Individuals who have either
had personal religious experiences or argue for the scientific acceptance
of such a higher intelligence certainly do not consider their contributions
as irrational. As exemplified by the above quotations, many in the philosophic
and scientific world do consider as irrational the assumption that such
an higher intelligence needs to be supernatural in character and this
has inspired their attempts at rationalizing religious experiences,
or ignoring creation-science models and evidence for the acceptance
of such models.
If it could be demonstrated
scientifically that assuming the existence of a supernatural higher
intelligence is rational in character, then this would destroy, utterly
and completely, the philosophical foundations for the philosophy of
rationalism as it is applied to religious experiences and thought. It
would eliminate the basic philosophical argument against the existence
of a supernatural deity. Atheism would have lost its most profound intellectual
foundation. Further, the necessary conclusions of information theory
applied to the DNA molecule would be upheld and, indeed, the basic foundation
of creation-science could no longer be rejected on scientific grounds.
But what would constitute a scientific demonstration that it is rational
to postulate the existence of a supernatural higher intelligence?
Timothy Ferris (1979, p.
157) writes: "Scientific theories must be logical. They must be
expressible in terms of mathematics, the most rigorous logical system
known." Ferris overstates his conclusion when he writes that this
"must" be the case. Actually, the modern scientific approach
to theory is rather more vague on the subject of rationality. What can
be said is that if a theory can be closely associated with a mathematical
structure, then it would follow the most rigorous logical system known.
No attempt will be made
in this paper to give a nearly complete definition of human intelligence.
But one of the crowning achievements of humanity has been the construction
of a symbolic language as a substitute for oral expressions. Modern
computer technology also allows for visual or audio impressions that
are captured by mechanical devices to be translated into a symbolic
language that can later reproduce, with great clarity, the original
visual or audio content. Thus, for our purposes, human intelligence
will include the ability to express thoughts and perceptions in a symbolic
language comprehensible by others and, further, to present written arguments
that follow patterns that correspond logically to procedures accepted
by the majority of humanity.
Throughout this discussion,
it will only be assumed that a symbolic language corresponds to a portion
of human oral expression, human perception and mental impression. A
symbolic language L is constructed intuitively from two or more symbols
by juxtaposition and yields geometric configurations called symbol strings
(i.e. strings of symbols). For every natural number n, there theoretically
exists more than n distinct symbol strings by this process. Similar
symbol strings are recognized by human perception to be equivalent.
In 1930, Tarski characterized
and abstracted mathematically those general procedures that correspond
to the most significant human mental processes that, for finite collects
of such symbol strings, yield deductive conclusions. The mathematical
operator so obtained is termed a consequence operator. In modern mathematical
logic, there are two types of such logic operators. The most basic is
the finitary consequence operator of Tarski (1930). However, there is
a similar operator that is more general in character and is often termed
simply as a consequence operator.
The small amount of set-theoretic
language that is employed in this paper is taken from a standard high-school
algebra course and, in some cases, is only considered as an abbreviation.
Indeed, each abbreviation is specifically defined. No actual mathematics
appears in this paper. The formal mathematics can be found in Herrmann
(1987, 1991). The symbol used to represent the finitary consequence
operator is the symbol Cn. The more general consequence operator is
often denoted simply by C. Informally, such operators take any subset
A of L (i.e. A subset L) and yield all those members of L that can be
deduced from A (i.e. Cn(A)). A basic requirement is that the assumed
premises can always be deduced logically (i.e. A subset Cn(A)). Once
a human being has deduced all of the consequences, then no more consequences
can be deduced from the same set of premises (i.e. Cn(Cn(A)) =Cn(A)).
For C, if one set of premises B is a subset of another such set A (i.e
B subset A subset L), then deductions from B form a subset of those
deductions from A (i.e. C(B) subset C(A)). For a finitary consequence
operator, the human argument of using only finitely many symbol strings
from a set of premises A to obtain a deduction is modeled by the additional
requirement that if x is deduced from A (i.e. x in Cn(A) or x is a member
of Cn(A)), then there is a finite set of premises F subset A such that
x can also be deduced from F. One can show that this last requirement
also implies the last property listed for the general consequence operator
C. Consequence operators that correspond to specific deductive processes
such as those defined for propositional, predicate, and higher-order
formal languages (i.e. those logical processes used in modern scientific
discourse) can be further characterized so that each can be differentiated
one from another.
