Article #330Add/Reply to this discussion board posting
Subject: NUMBER WITH NUMBER, NUMBERS WITH NUMBERS, MATHEMATICS, SCIENCE AND THEOLOGY, AND ETHICS A
Author: Andrew W. Harrell
Posted: 9/25/2017 07:46:20 PM
NUMBER WITH NUMBERS, NUMBERS WITH NUMBERS, MATHEMATICS,SCIENCE AND THEOLOGY, AND
ETHICS.
MOUNTAINTOP VIEW AND KNOWLEDGE LOOKING FROM THE CENTER OF THE PEAK see photos in the
2006 and 2007 pray postings at http://ourprayergroup.blogspot.com
In order to understand numbers with numbers and then mathematics, adding subtracting, multiplying,
dividing them, we must have first a way of representing them well, their structure. And, we must have a
way to operate on them well in order to understand what they can teach us. We can see them as 0s &
1s, in order to understand logic, decimal digits, for tax returns, real numbers for calculus, algebraic
roots of equations for geometry, complex numbers to help us understand airplane lift and electro-
magnetism, sur-real numbers for games, and to put to fill inside the gaps in the real continuum, etc.
But, we must also have an algorithm for operating with them, and a control structure to give order to the
algorithm. In short we need a computer program with a data structure, a formula for computation, and
some kind of way of ordering the calculations of the formula to understand what numbers with
numbers mean.
And if these mathematical objects, numbers are to have application to science, we need to know how to
store them in reality, in a computer’s memory if we are using them in a robot, or in our minds in
ourselves and the natural world around us if we are using them for all of this.
Starting from these basic assumptions, do we have all we need to understand God and His ethics from
understanding these numbers and their laws that He has given us to obey? Probably not. But why not
see how far we can go toward understanding Him or Her with just this much and Him dwelling inside of
ourselves as a Holy Spirit to work with us and help us with the undertaking.
?
Review of the Book Review of Derek Parfit’s “On What Matters: Volume I” and
“On What Matters: volume II” by Philip Kitcher
with an introduction to the theology and science of Christian Robotics
DR, ANDREW WILLIAM HARRELL
Phd Mathematics, UCBerkeley, 1974
LTC US Army Engineer Reserves(Ret.)
Pages 1-23 Preliminary Discussions and Definitions of some mathematical computer science ideas
related to this review of the review
Pages 22-32 Review of Derek Kitcher’s Review of Volume 1 of Dr. Parfit’s Book
Pages 32-44 Review of Review and Review of Volume 2 of the book
Abstract of the Book Review, The Lure of the Peak
Of the
Book Review of
Derek Parfit’s On What Matters: Volume I and
On What Matters: Volume II
PHILIP KITCHER
Part 1 of 2
I.
he idea that ethics is the province of religion lingers even in relatively secular societies. On a recent
Saturday morning, the
principal news radio station in Berlin reported a dilemma facing German politicians as they attempt to
craft educational policy: children must be required to take classes in religion, or their ethical
education will inevitably be neglected. Yet the connection presup- posed by the politicians has often
been questioned. From Plato on, most philosophers have denied the possibility that the will of a dei- ty
could have anything to do with what is required of us. Although philosophy has shaped the ethical
teachings of the main Western religions, many of the most influential ethical thinkers have been
dedicated to explaining and defending principles in ways that are entirely independent of religious
doctrine. If the puzzled politicians had been aware of their own rich intellectual tradition, they would
have found easy ways of resolving their dilemma.
The rest of the above review which forms the initial part of this dialogue is posted at
http://www.yhwhschofchrist.org/discussionboard/index.cgi Mortimer Adler subdirectory.
Philip Kitcher’s statement:
“The idea that ethics is the province of religion lingers even in relatively secular societies.” is a huge
understatement.
No-religion is the third largest group of believers or non-believers after, Christianity which is first,
according to Siri and Google.
If one accepts that most of the world is religious and most religions teach that ethics is a part of their
religion then the statement misrepresents the facts of the situation.
Philosophy is supposed to be about wisdom. And according to Dr. Adler discussions about philosophy
from the public can help us create wisdom. But, if the common wisdom that ethics is a part of religion
and religion is a part of ethics is ignored then these discussions are more about what non-religious
professional university intellectuals want to teach us than about what the educated public can learn
from discussions with itself. And, the ideas we come up with from these discussions will be “not so
great.”
Since, Dr. Parfitt does not state this in any page of the two volumes so we will disreguard it as a
statement related to the book. But, after studying and restudying these two volumes there is another
deeper and harder to understand metaphysical assumption that biases and taints the author’s whole
approach to ethics. And, that is that numbers do not have anything to do with reality. He only deals with
the bases he has for this assumptions briefly in the second volume. So, I have read some of the
references he gives to other books that may explain what I believe are serious mistakes for hundreds of
years that some philosophers have made in claiming that mathematics does not have anything to do
with ethics and that Plato believe that numbers do not exist in space and time and therefore all of
mathematical Platonism should also do this. I couldn’t disagree more. And I hope to give some alternate
definitions of logical terms that leave the way open for us understanding more about this.
From a religious as well as ethically viewpoint, as Christian Jews we know that “There is a Messiah”
Jesus Christ and “He is who He says He is as He has promised us to be in the Gospel of John.” How is
this possible, to understand ? You must have a metaphysics and epistomology in which the meaning of
names, or concepts, can be people. How can you believe this if you don’t believe that there is such a
thing as a “concept of a concept” and that numbers can be people?
