural law and scientific theory, as represented by an operator C, displays a higher-intelligence ID-signature. This occurs when the standard characteristics displayed by C are extended to those that characterize the, automatically obtained, "extension" *C. This *C operator's ID-signature indicates that it is controlled by a higher-intelligence. For a description X, the mathematics automatically produces *X. The description obtained when C is applied to X, as denoted by C(X), is contained in *C(*X) and, usually, there is more descriptive content in *C(*X) than in C(X). This additional content has significant uses.
The basic GGU-model utilizes event sequences . . . ,F(k), . . . ,F(j), . . . , where usually k < j. For our specific universe, this article is mainly concerned with the processes that produce or alter the symbolized event F(k) and that yield the "next event" in the sequence, as symbolized by F(k + 1), and that give evidence that all such alterations are intelligently designed. (Technically, this sequence is considered as a collection of descriptions. (It has a special name.) Or, since each description corresponds to a physical event, the sequence can be considered as a sequence of physical events. These two sequences are considered as equivalent when the unqualified term "event" is used.)
It's important to realize that the direct evidence for intelligent design and indirect evidence for design by a 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 in the sense that the evidence only depends upon the rationally obtained physical regulations and accepted scientific theories.
The remainder of this article is composed of the following sections, (A) Natural Laws, (B) Scientific Theories, (C) General Applications of Natural Law Statements and Scientific Theories, (D) More about Evidence, (E) Illusion, (F) Direct or Indirect Evidence, (G) (A link to) The Fundamental Universe-Generating Processes.
(A) Natural Laws. How does the dictionary define a law of nature? 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 natural 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 a hypothesis (b). As demonstrated below, a natural law statement (b) is intelligently designed so that rational processes lead to (a) and to data verification. Hypothesized natural law statements that do not allow one to test the required unvarying uniformity may or may not be accepted as natural laws. Even if testing is possible over a specific interval of observer time, there is no scientific way that absolutely determines that the natural law will remain unvarying and uniform during a "future" time period. Moreover, some science-communities may require a natural law statement to be tested in a specific way. It is not relevant to this article how one obtains verifying natural law data and whether data exist prior to or after the natural law statement is proposed.
(I) The existence of the collection of all described natural law statements indicates that our universe is designed in a special manner. This is, human intelligence can devise natural law statements using languages and other devices that mimic processes that produce or alter natural-system behavior, or produce or alter natural-system characteristics.
(II) (a) A natural law statement is intelligently design in such a manner that basic logical processes can be applied. In order to verify experimental data or predict experimental data, a natural 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 directly determine physical behavior without requiring additional assumptions, then such data need not be modeled by GID. Such data would 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 natural-system, or the production of or alterations in a natural-system's characteristics produced by application of a natural 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. Hence, the structural or behavioral patterns produced are intelligently designed. (b) In the absence of any presently known natural law statement, the production of or alterations in the behavior of a natural-system, or the production of or alterations in a natural-system's characteristics is modeled by the underlying *S operator. There are examples where describable mental processes applied to descriptions for natural-system behavior falsify the GID-model. (See page 73, of Herrmann (2002).)
The term "natural 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 "natural law" refers explicitly to a physical regulation and possibly other accepted types of "natural laws" that fit the physical circumstances.
Although a (humanly) comprehensible natural law starts as a "statement" that can be logically applied more than once to physical situations, this does not mean that such an 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. (As show below, technically, a natural law statement also yields a theory and its own operator.)
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 natural law statements can include descriptions for how we comprehend the combining of various "simple" levels of the universe-wide frozen-frames (also called "slices.")
The history of how natural law statements are obtained clearly indicates that all have developed through human mental procedures that 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 a 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 natural 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 a hypothesized natural law statement must satisfy the data. Establishing this correlation 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 natural law statement must satisfy the requirements for a logic-system if that natural 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 natural 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 being investigated.
***As examples show, statement (III)(a) is established by considering the application of each natural law statement to members X of a language L and applying the required logic-system rules. This yields a collection of statements Y that includes the data being tested. As the X is varied over all collections taken from L, the results obtained define an operator. Hence, this intelligently designed operator N is a model for application of the natural law statement to the physical world. When applied, N has an ID-signature as well. This operator produces another operator based upon a science-community defined collection of perceived physical entities or characteristics. These are the "behavior-signatures" as defined in this paper.
