**THE
NATURE OF REALITY AND THE MIND OF GOD**

**©
Copyright July 2022, Edward R Close**

*“As a man who has devoted his whole life
to the most clearheaded science, to the study of matter, I can tell you as a
result of my research about the atoms this much: There is no matter as such!
All matter originates and exists only by virtue of a force which brings the
particles of an atom to vibration and holds this most minute solar system of
the atom together. … We must assume behind this force the existence of a
conscious and intelligent Mind. This Mind is the matrix of all matter. … **I regard consciousness as
fundamental. I regard matter as derivative from consciousness. We cannot get
behind consciousness. Everything that we talk about, everything that we regard
as existing, postulates (the existence of) consciousness.”***-
Max Planck, the First Quantum Physicist**

**I completely agree with
these statements by Max Planck. My agreement is based on more than sixty-four years
of my own on-going study and research that has convinced me that, far from reflecting
outdated unscientific religious faith, as many mainstream materialists like to
think, Planck’s conclusions gathered above were, as he implies, based on a clearheaded
appraisal of scientific investigation based on meticulous experimental design
and real data. He was not expressing a wishful fantasy or subjective opinion. He
was articulating a set of valid logical conclusions and predicting the science
of the future. In my opinion, the conclusions clearly articulated above were
written by a genius who was far ahead of his time!**

**It is, however, easy
to say that we, and all of the details of the reality we experience, are
materialized thoughts of a higher form of intelligence that is beyond our ability
as human beings to comprehend. That appears to be the basis of traditional
philosophies of religion and spiritual mysticism. But if Max Planck’s scientific
view of reality is correct, and everything is materialized thoughts of an
omnipotent transcendental mind, then exactly how does that work? Is it possible
that we may be able to understand the processes and mechanisms by which an
infinite mind is thinking us into existence? If this is the case, then discovering
and understanding those mechanisms and processes will be of immense importance
to us as individuals, and even more vital to the future of humanity.**

__The Way Forward __

**The last statement of
the last discussion, posted July 2 ^{nd}, listed the three types of potentially
consistent logical systems that make up the reality we experience. They are: 1)
**Incomplete parts of reality that are perceived
by individual conscious beings primarily through the senses, 2) Mathematical models
of the logical systems of the laws that govern reality, and 3) The finite objective
universe visibly expanding into infinity.

The full statement, which is consistent
with Planck’s statements, also says that those three logical systems, which are
by definition, subject to the conclusions of Gödel’s incompleteness theorem, reflect the innate patterns
of logic existing in Primary Consciousness, i.e., the mind of God. But is this merging
of science with spirituality actually warranted by empirical evidence? And is
there a paradox? Yes, and yes, of course there is, and we shall see that,
instead of being a problem, that is a profound blessing and an opportunity to
learn!

__The Mind of God Paradox__

If the three logical systems that form
the reality we experience are incomplete, and they are reflections of the
logical patterns of the mind of God, then the proof of Gödel’s incompleteness theorem implies that the mind of
God is incomplete! This conflicts with the traditional religious belief systems
that proclaim the absolute perfection of God. And this conclusion that the Mind
of God is incomplete could even be considered as evidence that, instead of
being created by a higher form of intelligence, we are, in fact, only creating
the concept of a God-like potential ourselves, as we try to expand our collective
consciousness by accumulating more and more factual knowledge and understanding
more about the nature of reality.

Now, what we have here is what I like to call a Niels Bohr moment! Recall
that Bohr said:

*“**How
wonderful that we have met with a paradox**. Now we have some hope of making progress!”*

Here’s
the crux of our paradox: *How can a Perfect, Infinite God have an
incomplete mind?*

Let’s
remind ourselves what the incompleteness theorem says:

*I**n any consistent logical system, contradictions
may arise that cannot be resolved using the logic of the system within which
they have been stated.*

Or as Einstein put it: *“We cannot solve our problems with the
same thinking we used to create them.” *

It is very important to realize that the
incompleteness theorem proved by Kurt Gödel does NOT say that there are paradoxes that can
never be resolved. It simply says that there are perfectly valid questions that
can be asked in any consistent logical system (modern science, for example)
that cannot be answered within the system of logic in which it was articulated.