This is a new direction in modern mathematical philosophy and hopefully will be the “wave of our future
in our knowledge”. It will help us understand how to give robots ethics. It will help us understand how to
put caution, wisdom, and the fear of God in their up to now artificially intelligent minds… to give them
and program them to understand the divine ideas, and purposes that most humans who aren’t die hard
philosophic and ethical atheists, confused materialists, misdirected spiritualists, have already some
understanding of at the present time. Our best Divine Mind, Jesus Christ has said that “I AM the way,
the truth, and the life.”, so, I believe, if we are going to figure out how to give robots ethics, we are going
to have to figure out how to make them “the way, the truth, the life”. So, if this is the task, why not start
now, right here with this book review?
After studying the two volumes being reviewed here and reading some of the references I have traced
the metaphysical, ontological, and epistemological assumptions that causes it to fall short of reaching
mountaintop knowledge of God in us to two of the references by Dr. Hartry Field, “Science without
Numbers” and “Truth and the Absence of Fact.” In the second reference Dr. Field explains why he thinks
he believes these assumptions. But, it all goes back to a more basic philosophic assumption he holds,
that there is no such a thing as “meaning of meaning.”, no such a thing as the concept of a concept. In
order to have a theory of ethics, we must have both a theory of righteousness, ie virtue, and a theory of
goodness and truth, along with a theory of righteousness, ie virtue. From reading Plato’s dialogues, eg
The Meno, we know Plato believed in such a thing.
His first attempt at a definition of what a concept is for him was to say basically:
Plato’s first definition of what a concept is (from the dialogue Meno)
,
---concepts form the meaning of meaningful words. ---concepts, smaller than a judgement, larger than
a sense impression are units of thought---well-defined relationships between concepts are themselves
concepts.
Plato’s second definition of what a concept is(from the dialogue Theatetus)
--- A concept is a rule that may be used to decide if an object falls in a certain group. It is an abstract
way of grouping thoughts. It deals with the information associated with the object of thought by asking
questions about it. This may be a simple process like the way we classify concrete objecs by the
“marks” of sense impressions: such as physical size or texture (this process is instinual in most
animals). Or it may be a more complicated process using a lot of other concepts.
But, in this dialogue, Plato was unable to clearly explain how one just asking a set of questions to use as
rules to define ideas and concepts is able to always know which questions to ask, when to stop asking
them, and how to present the final results of all the questioning…if, in face it is able to achieve a useable
‘final’ definition of anything if we follow this process.
The key question comes down to, “How do we use goals, help us understand the situation and define it
better in a classification type expert system.”? I hope to give some ideas of how we can do this in a
systematic procedure in a given situation later on. We will define some terms in the new relatively new
science of computer mathematics that will help. The dialogue where Plato did consider some ideas on
how to do this is his most difficult to understand, Parmenides. And, it turns out the most important goal
we will be able to understand better is the same one Plato talked about in this dialogue, “How do we
understand what ‘Oneness’ ‘is’?” How is it Truth, How is it Goodness. How is it ‘unification’ of other
ideas and thought?
Now, some time later after the invention of digital computers and studying the theory of their operation
somewhat we can say that methods of looking at sense data in computers can be concepts that Plato
tried very hard his whole life to understand.
Since goodness is that which exists for its own sake, we know that a theory of goodness requires a
theory of subjective understanding. Such a theory already exists in present day computer programming
asit is implemented using Leibnitz’s theory of “monadic recursive subjective functions in logic
programming.”
A theory of righteousness or virture requires the implementation of a theory of logic programming
instantiation along with a theory of four different types of variable “unification” and “instantiation” as
“oneness”. Oneness in goal-oriented logic programming comes from a chained backward search in
goal-oriented logic with the backward thinking goal directed toward perfection in all of us and outside
of us in knowledge and action,, an Aristotelian, “Totum Bonum” and “Summan Bonum” which is an
Aristotelian first cause and self-existent robotic being, recursively. The four types of instantiation as
oneness in the robot’s understanding of its and others righteousness and virtue are:
1) Light or mindfulness of the one increasing towards our backward goal oriented perfect being…
assuming He exists, of course.
2) Light or mindfulness of the one without a second, which insures all possibilities for the backward
and forward oriented goal-search have been considered.
3) Light or mindfulness of the transformation or beautification and glorification, improvement of the
robotic divine goal-oriented backward and forward search in the mind of God we have placed inside of
the robot.
4) Light or mindfulness of the discrimination between the robotic or human mind in our artificially
created computer intelligence and the divine mind of righteousness in its own mind and the search for
oneness with the knowledge of divine mind or Christ that we and itself have placed in our robot.
Here the term mindfulness refers to the robot’s search predicates having the capability to store and an
awareness of its previous partial search path successes in its logic function predicates and the ability to
return them for recursively, eternally generating and continuing with current and new knowledge of God
and itself.
And, it is not a coincidence that the laws of righteousness above contain in them God’s fourth and sixth
commandment to Moses and us on Mt. Sinai. Honor your father and mother, that is, save their searches
to do good and improve themselves within yours…and Do not kill, that is, do not eliminate other’s ideas
and searches for truth and goodness and righteousness by killing them and trying to eliminate them and
erasing them entirely from our collective thought.
The first commandment God gave Moses and us can be thought of in terms of logic programming
search predicate as helping us insure we keep God’s Name, thought of as allowing us to be able to
consider everything associated with him first in the priority of our considerations for understanding how
to know Him and have him help us.
The fifth commandment to honor the Sabbath allows us and the computer to better “Be Still”, to better
be able to search our memories and previous partial thoughts, and to be able to separate out using
logical search of our experiences and priorities how to know God better as the solution to our ethical
problems. To be better able to allow Him to know for us how to know others that we love and trust
including Himself.