In more detail, contained in L is a defined set P' of descriptions for what a science-community considers as perceived. A designed, but slightly modified, N (as discussed below) is applied to a set of descriptions X contained in P' and this determines a set P(X) of descriptions that correspond to members of the set P'. It has been shown that the operator N' generated by the collection {P(X)} eliminates all extraneous material, if any. Depending upon how the natural law is expressed, the natural law statement is also eliminated. The set {P(X)} immediately generates an intelligently designed physical process operator. Hence, for the GID-model, the application of any natural law statement (b) generates perceived events. Each step in the procedure yields an ID-signature. Thus, the structural or behavioral patterns produced are also intelligently designed. But, the physical process operator is intelligently designed only when it is determine by a general logic-system.
Each of the operators used to produce the physical process relation can be extended so that the intelligence being displayed is a restriction of a higher-intelligence. However, as would be expected, there is no converse to this process. The physical process operator does not directly yield a natural law statement. This is demonstrated by the box-law example (discussed at the next link) that, without further analysis, generates an operator that does not correspond to the observed data. Physical science continues in its efforts to predict each recognized cause and effect physical process relation from hypothesized entities or behavior. ***
For a falsifying example and how more detailed observations lead to an intelligently designed natural law operator, see empirical.htm, where the "box-law" is examined.)
The box-law can be generalized, not necessarily over the objects used, but over repeated time-dependent applications. This box-law example demonstrates specifically that sensory observations can be made that yield 8 relations, P(X), as X varies over all of the language used. Each relation taken separately is a logic-system. But, there are two relations that when combined do not generate a logic-system that yields the data. This is due to the logic-system algorithm employed to generate an operator. (Below is a link that leads to an article that discusses this algorithm in more detail.) Indeed, for this example, there is no logic-system that yields the original two relations. Thus, these unmodified observations yield one-way to falsify the contention that there is a logic-system that yields the combined behavior. This contradicts a GID-model basic characteristic for a natural law operator.
Each individual observation is still intelligently designed, where intelligence is required to follow the simple rules. These rules allow for construction of the rules of inference and require a simple application of the basic logic-system algorithm. This does not preclude there being some sort of "law" that does predict these 8 outcomes. But, such a law would not follow the most basic aspects associated with human deductive thought. To obtain a new box-law that can be used within physical theories, further analysis is necessary, where an unobserved hypothesis is adjoined to the observations.
It is a fact that there are many relations between descriptions that do not satisfy finite consequence operator axioms. If any natural-system followed one of these before-and-after relations as operational presented and there is no other logic-system basis for the descriptions, then as a combined collection of observations they cannot be included within any other scientific-community's general logic-system. For if they were included, then this leads immediately to a contradiction within the combined logic-system. They can be used separately. But, this box-law example shows how additional human mental processes can lead from such data to a "physical" box-law that does satisfy operator properties. On the other hand, if a natural law statement is included as part of a science-community's logic-system and the law is verified by laboratory data, then no behavior that represents the data will contradict the general logic-system.
Consider a collection of natural law statements, each obtained from human observation, which are used to build our man-made universe. There is a certain amount of intelligence needed to conclude that a set of data does correlate to a specific description. But, the amount of intelligence needed to insure a non-contradictory coalescing of the entire collection of empirically verified natural law statements and natural law operators is especially great. Thus, from the GID-model viewpoint, the fact that each operator N has an intelligent design signature pales when compared to the intelligence required to apply to the entire universe the unified logic-system generated by all of the accepted natural law statements.