What Tarski did was to take
a concrete everyday experience and mathematically abstract its most
basic properties. From this abstraction, mathematical arguments establish
other properties. These other properties may then be interpreted with
respect to the original linguistic terms that generate the Tarski abstraction.
Thus new insight is gained into what constitutes human thought patterns.
As will be discussed later, the same type of formal abstraction is possible
for certain dialectic logics.
In 1978 (Herrmann, 1981),
Tarski's consequence operator theory was investigated through application
of the new mathematical discipline called Nonstandard Analysis for the
specific purpose of finding a nonnumerical model for the concept of
subliminal perception. Nonstandard does not mean that different mathematical
procedures are employed. This is a technical term relative to abstract
model theory. After many years of refinement, the basic properties of
nonstandard consequence operators appeared in mathematical journal form
(Herrmann, 1987) and book form (Herrmann, 1991). Cosmological interpretations
of these results have been reported upon numerously many times within
other scientific and philosophic journals as well. However, also of
significance is a linguistic interpretation of these fundamental results.
Generating the mathematical structure is not extremely difficult. But
interpreting it linguistically has been arduous.
A Special Linguistic
In order to interpret a
formal mathematical structure relative to different disciplines, a correspondence
is created between terms in one discipline and the abstract entities
of the structure. This actually yields a many-to-one correspondence
since numerous disciplines can be correlated to the same mathematical
structure. Each time this is done, a mathematical model is constructed.
Our interest in this paper is a specific correspondence between some
terms relative to intelligence, linguistic, and similar human activities
associated with a physical world and the mathematical structure. With
respect to nonstandard structures, however, many new objects emerge
that are not present within the standard structure. Although these new
objects have all of the properties of the original entities and thus
the same properties as the nonabstract objects from which they were
originally abstracted, they also have many additional properties not
shared by any of the original entities. What one does, in this case,
is to created new terms that have a similar linguistic-like character
as the original linguistic terms and assign these new terms to appropriate
unassigned entities within the nonstandard structure. But can you assign
a concrete dictionary meaning to these new terms?
A dictionary meaning to
these new terms will not carry the appropriate content. One reasonable
method to obtain an in-depth comprehension is to have a strong understanding
of the workings of the mathematical structure and to reflect upon the
relations between these new linguistic-like terms themselves, as well
as between the new terms and the standard linguistic expressions. What
this means is that you must study the written statements depicting these
relationships. The model that this creates forms a portion of the deductive
world model or, simply, the D-world model. There is, however, a new
method that has been devised that renders these new concepts comprehensible
without the necessity of an in-depth study. The method is termed negative
Negative comparison is a
description as to how these new concepts negatively compare with the
original standard concepts. Certain aspects of such linguistic type
interpretations have been discussed elsewhere (Herrmann, 1991) but not
as it directly relates to the concept of a higher intelligence. Further,
this present interpretation uses a few special terms not previously
introduced. The linguistic-like terms that correspond to new abstract
entities that, at least, have similar properties as the original have
the prefix "ultra-" attached. It is always to be understood
that prior to each statement one should insert an expression such as
"It is rational to assume that . . ." where the term "rational"
means the logical processes science uses to develop its most cherished
theories. To be as simplistic as possible within this section, only
one of many distinct logical processes will be compared. What can be
said about this one process will hold for all similar processes that
can be characterized by the consequence operator. Note that logical
processes are also termed mental processes.
The use of the "ultra-"
prefix does not remove the term from being only a defined mathematical
abstraction. Within a description, additional phrases that correlate
such terms to a specific discipline are either inserted or, at least,
understood by the reader. Relative to a supernatural higher intelligence,
one basic correlating phrase is "entity within the universe."