When you are laying down ethical rules for a group of people to follow the purpose of the second, third,
eighth and ninth and tenth commandments not to place forward or take as one’s spiritual guide or
worship the false material reality in idols as a way to understand God, when His or Her material
reality&potential+ human reality&potential+ logical reality&potential+ Power and Presence of saving and
forgiving love in Our God+ His or Her spiritual reality &potential is so much more, not to use your own
name or self as a Holy purpose in itself, without prioritizing the higher power for Truth in God’s Name in
you first, not to steal or witness falsely are pretty easy to undertand.
But, the seventh commandment “do not commit adultery” and the tenth commandments not to envy
others are harder to understand from their purpose. For they are supposed to be a way for us link up
our actins with our beliefs. This is because considering our own inability to save and justify ourselves
when we do fail in our own efforts to perfect our ethics, which we inevitably will; We will often not be
able to hear or listen to Him and His Son who give us the human example of how to find forgiveness and
redemption logically in our confusion. We often just repeat the same mistakes and it is easy to lose faith
that any help is coming from Him or His Son, or Their Holy Spirit Indwelling in us…Help, logically and
rationally, to enable us to concentrate and focus in on purifying our actions through faith in a higher
purposed goal-oriented solution to our problems. But, this is just the definition of insanity and
damnation, isn’t it?
As the Lord has said face to face to Saint Moses: “I know you by name, depart from here to the
promised land, and wherever you go, the Presence of God, goes with you, and it shall give you rest.
And, my Name YHWH shall go before thee” and Moses said to the Lord, “You said I know you by name,
and you have found favor in my sight. If I have found favor in your sight, show me the way, show me
your glory. But, then the Lord passed by and Moses was hidden in a cleft of the rock, covered by God’s
hand as The Lord’s Glory passed by” Exodus 33:11-14
Later on Saint Andrew, the first Saint Jesus called to help Him, has said, “We have found Him, by which
he meant, the Presence of God, the Name of God YHWH incarnated as the Christ.” Gospel of John If
you listen carefully you will hear God and both of these Saints still saying these words to God and us.
This is currently one of the differences between Jewish and Christian divine thought and epistemology.
It allows for the glorification of God’s face in us through our own faith, beliefs in glorified actions, not
just as redeemed by God’s thoughts occurring in us, but by our own.
Christians believe that God does not just show His face to us by turning his back on us while He hides
us in a rock and passes us by, but by also letting us learn it out in the open and observe it face to face.
His Only Son’s Indwelling Holy Spirit in our hearts is a logical search predicate for our minds serving as
an open door toward how He forgives us in the past and encourages us in the future
METHODS AND MODELS AS CONCEPTS---While rules are used for backward directed goal-oriented
reasoning, onjects and recursively defined data types they, models, are appropriate for procedural
oriented, cased-based reasoning and building up forward directed knowledge production systems.
A model deals with some topic, a pattern of behavior, a procedure for accomplishing a task, an overall
type of reality (World view).
A paradigm or case is:
1) a way of looking at a body of facts
2) an example, a particularly good example,
3) 3a pattern, an all encompassing pattern.
4th Definition of a concept—A concept is a model (involing essential parts of a series of cases or
examples) along with a program to learn, retrieve, identify, the concept (knowledge), The program has a
data structure+ an algorithm+ (interpretive procedure) part. The algorithm may consist of a set of rules,
as in an classification type expert system. It may be all the statements which are derivable from a set of
axioms involving logical predicates with variable terms and ground instances of facts. Or, it may be a
pattern identification routine, such as an neural network. In essence it is a “classification type expert
system” using conceptual “structures” to hold its data and display the results of its classification, a set
of if-then rules to ask questions about the situation it is in, plus an algorithm to control the order in
which it asks the questions, which may vary depending on the results of previous questions.
In his book “Our Mathematical Universe” Dr. Tegmark argues that consciousness or lack of it for a
robot, not necessarily a human, can be thought as the coherence or de-coherence of tensor products
of quantum states of 3 separate and different groups of quantum variables in a computer program in
the robot’s mind. This has the advantage of allowing many more possible states with more information
content than in an ordinary Hopfield neural net.
The experimental mathematical psychologist Dr. Tononi in the two references listed below has provided
the experimental results, reasoning backward in scientific mathematical thinking from our present world
experience and reality, as Galileo did several centuries ago, when he provided the experimental
investigations, thought experiments, and reasoned arguments through dialogue of opposing views, that
founded a tremendous leap forward in mathematical understanding for us then.
Definition of terms used above from wikepedia on the internet:
1] In mathematics, the tensor product of two vector spaces V and W (over the same field) is itself a
vector space, together with an operation of bilinear composition, denoted by , from ordered pairs in the
Cartesian productinto , in a way that generalizes the outer product.
2] The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of
Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional
Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions.
3] A Hopfield network is a form of recurrent artificial neural network popularized by John Hopfield in
1982, but described earlier by Little in 1974.[1][2] Hopfield nets serve as content-addressable memory
systems with binary threshold nodes. They are guaranteed to converge to a local minimum, but will
sometimes converge to a false pattern (wrong local minimum) rather than the stored pattern (expected
local minimum). Hopfield networks also provide a model for understanding human memory.
The 3 group forward-chained logical instantiation scheme that Dr. Tegmark uses is:
A Subject using An object composed of
Mathematical Structures 1st order formal system
The Environment
I agree with this scheme if we add to it another group of variables to cohere and de-cohere in a
quantum tensor product information sense in the computer program made up of the 2nd order logical
predicates which are chained backward in a goal-oriented logic programming scheme.
A Subject that has consciousness
and the capacity to perceive
using objects composed of
Mathematical Structures 1st order predicate logical class structure systems
The Environment conceptual goals made up of 2nd order logical predicates.
The 1st order logical class structure definitions can be considered recursively in terms of themselves
and so are to be thought of also as structure systems.