How does "nature" actually reveal uniform physical processes? I have never seen a stone or any physical object where "nature" has carved into the object numbers that denote its mass. I have never seen a region in space where the stars or any objects, in any symbolic form, state the area, or volume, density or the like for the region. I have never seen a carving produced by pure natural means that relates mass and energy. I have never seen a natural-system that has the exact form of various objects studied in Euclidian geometry. Of course, "we" build measuring instruments that yield observed numerical values. For example, consider an ammeter and voltmeter as measuring voltage applied and the current for a resistive material that is kept at constant temperature and pressure. The voltage is varied 10 times and 10 different ammeter values are observed. But, using these instrument values there is no indication, within the physical world exterior to our brains, that the voltages and measured currents are related by the same constant of proportionality. Ohm was the first to make such a declaration. All that "nature" reveals is a physical process relation that might be obtained from a natural law operator.
What is actually accepted as a natural law statement depends upon the science-community. Definition (a) is still applied but a science-community might allow perceived and not observed entities or processes to be included. 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 satisfied the data. Technically, this effect is not observable but this numerical result is perceivable. Notice that deduction is a required aspect for determining whether a statement is a candidate for been termed a natural 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 yielding observable data since I know of no instance where the ejection of an electron has been observed. This second statement uses the perceived notion.
(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)mv^2, where v is the electron's relative speed. An equation hf = (1/2)mv^2 + 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 is observable and the equation 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 natural law statement.
Suppose the 1901 Max Planck general logic-system that uses "electromagnetic energy elements" is applied and this equation is re-interpreted using a different physical language. By intelligent finite choice, let h be Planck's constant and then let hf be imagined as a single "bundle" of energy, 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 natural 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. Let p = light of a specific frequency falls on a photoelectric surface. Then consider the following, PA, tentative natural law statement, where for many scientists, the PA description is perceivable.
(p,(a) = light energy (a photon) is absorbed by an electron)
(p,(b) = a photon is essentially absorbed instantaneously by an electron)
(p,(c) = all of the photon is absorbed by a single electron)
(p,(d) = a portion of the absorbed energy is used to free the electron from the surface)
(p,(e) = 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 five ordered pairs form a "general rules of inference." To use this general rules of inference an algorithm is applied, where the first step is to consider the one hypothesis p. Then these five characteristics are predicted.
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 natural law operator. The obtained physical process relation satisfies all of the data and the natural law statement is certainly intelligently designed to fit the data, assuming that you believe that Einstein was intelligent. 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 natural law statement is obtain by writing the (cause) p statement. Then the rules for deduction yield effects statement (a) - (e).
The GID-model states as a hypothesis that duplicating such physical behavior via general logic-systems is an ID-signature for an intelligent ultimate cause.
N(1) Although, generally, science-communities do not use the PA form for a natural law statement, all cause and effect statements can be expressed this way. For example, using another form of the photoelectric effect, (p, an electron is ejected). The PA statement can be repeated for each photon frequency. Such an extended PA can be adjoined to whatever general logical-system is being used. Such PA forms yield direct evidence that natural laws in either (b) or (a) form are intelligently design on, at least, the human level of intelligence.
N(2) The binary relation PA is not the customary way a natural law statement is presented, when propositional (i.e. customary) logic is employed. General logic-systems allow one to write a set of statements, the hypotheses, as separated from the rules of inference. These statements are called premises or hypotheses and correspond to the (b) definition. For the photoelectric effect, such a set can contain the statement "If p, then (a) and (b) and (c) and (d) and (e)." Using one rule of inference for the propositional logic, "modus ponens" (the rule of detachment), yields "(a) and (b) and (c) and (d) and (e)." The logical-axioms used for the propositional logic-system then yield (a), (b), (c), (d), (e) as individual statements that are now deduced from p. Thus PA can be considered as a condensed form of aspects of propositional deduction. Once again the deductions can be specifically written and this form also yields direct evidence for intelligent design. (For the example in N(1), "If p, then an electron is ejected.")
N(3) One can also allow the natural law statement to be stated by five "if" and "then" statements "if p, then (a)" etc. Then from "p" each (a), (b), (c), (d), (e) is deduced. These simple results show how distinct general logic-systems yield the same conclusions (consequences).
But, such "laws" do not appear in these forms within nature. These representations for a physical law are used so that humankind can comprehended the law. They "represent" a physical relation between assumed physical entities that we may not be able to comprehend in any other way. This is why GID is called a model. We have been accorded the mental capacity to recognize these relations and represent them rationally.