As I have pointed out before, reality is
the ultimate logical system, and paradoxes arising in a consistent system of
logic are evidence of either an incorrect or incomplete set of *a priori* (self-evident)
assumptions. Paradoxes can actually be resolved by making appropriate changes
in the system of logic we are using. How do we do that? We have to start by
critically examining the relevant existing *a priori *assumptions of our
system of logic. What are the *a priori* assumptions in this case? They
are assumptions about the existence and nature of ** time** and

**.**

*infinity*So, let’s first have a look at the
assumptions underlying the concept of infinity, The average person rarely
thinks much about infinity, and those who do, including most mainstream
scientists, assume that infinity is unattainable in the real world and
therefore impossible to define, study, or further analyze. In the late 1800s, however,
one mathematician in Germany disagreed with this assumption. That mathematician’s
name was Georg Cantor.

__Set Theory and Cantor’s Infinity of
Infinities__

The Russian-born German mathematician, Georg
Cantor (1845 -1918), like Max Planck, was a genius 100 years before his time.
He boldly investigated the concept of infinity, even though most of the mainstream
scientists and mathematicians of his time considered infinity to be a concept
of religious philosophy, and therefore, not at all a proper thing for a
mathematician to study or even to consider as a real thing. Cantor paid a
terrible price for his heresy against the mainstream establishment. After his
brilliant discoveries were rejected out-of-hand by a leading member of his
chosen profession, he suffered a series of nervous breakdowns and died in a psychiatric
sanitorium in Halle Germany at the age of 73.

About 20 years after Cantor died, the
methods that he developed to study infinities were generally accepted. Interestingly,
they are the exact same methods used by Kurt Gödel to prove the incompleteness theorems. What are
those methods? They are the fundamental methods of what is now known as Set
Theory, a theory of mathematical logic that has proved to be very useful in
many fields of scientific investigation. The concept
of “a set” is so simple that it is often introduced in basic math classes as if
it were a completely self-evident concept. Examples of sets are everywhere:
like the set of desks in a classroom, the set of students in a class, the set
of cars in a parking lot, etc. The concept of set is strongly related to the fundamental
functioning of consciousness. So how does set theory handle the concept of
infinity?

From a purely mathematical point of view, there
are an infinite number of infinities, and every infinite set is based on one or
more provable axioms or *a priori *(self-evident)* *assumptions. The
idea that there could be different sizes of infinity seems counter-intuitive,
but an example of a set of infinities of different sizes that can be easily visualized
is the set that includes the infinite set of points on a line, the infinite set
of points in a plane, and the infinite set of points in a volume of space. These
form a sequential set of infinite sets where the first set is a subset of the
second set, and both are contained in the third set. The number of points on a
line is infinite, but since a plane contains an infinite number of lines, the
infinity of points in a plane is larger than the infinity of points on a line,
and the infinite set of points in a volume is even larger. While this seems
intuitively obvious to me, a rigorous proof that there are infinite sets of at
least one size between the size of countable sets and the size of uncountable
infinite sets depends upon a famous proposition, the continuum hypothesis,
being false. FYI, Cantor postulated that the continuum hypothesis is true, but
failed to be able to prove it during his lifetime.

The continuum hypothesis says that there are two
different sizes of infinite sets. The smaller-sized infinite sets have a
one-to-one correspondence with the members of the infinite set of integers (1,
2, 3, …). Cantor called such a set a *countable* set, for obvious reasons,
and the larger size of infinite sets is represented by the infinite set of the real
numbers (the integers plus the rational numbers existing between them), which
Cantor called *uncountable* because they could not be paired with the
infinite set of integers. The importance of proving whether or not the
continuity hypothesis is true, was emphasized by David Hilbert when he made it
number one in his famous list of 23 important unsolved problems of mathematics,
published in 1900. Only eight of the 23 problems have been resolved to date according
to the consensus of professional mathematicians, and the continuum hypothesis
is not among the eight that have been resolved.