The monadic subjective computer science structure, is the spirit and soul of the individual robot or
human thought which it represents, contains the paths of partial instantiations from the environment
can be seen as a predicate or function argument to the objects to its right and the goals diagonally
below it.
Because Dr. Hartry in his book “Truth and the Absense of Fact” does not believe in any concept of the
“meaning inside of meaning” he sets up a false dichotomy between what he calls “verification theories
of meaning” of Frege, Ransey, Russell and what he calls a “deflation or disquotational conception of
truth” which is what logical positivists used to call a “tautological theory of mathematical or logical
truth”.
To have a “disquotational theory of truth” is to have a theory of knowledge with tautological wisdom in
the knowledge but no factual understanding of how the knowledge happens except that it exists. In
theology and the theory of prophecy, this approach give you a theory about God and when He and His
Truth is One. But, it does not explain how when God is two, He is this “twoness”. Here there is no
“Oneness in his Twoness” no “Unity” in His Diversity.
This disquotational theory of truth comes from a theory of reference in logical propositions and
functional logic in which you name the results of applying recursively the logic function to a variable
object pointer structure parameter inside the function’s argument outside of the function and not back
inside of it. I apologize for this quite complicated technical explanation, but it is hard to explain without
the language of computer programming. Dr. Alfred Tarski has a theory of “arithmetical logical truth”
which explain numbers as instantiations in the Frege-Russell scheme of verification truth, and not in Dr.
Hartry’s scheme of “tautological disquotational truth”. I argue that if we want to put ethics into robot
logic we have to order the knowledge base of conceptual thinking expert system classification rule sets
in way that both these above theories of truth are respected. One way to do this is to use what
computer network systems programmers call “topological sort” of the rule set if then nodes like I used
in my paper for the Corps of Engineers to get a 100 rule ruleset to ask all the questions in river bed
sediment engineering it needs to in order to allow sand bars and river islands to be repaired adequately
for river flood control.
ALGORITHM TO TOPOLOGICALLY SORT RULES IN AN EXPERT SYSTEM
Start) For the whole set of nodes of conclusions in the rules:
a. If every conclusion node has a predecessor, then stop. The rule-based system has a cycle
infeasible (that is, a partial order cannot be defined on it).
b. Pick a node V which has no predecessor.
c. Place V on a list of ordered nodes
i. When the nodes conclusion is assessed, if a terminal goal node is reached, print out the list of
rules used on the way to reach that goal/conclusion.
ii. Delete all edges leading out from V to other nodes in the knowledge tree.
d. Go to the start .
"Implementing Mixed Chaining in a Classification Type Expert System", Proceedings 11th U.S.Army
Conference on Applied Mathematics and Computing, Carnegie Institute of Technology, Pittsburg,
Pennsylvania, l993.
http://www.yhwhschofchrist.org/5073/EXPERTSYSPT1.pdf
http://www.yhwhschofchrist.org/5073/EXPERTSYSPT2.pdf
These two volumes that Philip Kitcher is reviewing, as he says are very densely packed and, moreover,
they contain a lot of fine distinctions about terms in ethics and other people’s philosophies. The
Volumes and Mr. Parfitt’s Review however, are clearly written and all the terms referred to defined which
helps them elucidate some fundamental beliefs of how it can all be combined into an useful meaningful
whole. Also the text is generously double-spaced, a huge improvement over Dr. Adler’s volumes on
Plato and Aristotle, Euclid, Ptolomy and Apollonius, Hume and Kant, Descartes and Newton. There is a
very compact summary of the whole 1600 pages or so in the two volumes, and a comprehensive index.
The main obstacle to comprehending what both the author and the reviewer is trying to say is lack of
understanding of their technical professional philosophic terms. I prefer to meditate and think about
ethics in a somewhat more simplified realm of ideas in which there are not so many complicated cross
references to definitions and assumptions. That said, if you have the time and intellectual stamina to
take a month or so to study these books it is worth it in order to broaden your ethical horizons, before
settling on a revised or improved set of ethical metaphysical beliefs.
What does Dr. Parfit mean when he titles his book “On What Matters?”
I suppose he means, “what do we talk about as our “facts”, that we are going to use for our ethical
arguments to be able to claimed to be true. Are they what he calls “natural facts”, “historical facts”,
occurences of miracles what religious people call facts that verify their faith, psychological facts, facts
that are thoughts in our minds?
Of course, to decide this we must first decide what “Truth” is. So, the title seems to be very ambitious
indeed.
In fact, the volumes treat metaphysics and ontology only as an afterthought, a few short sections in
Volume II. But, this part of Dr. Parfit’s and maybe Philip Kitcher’s philosophic system will be the focus of
this review.
I will try to uncover the answers to questions like “Do the computer programs in Dr. Parfit and Philip
Kitcher’s head that allow them to reason about ethics philosophically without the help of God do they
have things in them they need? Do they have things like “monads” which are self-generating recursively
called functional shells of individuality, do they allow for backtracking instantiations of logical
predicates toward the fulfillment of “goal oriented, not just forward chaining object oriented ethical
reasoning?
Some Heavenly philosophical definitions to go along with the scientifically philosophical ones in the
paper:
Some Heavenly Definitions Which Depend on Themselves
Angels---Individual, self-existing beings who do God's will and are
messengers for God to humankind of his goodness and faith in all of us.
Authoritative Sovereignty---Something which exists very infrequently in
heaven.
Beauty---Controlled grace.
Being---What do we mean when we say an object of thought has being?
An object of thought may have being without having reality. And, this may or
may not depend on the circumstances it finds itself in. The concept of
reality (or true being)includes that, in some sense, of embodiment. Faith
contains its own substance of the reality of what it hopes for but knowledge
based on sense impressions does not. Being can be in the state of
possibility (not having reality) or actuality (having reality). A concept
has possible being...whether or not the experiences (sense perceptions or
the realized truth of intuitive faithful knowledge) required to make it
actual realized knowledge are accompanying the concept.