For the photoelectric effect, the observed results include the movements of mechanical devices. However, as indicated, the above three approaches can be further supplemented with an additional scientific theory and the mechanically obtained values are predicted. The process of hypothesizing unobserved behavior, such as represented by the above three cases, is a major aspect of modern scientific theories. This is a viable approach. In such a case, descriptions and physical process relations are extended to include this approach. Let any of the above approaches be used. Then p and statements (a), (b), (c), (d) yield physical behavior that is only "indirectly" verified. But there is direct evidence that the natural law statement and its results are intelligently designed and the structural and behavioral patterns it produces are intelligently designed. Notice that Quantum Electrodynamics is based upon the acceptance of the "law" (p,light energy (a photon) is absorbed by an electron) where the electron can be replaced by other entities.
N(4) The scientific method allows a natural law statement to be expressed in yet other ways. Induction, as practiced by science-communities, requires the notion of "generalization." Generalization is an accepted deductive process (Cohen and Negal p. 175). To include generalization, an extended general logic-system is employed to generate the natural law operator. For this example, the domain of application can be considered as a large collection of photons represented by their frequencies. Then induction (generalization) demands a different form. For example, consider (1). For each photon frequency x, if (P'(x)) an absorbed photon with frequency x has the energy measure hf , then (Q(x)) an ejected electron with mass m has measured speed v and these values satisfy the equation hf = (1/2)mv^2 + hf_0. Generalization adds the words "For each" to the statement. This is the induction step. This generalized physical behavior is based upon a limited number of such photon experiments. The statement (1) is an accepted natural law statement. Also the generalization process and the customary logic-system includes the process of substituting a constant name for each specific x. In this case, this constant name is taken as the frequency numerical f.
N(5) The following easily defined relation incorporates the notion of generalization for a general rules of inference. Consider an appropriate set of frequencies as numerically represented by f, where f appears in the language being used. Usually such a set is rather large. For a given photoelectric substance, hf_0 is a constant. Then conceptually consider a modified set of 3-tuples R, where R = {((1),(2),(3))}. But, statement (1) is modified to read "If P'(f), then Q(f)," (2) reads P'(f) and (3) reads Q(f) and f varies over the set of selected values. Note that what I have done is to apply my "intelligence" to construct conceptually this portion of the general rules of inference. (This, of course, is not the only general rules of inference that uses the natural law statement in (1) and predicts Q(f).) Generalization allows R to be replaced with one statement "For each f, if P'(f) then Q(f)." But for this statement to be applied to any physical realm, the f must vary over some defined collection. Hence, rule R is equivalent to logical generalization when applied. Usually, there is an axiom for the predicate logic that, via deduction, yields the statement "If P'(c), then Q(c)," where "c" is a language constant, from "For each f, if P'(f) then Q(f)." Then the rules of inference contain a modified R, where each frequency is denoted by a distinct c. Hence, from the hypothesis P'(c), the Q(c) is deduced. When a science-community uses induction and classical logic to intelligently express a natural law statement, this is how one arrives at the prediction Q(c) from each P'(c).
Let a basic natural law statement be represented by any of the forms N(1), . . . , N(5). For various applications, almost all individuals who construct physical theories utilize the classical rules of inference. These theories use appropriate natural law statements and general rules of inference that correspond to that used by a theory constructor. Modus ponens as well as generalization are exceptionally significant when classical logic is applied.
Although what comes next can be separated into distinct steps, usually, the natural law statement relates various physical entities or characteristics. For a given general logic-system and language, a specific theory is all that one can deduce from a specific set of hypotheses taken from the language. A basic definition of a natural law theory uses the natural law statement as a set of hypotheses. The theory may use auxiliary statements as part of the science-communities general logic-system, and the logic-system "predicts" how the natural law statement affects physical behavior where the natural law statement is in hypothesis form X. That is, the theory is obtained when a general logical-system is applied to the natural law statement X. (This is the narrow definition and the one used in mathematical logic.)