This signifies any corporeal entity of which the human mind can conceive
and which makes its home within the material universe. The insertion
of this phrase is the basic change in the interpretation from those
previously used. Other obvious correlating terms will appear when relationships
between the ultra-objects and the concrete linguistic entities from
which the model was generated are discussed.
There exists an ultra-language,
denoted by *P, that at least has all of the properties of the most simplistic
of human languages, the propositional language P. The language P is
a subset of *P. A simple informal propositional language P can be constructed
from but two primitive words such as "house" and "door"
and the usual additional symbol strings such as "or" "and"
"not" and "implication." In this case, all of the
expressions in P are meaningful in the sense that they impress on the
human mind various images. Assume that all of the members of P are meaningful
in this sense. There are many members of the ultra-language *P that
cannot be used for any purposes by, and have no specific meaning to,
any entity within the universe. However, all members of *P are ultra-meaningful.
The mathematical model would require "ultra-meaningful" to
correspond to a statement such as "they ultra-impress on an ultra-mind
various ultra-images." Remember that deep understanding of what
these new terms might signify requires an investigation of the relationships
between such terms as expressed by hundreds of such statements. Suppose
S denotes the consequence operator that characterizes the simple human
mental process called propositional (sentential) deduction. Then S is
a finitary consequence operator and all of the consequences S(B) that
can be deduced from a set of premises B subset P are obtained by deduction
from the finite subsets of B. Now there exists an ultra-logical process,
denoted by D, defined on subsets of the ultra-language *P, where D has,
at least, the same properties as those of the logical process S when
D operators on finite subsets of the humanly comprehensible language
P (Note 1).
What happens when the ultra-mental
process D is applied to any finite subset F of the humanly comprehensible
language P. The set of consequences D(F) contains all of these consequences
S(F) comprehensible by entities within the universe (i.e. S(F) subset
D(F)) and many that are not comprehensible by entities within the universe.
Using consequence operator terminology, when this occurs, the ultra-mental
process being modeled by the consequence D is said to be stronger than
the mental process modeled by S. It is this and other, yet to be described,
properties that led to the selection of the term "ultra" as
a prefix. Further, no entity within the universe can duplicate the ultra-mental
process D, and this process also has numerous properties that are not
comprehensible by any entity within the universe (Note 2).
There is a delicate analysis
that can reveal the composition for some of the ultra-words in *P, where
w in the ultra-language *P is an ultra-world if it is not a member of
P. What this analysis details is often quite startling. For example,
there are ultra-hypotheses, a single one of which is denoted by w, that
cannot be comprehended by entities within the universe and that, when
the ultra-mental process D is applied to w, yields a consequence that
can be comprehended by entities within the universe. These ultra-hypotheses
exist in subsets of *P that, at least, have the same characterizing
properties as sets that describe human behavior, natural laws and the
like. For example, if a sentence x in P describes a certain human behavior
trait, then, although there may not appear to be a hypothesis h in P
from which x can be deduced by the human mind, there does exist in *P
an ultra-hypothesis w such that the ultra-mind process D when applied
to w yields the conclusion x.
There are other mental processes
that seem to correspond to intelligence. One of these is choosing from
a list of statements, that is potentially infinite, a specific finite
set that is meaningful for a particular application. Embedding this
finite choice process into the deductive-world model yields the same
type of conclusions as those for the ultra-logic D. This ultra-mind
process cannot be duplicated by any entity within the universe, it is
stronger than all such mental processes and has properties that in all
cases improve upon the mental process of finite choice (Herrmann, 1991).
Another human reasoning
process is the dialectic. Basic characterizing expressions can be listed
for many such dialectics (Gagnon, 1980). Such dialectics can be applied
to any language E constructed from two or more symbols. The basic ingredients
are a set of theses T, a set of antitheses A, and an operator Sy, among
others, which yields a synthesis z for any t in T and some a in A. For
all the dialectics listed by Gagnon (1980), it is not difficult to show
that there exist sets of symbol strings T and A and operators such as
Sy that when embedded into the deductive-world model become sets of
ultra-theses, ultra-antitheses and, an ultra-mental process, the ultra-synthesis
operator *Sy (Herrmann, 1992). Once again, the same type of conclusions
hold for these ultra-dialectics as holds for the ultra-logic D.