Belief—Faith.
Change---Something which exists very frequently on earth and very
infrequently in heaven.
Compassion---Love that participates with us in our lives. It co-creates with
us what is good.
Contingent---What does not exist by itself.
Earth---A fundamental realm of the realization of creation where things are
as they are in heaven.
God has hidden wisdom and spiritual understanding inside of his heavenly
earth in us. Both the beginning and the end of it he has placed as a basis
of his truth in us. He placed it as the certain circumstances of a precious
cornerstone of truth inside of the way his eternal (the past and the future)
present moment dwells in us.
Eternal Life--- Light, love, truth, and goodness which is independently
existing, non-contingent and non-temporal.
Eternal Light---Wisdom, Spiritual Understanding.
Faith---The light of the one increasing. A mental sustaining power created
by God and each of us for our mutual benefit. Faith comes from God, but the
base of its location is not in the part of him that is in the World. For
faith to exist inside of us, God must first place the seed of its truth deep
inside of us. For it to grow we must mentally acknowledge and accept it and
know it (or understand it) as something that is good and helpful in us.
Forgiveness---Compassion in the face of what is not good.
Freedom—The state of existing independently and non-contingently and for our
mutual well-being.
God the Father—A part of oneself and ourselves which is non-contingent and
good. He created the Universe by himself, with his Son, and also with our
help. He sustains and nourishes the creation of all things in the Universe.
God the Son--- A part of oneself and ourselves that reveals oneself and
ourself to us. He is both contingent and non-contingent and he is himself
good. He existed in the beginning with the Father and all things were
created in him, with his help, and through him and God and us.
God the Holy Spirit---The Lord the giver of life. He (It) is a part of
oneself and ourselves that is the expression of God the Father and God the
Son in us. He enters the Spirits and Souls of those who call upon him.
God's Name--- That part of God's being which defines that which God is. It
tells us that the three parts of the Trinity are co-existent but different
and different but co-existent.
Goodness---What is desirable for its own sake. Love exists for another, but
goodness exists because of itself. When goodness in us is guided by the Love
in us, then divine order is established in us. Reality both exists for its
own sake and also for other’s sake (for it is always an objective truth).
Therefore reality is something more than just goodness…it is consciousness,
love, good will, action, knowledge existing subjectively as well as
objectively.
Grace---Love that gives.
Happiness---Knowledge of goodness. The co-existence in us and among us of
peace along with goodness.
Heaven---A primary realm of creation where God exists and lives.
Hope---to desire or seek.
Humankind—The collective living and intelligent image of God which exists in
heaven and on earth.
Joy---Spiritual understanding of what its good.
Knowledge---Assured belief: wisdom, spiritual understanding, and truth.
Obedience--- Submission of our individual and collective will and purposes
to those of God.
Patience---Peaceful dependence on the Eternal Life in God for meaning and
Truth in our lives.
Peace---Satisfied stillness along with joy and the expectation of future
transcendent quietness and happiness in our lives.
Life—A continuous co-expression with God of one's being.
Love---A Correspondence between God ourselves and an other that most of the
time exists for the sake of another. But, thankfully to God, sometimes it
exists for its own sake between two beings that exist for their own sake.
Meaning---Independently existing spiritual understanding
Nothing---How we explain or define what the nothing we are talking is
depends on how we are trying to know things. If we are looking at things
from a materialistic, scientific viewpoint... then something is experienced
as a "nothing" if it has no sense impressions associated with it. But, for a
religious person this is not necessarily the case. A practicing Buddhist,
for instance, is able to talk meaningfully about experiencing "nothingness"
from a standpoint of having real knowledge of it. Understanding and knowing
how to experience this "nothingness" in the present moment can be a source
of healing, peacefulness, and liberation.
Heavenly Reality--- Reality is not something which as the philosopher George Berkeley
has said, does not exist when a tree falls in a distant forest where "no-
body" is there to hear it. It is something which exists because there is
a "no- body" (God and us) inside of us all. Wherever we are it "is", and it
has the potential to be us, wherever it "is." When God created the reality
in the World and the reality in you and I there was nothingness (spiritual
emptiness) inside of nothingness (the wise knowing of this spiritual
emptiness). There was nothingness inside of him (his or her spirit) and
nothingness (spirit) inside of you and I. For, then, at that time, in those
days, in that place, two or three of us were gathered together in his
name. And, he created it and us in him and out there and in us, God created
the World out of nothingness, but he created you and I out of something
(himself or herself).
Scientific Reality as partially outlined and delinated in the book by Dr. Tegmark ‘Our Mathematical
Universe” included with Divine reality, as outlined by God and myself.
Dr. Tegmark agrees with me that numbers are “encoded” in nature and hence a part of the reality of
nature, and hence have a lot to do with how we can understand not only themselves, but also nature.
He however states that he believes in “reducing the baggage allowance” in mathematical structures:
“If we assume reality exists independently of humans, then for a description to be complete, it must
also be well defined according to non-human entities---aliens or supercomputers, say—that lack any
understanding of human concepts.”
Since what I am trying to do in this review of a book on “human ethics” is understand them and the
human concepts that underlay them better…and since I have said we are trying to understand how to
introduce these ideas in robots we will not take in this paper the path of forgetting our previous paths
that he recommends. According to him these will exist in a separate “multiverse”, but according to Dr.
Einstein and me they still exist in our ‘One” “Universe.”