A natural law operator is obtained as follows: The natural statement is either part of the general logic-system as a physical axiom or is in a PA form. Consider each finite subset Z of the language being used to express the natural law statement X. Consider the set Z as the first coordinate of the natural law operator's binary relation. Let Y be all the members of L that can be deduced from Z. The rules for deduction state that it is always the case that Z is contained in Y. Notice that the language is arbitrary. (This definition is the broadest one used for a scientific theory.)
A natural law theory can be obtained and expressed in a modified way. The natural law statement can be expressed as a physical axiom X that is then part of the general logic-system. Or, it can be presented in the PA form. Then the natural law theory is obtained from the natural law operator by applying the operator to the empty set of hypotheses, Also the natural law theory is obtained by applying the natural law operator to the natural law statement in hypothesis form X.
In slightly more detail, to obtain the natural law (binary) operator, the Z is the first coordinate and the Y is the second. That is, (Z,Y) is a member of the operator N and notationally one writes Y = N(Z). This process is repeated for all finite subsets of L. Considerable intelligence is needed to obtain the Y. (Actually, the term finite need not be used, but the rules for deduction allow this restriction. For any nonempty Z, if a member y of L is deduced from Z, then there is a finite subset of Z from which y is deduced. So, using only finite sets yields the same results as not using them.) Notice that the language L and the general logic-system used by a specific science-community often contains a large set of additional axioms distinct from X. For example, mathematical axioms and procedures. All of these additional hypotheses and what is deduced from them are members of N(Z).
The next step is application of the "realism process" to each N(X). For the GID-model interpretation, this process is intelligently designed and requires intelligence to applied. It removes the collection X from each N(X). This process yields a "realism operator" R. But, R(X) may still contain many extraneous deductions. From this, an intelligently designed collection of behavior-signatures that predicts a science-community's perceived events is obtained. This eliminates all of the extraneous deductions. (How the behavior-signatures are formally defined appears in this article.) The resulting collection of behavior-signatures produces another operator. One more application of the realism process generates the physical process operator for perceived events.
Technically, in mathematical logic, the general rules of inference can have infinitely many members. Trained logicians locate the specific members of a general rules of inference since the rules have explicit forms. This algorithm requires mental activity that is summarized in the file algorithm . This mental activity verifies that the natural law operator is intelligently designed as is the set of behavior-signatures. It is self-evident that within many science-communities a general logic-system includes all of the predicted and perceived measurements. Significantly, the GGU-model shows that all physical events that are either the result of statistical models or perturbations are produced by intelligently designed regulations and procedures that follow patterns directed by an interpreted higher-intelligence.
There are hundreds of illustrations that describe how the laboratory "data-to-assumed-natural-law-statement" process requires a general logic-system. We don't observe a force separate from its effects. We can use the effects to measure it, whatever it is. We see a rocket burning fuel. Then we're told that it's burning the fuel at a constant rate. The rocket appears to be "picking up speed" as it rises into the morning sky. This "picking up speed" can be measured. We're told that the term for this is that the rocket is accelerating. In terms of the measures, the "force is equal to the rocket's mass, at the moment of observation, (times) its acceleration." But, we do not observe the "force" as an actual physical object, only its effects. Note that if you were to computer-animate this rocket's behavior, you would need to translate the F = ma, as m varies, into what would actually be observed. This would be the last "intelligently designed" step in applying a natural law statement to a specific situation. These computer descriptions represent observed effects. Of course, in a laboratory setting, the observed effects may only be the data being displayed.
The above method used to describe a natural law operator that governs the photoelectric effect can be applied to every accepted natural law statement. From the GID-model interpretation, this yields (II)a. The original box-law data illustrates the (II)b.