It appears that all forms
of such mental-like processes are improved upon, to an extreme degree,
by their corresponding ultra-mental processes. When the collection UM
of ultra-mental processes is compared, as a whole, with the corresponding
set M of mental processes that are displayed by humanity, then it appears
reasonable to characterize the collection UM as representing a higher
intelligence. The logical existence of UM is obtained by use of the
most fundamental tool of modern science and establishes that the acceptance
of the existence of a supernatural higher intelligence is scientifically
rational and verifies the conclusions discussed in the introduction
to this paper. Moreover, any properly stated model MH that either specifically
utilizes such a postulate or logically implies the existence of a supernatural
higher intelligence cannot be rejected as somehow or other not being
scientific in character. Indeed, if such a model MH explains past natural
events or human experiences, and predicts other events as they are observed
today, then the scientific method explicitly states that such models
are to be considered as good as or even better than other models.
Although this discussion
could be concluded at this point, one interesting question is suggested.
Has such a higher intelligence been previously described using terms
and concepts that parallel those for the above ultra-mental processes?
Significance of Results
Although a comparison with
the doctrine of all of the major religious belief-systems has not been
made, there does exist a strong correlation between these results and
statements that appear in the Jewish and Christian Bibles. The Bible,
when literally interpreted, often describes God's attributes in terms
of a linguistic or a mental model. This is especially the case when
the mind of God is compared to the mind of man. In every single case,
the "mind of God" Scriptural statements are modeled by the
above special deductive-world interpretations. This is a startling fact
since the deductive-world model was not created originally for application
to theological concepts.
As examples, every time
the Scriptures state that God "speaks" to a prophet, or a
Jew or Christian then the above special interpretation is verified.
Indeed, all statements that compare God's wisdom, intelligence and the
like with that of humanity are satisfied by this special interpretation
as are numerous statements relative to the supernatural means that God
employs to communicate with an individual.
Here is a partial list of
such statements. Genesis 1:26; Numbers 23:19; Deuteronomy 33:26; 1 Kings
8:23, 27; 2 Chronicles 2:5; Job 9:4, 10, 11:7, 8, 12:13, 15:8, 28:12--13,
20--24, 32:8, 33:12, 14, 37:23, 38:33, 36; Psalm 35:10, 53:2, 77:13,
86:5, 93:5, 94:11, 119:27, 99, 100, 139:2, 6, 17--18, 147:5; Proverbs
2:6: Ecclesiastes 2:26, 3:11, 8:17; Isaiah 55:8--9; Jeremiah 10:10--
13, 17:10, 31:10; Daniel
2:21--22, 46; Matthew 10:20; Mark 13:12, 13; Luke 6:8, 10:21, 22, 21:15,
24:45: John 8:47, 10:16, 27, 12:40, 14:26; Romans 11:33--34; 1 Corinthians
1:10, 19--20; 2:10, 13, 16; 2 Corinthians 10:4; Ephesians 1:17; Colossians
2:3, 4; 2 Timothy 2:7; James 1:5.
Even if not specifically
related to doctrinal statements, the logical existence of a supernatural
higher intelligence is obviously significant for any supernaturally
related belief-system and modern creation-science. It is no long advisable
to categorize human religious experiences and scientific models that
are associated with a supernatural higher intelligence as being somehow
or other irrational in character. Indeed, if such experiences or creation-science
models directly correlate to a literal Bible interpretation, then the
assumption of irrationality can be scientifically proved to be false.
Finally, since application of the basic tool used for modern scientific
research has established that it is scientific to assume the existence
of a supernatural higher intelligence, a properly constituted creation-science
model that relies upon this assumption is not "pseudoscience"
as has been claimed. Note once again that if such a model increases
our capacity to understand the workings of the natural realm, then the
scientific method specifically states that such a model is the preferred
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