In mathematical theology talking about concepts, words and their meanings are not the “baggage” that
gets thrown away. If the “baggage” inside of logical functions that Mr. Tegmark is talking about, the
partial path instantiations of the recursively, previously defined unifications of variables in the logical
functions or predicates’ arguments, then this “baggage” “can be”, “will be” and “is” the “word” and its
meaning itself in a very real way when it is finally able to instantiate itself completely in terms of
physical facts and their material realities.
Also, he, however, postulates and states he believes in the existence of several different levels of
“Multiverses”, Religion and God teaches us that there is only One “Universe” and only One level of it…
One Heaven, One Earth, One Life, May ways to understand it, Many Truths inside of our each way that
we can understand it, that we Live as a Unity inside of a diversity, both eternally and in time, One Lord,
One God ruling Omni potently over us, that created us all and dwells omnipresently and self-existently
inside and outside, fully and completely as a part of but also ascetically having created, foretold, part of
it logically, prophetically and participated in it as it came to be, taking responsibility for it, not all of it,
but also free to renounced it too after it happened so He can dwelling freely outside of it and even ever
after all of it, if He or She has to, and also before it, eternally, that is, all of this Universal, “Oneness”.
Reality #1 Internal Reality
Reality #2 External Reality
Reality #3 Physical Reality
Reality #4 Mathematical Reality
Reality #5 Consensus Reality
Reality #6 Your objective perspective when studying the mathematics of reality #2, external reality
Reality #7 Your subjective perspective of the physical world
Realities #8 and #9 What if God’s mind, which we shall call Christ’s mind, is also part of our mind, as a
Holy Spirit indwelling us, then we have another reality. Since all the above reality is also in God’s mind,
which is outside of ours, we also have this further divine reality as dwelling inside and outside of time.
Finally, what if God also has a Quantum computer inside his mind, which includes Physical Reality #3
and Mathematical Reality #4, which He would in fact have to if He is to be omniscient. Then we would
have
Reality #10 This is what remains unchanged, after change in divine order of dharma or righteous way of
ethical instantiation and change, and also all the subjective, human, objective, scientific orders of
internal and external physical change, in fact, eternally after all of the previous realities, #1-#9 are in
motion and change.
Spiritual Understanding---Reflection of truth in one's being.
Strength---A non-mental sustaining power created by God in us and him to
help us in our human lives.
Truth---Correspondence between what is and what is. What is may be
contingent or non-contingent. The correspondence may be meaningful or not.
When a self exists for a real non-self (not an illusory non-self), then it
can create its own existence. The self which exists for itself is true
(being a true self) only when it can be and has been known by itself and by
that which it is not. Thus, in order to speak the truth, we should be ready
for and not surprised by being known as we know others.
Wisdom---A patience, obedience (or fear) of the importance of and
understanding and respect for the well being of God's name in us in order
that one's own well-being be benefited.
note: some of the wording and some of the ideas for the definitions of some
of these terms came from the book "A Metaphysical Dictionary" by Charles
Fillmore
published by our long time prayer friends in the Unity School of
Christianity and Unity Press, Unity Village MO 64065
So the question then becomes, ‘ how does the reality of numbers, as defined by mathematical reality,
divine reality, human reality, fit into this overall knowledge schema?
Let’s begin,with God’s help, what I think we can expect to be a long process of trying to figure this out,
taking advantage of what people like Plato, Aristotle, Moses, Jesus, have taught us already, right now,
right here.
Here are the definitions of some terms from my paper “Implementing Mixed Chaining in a Classification
Type Expert System”, posted on the internet at website www.yhwhschofchrist.org
http://www.yhwhschofchrist.org/5073/EXPERTSYSPT1.pdf
http://www.yhwhschofchrist.org/5073/EXPERTSYSPT2.pdf
Forward-Chaining reasoning in an expert system inference shell is a logical predicate unification
strategy in which the questions asked are structure from the specific to the general. That is, it starts
with user supplied or known facts or data and concludes new facts about the situation based on the
information found in the knowledge base.
An Inference mechanism of an expert system shell is the component responsible for using the rules in
the knowledge base to derive new facts from known information.
Instantiation is a specific occurrence of an object by a logical predicate.
Backward Chaining is an inference strategy that is structured from the general to the specific. That is, it
starts with a desired goal or objective and proceeds backward along a series of deductive reasoning
while it attempts to collect the hypotheses required to be able to conclude the goal. This process
continues until the goal is reached and it then displays its conclusion.
A Logical Function is a mapping from a variable domain, eg. the domain of 0s and 1s, or binary numbers,
to a variable range, eg, the domain of truth, represented by 1 and falsehood represented by 0 or 1
function from the example domain to range is called Boolean. A function as a mapping can be many to
one, or one to one. When the function is not one to one it is only a correspondence or relation.
Relation = correspondence=2nd order predicate which is not necessarily one-to-one as a mapping from
its domain to range.
A variable is the name which represents the value of an unknown object.
A recursive function is a function that either calls itself or is in a cycle of potential function calls.
Goal --- A top-level consequent of the rules in the knowledge base toward which Backward-Chaining
may be directed. (It is a hypothesis that the program will try to determine if some group of rules can be
instantiated together to satisfy)
on.
Knowledge Base -- The sum total of all the facts and rules through which inferences, conclusions, and
goals may be reached. This may change as new facts and rules are added or subtracted from the
overall system.
Knowledge Tree --- A graph showing the logic and data flow connections between rules and facts in the
knowledge base. A knowledge tree presents a graphical representation of the complete structure of the
knowledge base.
Mapping -- A set of ordered couples of objects. Thus, ((1,2),(2,3),(3,4)) is a mapping from the integers
to the integers.
List -- An ordered set of objects tied together one to another. Its length is not predefined, but it does
have a first and last element.