***Although natural law behavior-signatures are evidence for GID, it is the use of such additional notions as "energy, force, mass, virtual process, virtual particles" and others that do not correspond to actual observable objects that imply that constructed natural law operators may be but modeling "something" else going on within our natural environment that preserves the properties of intelligent design.***
General logic-systems are more fundamental than the generated operators since general logic-systems give the details of how natural law statements affect a natural-system's behavior. Thus, the actual natural law statements require intelligence to determine and express. An H operator models this, in general, within the GID-model interpretation. What this demonstrates, is that, when (II)(a) and (III)(a) are taken together, the production of or alternations in natural-system behavior, or production of or alterations in a natural-system's characteristics produced by accepted physical regulations occurs because "something" has produced regulations through procedures that, at the least, model human general logic-systems. From this viewpoint, this verifies the De Broglie conjecture that "Our material universe has something in common with the workings of the human mind." In particular, it has a rational structure as modeled by the GID-model and intelligent agency. Significantly, all of the different operators discussed here have *-extensions as do the (A) - (E) steps . Hence, intelligent actions applied by a biological entity can be interpreted as a restrictions of those actions applied by a higher-intelligence.
(For a further discussion of the notions of "direct" and "indirect evidence," see (F) near the end of this article.)
***In summary, all of the different types of operators and general rules of inference used to construct the GGU-model are intelligently designed. For physical regulations, mental processes are used to obtain a natural law statement. Applications of customary logic yield the natural law operator. Next, a defined and simple one step realism process yields a realism operator. This operator yields a collection of behavior-signatures, which forms a general rules of inference. This set of rules defines an operator and application of the realism process produces a physical process operator. It is the physical process operator that duplicates observed or unobserved but assumed physical behavior.
Using the mathematical "composition" notion and operator-language, the natural law operator is composed with a realism operator, then with an operator formed from the behavior-signatures (the theory-signature operator), and, finally, another realism operator. This composition yields a single physical process operator. Generally, the physical process operator does not satisfy all consequence operator axioms. However, it is obtained from two (finite consequence) operators. Properties of these operators, as coupled with the intelligently designed realism operator, yield the physical process operator's ID-signature. This interpreted signature indicates that each application of the physical process operator is an intelligent action. And, the patterns produced are intelligently designed. These conclusions yield strong evidence for the GID-model interpretation. They are not RID conclusions.
What all this means for the GID-model interpretation, since all of the mental steps can be described, is that (I) is direct evidence for intelligent design. Further, (II)(a) coupled with (III)(a) is direct evidence for intelligent designed. Type (III)(a) evidence is not RID evidence. Type (III)(b) may satisfy RID. And, (I), (II)(a), (III)(a) and (b) also indirectly verify the higher-intelligence hypothesis.***
(B) Scientific Theories. For this article, a scientific theory is considered in the broadest sense. It uses a set of natural laws as hypotheses or other working hypotheses, where the working hypotheses need not be considered as uncontested natural law. It is not the purpose of this article to discuss the science-community conditions a hypothesis needs to satisfy before it is declared a natural 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.
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 natural 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 S_N as they appear in some of my older publications do not use the PA form but employ natural law statements in hypothesis form. For a specific purpose, the S_N are used to define the operator S_N^V. This operator appears in Herrmann (2002) and elsewhere. However, it still generates extraneous results and has been replaced by the a set of behavior-signatures that yield the theory-signature T. The T operator obtained still predicts the same natural-system descriptions. Physically, in this case, this T operator models correlations between physical descriptions or characteristics and, hence, descriptions or characteristics that lead to verification of basic natural law statements or working hypotheses, which are not now stated specifically.
As with natural law operators, a realism process applied to the theory-signature T yields a physical process operator P. The P-operator can be substituted for the S_N operator. The natural law statements, working hypotheses or additional complexities employed to construct the scientific theory are no longer part of the predicted results. Of course, this is how "nature" appears to do it. As demonstrated in this article, in modern scientific discourse, what is defined as a natural 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 natural 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 natural 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 by from the theory of gravity?
***Portions of how a physical process operator is obtained from a scientific theory need to be slightly detailed and are worth repeating. From the scientific theory operator S_N, the realism relation is applied. From this, the theory-signature general rules of inference yield the theory-signature operator which, after the realism relation is applied, duplicates the physical process operator. (See this URL, previously mentioned for the definition of the theory-signature general rules of inference.) Depending upon what one accepts as observable, a great deal more can be eliminated such as so-called virtual objects. These intelligently designed processes reveal an ID-signature that characterizes intelligent actions. In general, for any theory that predicts probabilistic behavior, the GID-model displays a second ID-signature. This second intelligent action signature is represented by an intelligently designed pure ultralogic. This ultralogic guides the physical behavior being depicted in that it controls the actual occurrence of a physical event. It does this is such a manner that the probabilistic character of an event's occurrence is preserved. (See this URL for the stored version of the paper that establishes this.)