There are ten basic axioms that are typically introduced by a
mathematician in a formal presentations of set theory. [An axiom is defined as a statement that is either assumed as *a priori* (i.e., self-evident),
or has been proved with rigorous logic from an *a priori* assumption, and
is therefore accepted as true.] There
are potentially an infinite number of set theory axioms because some axioms are
themselves infinite sets. However, in our effort to resolve the Mind of God paradox, we only need to undertake
a critical examination of the *a priori* assumptions of set theory that
are directly related to the fundamental concept of the existence of infinite
sets. Here is a set of relevant axioms and axiomatic definitions:

·
The axiomatic definition
of set
theory: Set theory is the system of mathematical logic that deals with collections
of similar objects called *sets*. The objects
that make up the sets are called *members*, or *elements*, of the set. Pure set
theory is a calculus that deals exclusively with sets, so the only sets under
consideration are those whose members are also sets. The theory of the *hereditarily finite* sets, i.e.,
those finite sets whose elements are also finite sets, the elements of which
are also finite, is actually formally equivalent to the calculus we call arithmetic.
Since arithmetic is already well-defined and axiomatically sound, the main focus
and purpose of set theory is the study of *infinite* sets.

·
The axiom of the
existence of infinity: There exists an infinite set that contains all
definable sets (both finite and infinite) as elements or subsets, including the
zero, or empty set.

·
The axiomatic
definition of countable infinities: An infinite set is countable, if and only
if all of its elements can be paired with the infinite set of integers (1, 2,
3,…).

·
The Axiomatic
definition of uncountable infinities: An infinite set is uncountable if its
elements cannot be paired with the infinite set of integers.

·
The axiomatic definition
of equally infinite sets: Two infinite sets are the same size, if the elements of
one set can be paired one-to-one with the elements of the other set.

·
The axiom of sizes of
infinities: There are at least two different sizes of infinities: The size of
countable infinite sets, which is equal to the size of the infinite set of
integers and the size of uncountable infinite sets like the infinite set of
real numbers, which contains the infinite set of integers and the rational
numbers existing between them, making uncountable infinite sets necessarily much
larger than countable infinite sets.

__Discussion__

The fact that the dynamic interactions of
the** existing logical
systems of the three types listed in the previous post and again above, have produced
**the stable reality that we experience, provides us, as conscious
beings, with a unique opportunity to investigate and understand the nature of
reality. In the process of doing so, we came upon a striking paradox that I
have called “The Mind of God paradox”.

Combinations of the three types of logical
systems cannot form a physical universe stable enough to support conscious life
forms, unless they **conform to the same symmetric patterns of rotational volumetric
extent that exists in the innate logical dimensional structure of space, time,
and consciousness. **The symmetry needed for the stability we experience
in our natural environment is provided at the quantum level by specific numbers
of triadic rotational units of equivalence (TRUE) of gimmel, the non-material third
form of objective reality, discovered while applying the calculus of
dimensional distinctions to analyze the stability of the combination of two up
quarks and one down quark in the formation of a proton. And, of course, as we
all know, each positively charged proton pairs with a negatively charged
electron to form hydrogen, by far the most abundant element in the universe.

What does hydrogen have to do with set
theory, the incompleteness theorem, space, time, consciousness, and the mind of
God paradox? I’m glad you asked! The hydrogen atom is a finite set with three
finite subsets: one electron energy shell, enclosing one proton, containing three
quarks, comprised of an asymmetric number of quantal units (TRUE) of mass and
energy, which is a rotational set of objects that only becomes stable in union
with an appropriate number of units of gimmel. Gimmel, like the dimensions of
space, time, and consciousness, has no physical existence, i.e., no mass or
energy, of its own, but the existence of gimmel in the electron and quarks, expands
the hydrogen atom into a symmetrical rotating structure that would be unstable without
it, in which case, there would be no universe to support organic life, the
vehicle of conscious minds, a finite set within the infinite set of logical
systems that is the Primary form of Consciousness called the Mind of God.

__Conclusion__

Our study of set theory axioms related to infinity has revealed an error in the assumptions that gave
rise to the Mind of God paradox. That error is the mistake of equating
perfection with completeness. The exact opposite it true: The Primary form of Consciousness,
i.e., the Mind of God, is infinite, but we didn’t realize that infinity is
never complete. This conclusion is consistent with the truth revealed in the
proof of the incompleteness theorem.** Expansion of the consciousness of the finite is movement
toward perfection, but perfection is a moving target, and that movement introduces
the concept of time. **

I mentioned that I considered the *a priori*
assumptions about *time *and *infinity *to be relevant to the *Mind
of God paradox*, and I chose to begin this critical examination of the relevant*
*assumptions underlying the systems of logic we know as mathematics and science by
first looking at assumptions about the existence and nature of *infinity*.
In the next post, I plan to continue with a critical examination of our
assumptions about *time*.

ERC – 7/7/2022

## No comments:

## Post a Comment