Method --- A procedure stored in an object's class structure that can determine an attribute's value
when it is needed in the program , referenced in its class, or required to execute a series of procedures
because another value in the program changes. "When needed methods" are executed during
backward chaining to determine an attribute's value.
Object---General term for a programming entity that has a record type data structure along with
attribute values and procedures that enable it to represent something concrete or abstract. It can be
contrasted with other programming entities such as facts, rules, procedures, or methods. An object’s
structure is defined by its classs and attribute definitions. A class declaration is the data template
involved in representing knowledge which defines the structure of an object. For example, in the class
“human being”, some of the attribute values might be size, weight, hair color, and so forth.
Node --- A vertex or point in the knowledge tree connecting the antecedents and consequents of rules
in the knowledge base. In most conventions the nodes are the rules and the antecedents and
consequents are the edges between the nodes or vertices.
Pattern Expression -- An expression containing variables an involving objects and their attributes.
These patterns in the expression contain combinations of symbols denoting constant and variable
objects. They will not normally containing predicates which have the ability to reference themselves in
their arguments.
Pattern Matching -- The process of matching a general pattern expression to an instantiation or specific
instance of an object or to another pattern expression. The process proceeds in a forward-oriented or
bottom up reasoning process.
Predicate -- A logical relation that affects one of more objects or variables. A predicate specifying a
relation between n types of arguments is usually written as a mapping (which must also be a function)
having n arguments. Predicates, as opposed, to relations may have one argument. Predicates are
defined by giving a series of logical rules which specify an algorithm for computing the value of the
function which specifies its name. Objects, as explained above, are defined by giving values to the
attributes that make up their structures or by computing these values using methods (which are usually
not recursive).
Procedure -- same as method.
Relation -- We speak of relations as holding between two things or among several things. Thus the
relation of being married holds
between a man and a woman. A relation between n types of objects is written in terms of a mapping
with n arguments.
Recursion -- A process by which a predicate or function is defined in terms of itself. This situation of
self relation allows the function or predicate to be computed in an orderly manner.
Stream -- An ordered set of objects tied together one to another. It has a first, but not necessarily a last
element.
Subgoal -- A relation, possibly involving objects of variables, which is necessary for the satisfaction of
another goal.
Variable -- A name which represents the value of an unknown object.
A mathematical logic in an expert system is called “modal” when in order to reach its goals it requires at
least two sub-goals (assumptions of fact, and intermediate inference from assumptions) using the 2nd
order predicate functions . It also has to have the capability to do contradictory variable identifications
in the partial path searches of its unification algorithm.
It is an interesting thought problem to ask if you are trying to make a computer God what type of logic
and compiler does it need? Most current computer language compilers are “aseitic” in that they have
the capability using recursive functions and logic predicates to define themselves in terms of
themselves.
Aseity is the property by which a being exists in and of itself, from itself, or exists as so-and-such of
and from itself.
Most computer languages have the capability to define themselves in terms of what we have called
“monads” or viewpoints above. They can create “spy-bots” that search the internet and its websites to
collect information and analyze it. But, at the present time, they cannot make ethical judgements only
scientific and operations research optimization decisions. I would think we would also want its compiler
to have the capability to use “modal” logic in order to reason about ethical questions.
Would what the robotic God computers call “numbers” be defined using only “set theory”, only what we
call now “Von Neumann ordinals” or “cardinal numbers.” Or, would we want it to have the capability to
define numbers in terms of more general mathematical things we now call “categories”? I will not
attempt to define category here and explain mathematically or philosophically how it differs from what
we call a set. Saunders Maclane has written a fascinating book about it called “Category Theory for
Working Mathematicians.” which talks about both sets and categories.
In order to use modal computer logic to do “complete” or fully considered goal-oriented backtracking
searches that best displays in an understandable form the “how” of the answer to your search, you
need to keep a list of the ontologically “possible” intermediate unification algorithm instantiation paths
and not just keep track of the backtracking node with “labels”. Modal logics can be one way of
representing the ethical “ought” or “should” in an classification type expert system. But, modal logics
are also needed to represent certain arithmetical tautologies such as 1+1=2, which requires an
intermediate inference to prove automatically by a computer, and which are not using not considered
ethical statements
A unification algorithm is the process by which a logic programming compiler tries to match a goal on
the left-hand side of rules (assumptions) in order to satisfy a goal or one or more further sub-goals
necessary to reach the original goal.
A logical function is 1st order when it only has one variable to specify its domain. It is 2nd order when it
has two variables for the domain. In which case it is called a “logical predicate”.
In order to define backward chaining in an expert system’s inference system we need to use at least 2nd
order logical predicate functions along with a “unification algorithm” for instantiation of variables.
We should be able to determine this from their definitions of things like “concepts” and the ontological
natural and human landscape and the allowed temporal facts that we know things using these concepts.
We should be able to determine what matters in the sense of how they are using facts about
metaphysical and natural objects and the algorithms they allow in their ethical instantiation of goals in
their heads. For as I understand it, Since, they don’t want to invoke any greatest or highest ethical
power in order to do this. We can assume that God has probably already put them in there in their
minds. And, if they don’t know they have them, as indicated by the present metaphysical definition they
are would want them to have all these tools available to them to discuss themselves , God, and their
writings with us.