These scientific theory ID-signatures indicate that when the operators are applied they reveal intelligent actions. Hence, whatever patterns are produced are intelligently designed. This is strong evidence for the GID-model interpretation, which is not RID evidence.***
I point out that if there is neither a production of nor an alteration in a natural-system, then the theory-signature indicates this. Mathematically, in the case that operator S_N is utilized, the set of all natural law statements in our general language L, when viewed from the "higher" language *L, contains "ultranatural" law *statements. Only a very few of these *statements have content that is comprehensible by any biological entity within our universe. Moreover, when the set of all events are viewed from *L, ultranatural events are obtained, which behave like a physical events, but cannot be described entirely by members of L. However, some descriptions for ultranatural events have comprehensible content.
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 usually 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 General Logic-systems and Consequence Operators that each operator is equivalent to a general logic-system. Hence, there is a specific physical process operator that corresponds to each informal scientific theory and yields an intelligent action produced by an intelligently designed general logic-system. I point out that general logic-systems and these operators are not based upon the notion of logical "values" such as two-valued models for "True or False" or any other valuation notation.
(C) General Applications of Natural 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 operator or equivalent general logic-system unification for any set of operators or equivalent general logic-systems, respectively. This result shows that any application, finite or infinite, of natural law statements and scientific theories is equivalent to a single unifying operator or equivalent general logic-system. For the GID-model, this unification is intelligently designed, at least, on the level of human forms of intelligence. (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 . . . Then there is the example discussed in the chance.pdf file in chance.zip.) Statements that describe emergent properties are also included within this unification. (Physical entities using informational ultrafast subparticles with correlating ultranatural events are compelled to display this properties.)
There may be those who reject any natural 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.
(IV) The 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|. Considered as an operator, the realism operator is applied. This yields an operator P| that is applied at each X|. Substituting X for X| yields a physical process operator P. The operator P is a type of universal physical process operator. Relative to restricted intelligent design, RID, upon restricting the event sequence to a specific natural-system M, the intelligently designed physical process operator P(M) can yield physical events that correspond to RID physical events.
(D) More about Evidence. It is fact that (A) statements (I), and (II)(a) coupled with (III)(a) and (b), (B) scientific theories as applied to the production of or alterations in natural-systems and (C) any finite combination of these, as well as (IV) imply that our universe is intelligently designed. Direct evidence for this is that, technically, the actual general rules of inference that produce such statements as (A), without III (b), (B), (C), and (IV) can be displayed using a language L. For (B), there are exceptions. Certain perturbations not predicted by a physical theory and individual event behavior that follows a probabilistic model are exceptions. Perturbations and probabilistic behavior are intelligently designed, but intelligent agency is only implied indirectly. [See Probability Models.]
Does all of this 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? This is similar to quantum theory or early history cosmologies where physical objects or processes are accepted based only upon deduction and indirect evidence. But, for the GID-model interpretation, designed ultranatural laws that yield ultranatural theories predict perturbations. These correspond to "pure" ultralogic operators. Further, pure ultralogic operators generate the individual probabilistically controlled events. The ID-signatures for these pure ultralogic operators is that of a higher-intelligence and only a higher-intelligence. Thus, by similar rational choice, one can accept, via indirect evidence, that a higher-intelligence produces and controls all there was, all there is and all there ever will be.
(E) Illusion. The existence of a higher-intelligence is a hypothesis that has a vast amount of indirect evidence. One can accept this hypothesis based only upon this rationally obtained fact. Further, its predictive power and relative simplicity is an additional reason for its acceptance. Within particle physics, the hypothesis of photon absorption is accepted for the exact same reasons. 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. Although this claim cannot be scientifically verified and, hence, it can simply be ignored, there are strong counter arguments to this claim.
In Herrmann (2002), I discuss, beginning on page 178, the notion of apparent design or illusion as stemming from a basic evolutionary explanation based upon how the human brain is claimed to have evolved and 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 interpretation of the GGU-model. Whether the maximum or minimum scenarios are employed, 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 perceive, and then describe or model physical regulations. Some of these are used to produce technical advancements. Certain of these technical advancements are used to describe or model additional physical regulations. Some of these regulations are used for technical advancements and so on. 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 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 "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 1000 different science-communities, and 1000 books that summarize, for each set of hypotheses X, all of the predicted results Y(j) that should be expected, as j varies from 1 to 1000. [These books are specifically presenting the results generated by a physical process operator.] I note that a science-community can be composed of one or more individuals and the community may concentrate only upon a very small portion of the area identified as "rational science." Many of the predictions Y(j), as j varies, are different since each community concentrates upon specific scientific hypotheses and specific and often narrow deductive conclusions. If X is equivalent to Y(j), then this simply means that the j science-community predicts no different behavior.
(A') Usually, to obtain detailed descriptions for natural-system behavior based upon X, the entire combined collection of book summaries Y(j) for X, as j varies from 1 to 1000, is considered. This is not only the usual approach but is the exact way such 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, since there are potentially infinitely-many general logic-systems that when method (A') is applied to two or more members of each of these general logic-systems the results DO NOT correspond to rational predictions.
The fact is that for many general logic-systems it is not typical for the (A') approach to correspond to rational predictions. Most physical-science communities do not know this fact. But, now, 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 to obtain rational combinations of all of the 1000 science-community deductions an immense amount of knowledge is required. [See General Logic-Systems.]
***(C') An individual would need to combine 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 leads to the least amount of unnecessary deduction. The (C') method yields the appropriate unification U for the logic-systems used by the 1000 science-communities. Even if each of the 1000 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.
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 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.
In practice, the unification does not alter any of the book summaries Y(j). However, there may be new results deduced that are not members of any Y(j). As shown above and on page 73 of Herrmann (2002), such general logic-system behavior is of a special type. More significantly is the fact that almost no human being has the necessary mental ability to apply the unified logic-system and deduce each of the 1000 book summaries. And, a unification is independent from such (A') properties. Sensory experiences need not lead to significant concepts and conceptual relations.
We have the habit of combining certain concepts and conceptual relations (propositions) so definitely with certain sensory experiences that we do not become conscious if 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.
Hence, due to these special (A') and U properties, I cannot argue, using the evolutionary notion of apparent design, that the special design represented by the (A') method and the unification U is illusion. This is especially so since the (A') method serves a specific purpose. The purpose is that rather ordinary human beings can apply results summarized by the (A') method to build our man-made universe. It appears that our universe and human beings are designed in, yet another, special manner to maintain this special coalescing for natural-system behavior.
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.
Most scientifically described cosmologies and the GGU-model cosmogony, are not constructed from explicit or hidden theological assumptions. The fact is, however, that they can usually be theologically interpreted after their construction. One such interpretation for the GID-model rationally satisfies many Biblical statements. We observe the results of one of His "invisible attributes," His higher-intelligence and His creationary "power" (Romans 1:20). Since we are "made in His image," our mental abilities are but an infinitesimal portion of His. He has given these to us for a specific purpose. We are to have "dominion over . . . the earth" (Genesis 1:26) and are to "subdue it" (Genesis 1:28). This corresponds to statement (I) for both natural laws and scientific theories.
(F) Direct or Indirect Evidence. 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 a 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. Recall that "direct" means that the entities and relevant measures can be directly observed by human and machine sensors respectively. 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 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 billions 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 by H 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 a 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.
(G) The Fundamental Universe-Generating Processes.
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 arXiv.org archives. However, I won't list all of these references in this article. Most of them appear in the zip file, bookmath and the necessary additional links are listed in prior portions of this article. It's best that you not concern yourself with the actual mathematics itself, due to its difficulty, until you grasp the intuitive basis for general intelligent design theory.
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.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 has the last improvements.) Or, arxiv:math/9903081 and arxiv:math/9903082
Herrmann, Robert A., 1986. D-world evidence, C. R. S. Quarterly 22(2):47-53
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