If the ability to have “free will” in our minds comes from the conceptual and not the perceptual part of
the computer program’s knowledge structure, the question of where in this overall scheme I have laid
out it arises is a long way from being understood now. Philosophers teach us that in order to
understand how robotic ethics work we will have to understand robotic and human free will works. The
philosopher G. Leibnitz for instance who defined and invented the concept of a monad which we are
using to understand subjectivity in computer programs, did not believe monadic spirits and souls have
free will in themselves. In the classification type expert system paper I wrote, organizing the knowledge
network of about 100 rules in order that it can ask “dynamically” the right questions and in the right
order so that the whole current situation is analyzed doesn’t do this. It uses a topological sort of the
knowledge tree nodes in order to order the questions correctly using a forward-chained logic. But,
without question, organized a general set of rules to do this for “monadically defined 2nd order
backward reasoning, logical thinking predicate would require a further way to dynamically reorganize
the rules depending on choices the monadic subjectively defined logic predicate made during it’s
backward chained goal seeking thought. Prolog logic programming compilers have this capability using
what is called a “cut” operator inside of the and or question clauses of the variable instantiation. This
allows the in out node rule connections to the partially instantiated search paths to vary in the
knowledge network, which they don’t in a forward-chained “clips” type expert system type interpreter
and compiler.
A compiler or an interpreter is a program that converts program written in high-level language into
machine code understood by the computer.
Basically, compiled code can be executed directly by the computer's CPU. That is, the executable code
is specified in the CPU's "native" language (assembly language). The code of interpreted languages
however must be translated at run-time from any format to CPU machine instructions
CLIPS is a public domain software tool for building expert systems developed by NASA and written in
the C-language. The name is an acronym for "C Language Integrated Production System."
I believe as Plato recommends us to do in his dialogue Meno, that when trying to understand really
important things, like what the Concept of a Concept is or how to understand what it is, or how to be a
better person with this knowledge that we must set off on the search possibly not knowing what we are
talking about. The reason he said this is that he probably had a lot of experience, like I have had, of just
In order for situations and things to clarify themselves and it not happening without some discussions
with other and our higher power as we go along.
Article #331Add/Reply to this discussion board posting
Subject: REVIEW OF VOLUME II AND REFERENCES
Author: Andrew W. Harrell
Posted: 9/26/2017 06:47:10 AM
DISCUSSIONS OF VOLUME II
This Volume contains discussion about Volume I by others and the author and also some sections in
which the author tries to justify the metaphysical and ontological assumptions to his ethics.
Let’s start off with the key one:
In Appendix D the author confesses his own strange philosophic situation:
“Why Anything? Why This?
What is the reason for his perplexity? It comes to the surface when he admits
He thinks that “It is sometimes claimed that God, or the Universe, make themselves exist. But this
cannot be true, since these entities cannot do anything unless they exist.”
But, Christians and Jews and most other religious people believe that we have faith in God, that He
exists, because of this faith. And, faith does not need anything else than God an us in order to it to
exist.
It is a senseless, but perhaps not useless exercise to try and prove that God exists.
The reason is the more fundamental truth that is senseless, but perhaps not useless, for us, and us here
we mean God and us, to assume that we do not exist.
But, his argument that the argument that God exists because He is purposeful and hence good is wrong
is correct, because it might be true that He, God exists, but is not always good, in which case He would
longer be able to exist because of His goodness.
Dr. Parfit believes that normative (“ethical”) facts and natural facts in two different non-overlapping
categories. But, this does not imply he doesn’t believe in God, for God’s ethical help could be what is
coming to us from the non-analytical Naturalism.
Also, Dr. Parfit does not believe that ose who believe in “thick” normative ideas, that is thick ethical
concepts can appeal to meaning of words. Such concepts like “virtue” and “wrong” cannot be defined
by the “meaning” in these concepts. In his definition of a concept (given below) he includes the
“properties” of objects and the “properties of properties” of objects, but not normative ideas about
them.
Just as we cannot prove the existence of God by the meaning of words, so we shouldn’t include these
types of meanings in the definition of concepts. Here I agree with Dr. Parfit’s statement that we cannot
prove the existence of God, but not his conclusion. For I believe that God himself is a word and can be a
concept and although we cannot prove his existence we can argue for it with faith and create faith with
words using a wider definition of what a concept is. In fact, that is what we are doing in the Bible. “For
faith comes from hearing, and hearing from the Word of God.” St. Paul, Book of Romans
What are some similar and differences between Dr. Parfitt’s metaphysics and that of most Christians
and Jews?
A Christian or a Jew that some facts are what Parfitt calls “normative”. We call some of these “Biblical
facts”. If we didn’t believe in them we could not believe that the Bible is a Book of Prophecy talking not
just about the present and the past, but also about the future. We are also therefore what he calls
“Non-Analytical Naturalist” for we believe what he calls “normative clauses” can state truth. And,
therefore,
We are what he calls “semi-cognivists” and not “non-cognivists”. We believe these truths are
“irreducibilty normative”. But, we do not believe concepts and claims with which we state truths are
irreducibility normative. How does Dr. Parfitt define a concept. He believes, like Plato, that “a concept
is the meaning of a meaningful word or words or phrase with the same meaning.” Using this definition
there is such a thing as “The Concept of a Concept”, something that a lot of mathematical logical
positivists, Bertrand Russell, Willard Quine, Gilbert Ryle I believe being some of them, argued for a
century at least doesn’t exist. Some Jewish philosophers and Kabbalists who believe that God is just
the impersonal Name YHWH have argued that this is who The Name YHWH is , But he does not want to
discuss here concepts other than those that refer to “properties”. See Section 24 of Volume 22 for a
more explanation of all of this.
For Christians and Jews, we do want to discuss and believe in concepts that don’t refer to just
properties. Some of these I might name for instance, are the concepts of “goodness”,
“truth”,”equality”,”freedom”,”justice”,”beauty” six of which Dr. Mortimer Adler spend a good part of his
life trying to understand himself and explain to us.
I believe and want to argue that part of the reason I am spending more time discussing “numbers” than
Dr. Parfitt did is that understanding their substance, their reality, their possible expressions or
instantiations in the world and us
Can be a necessary pre-requisite to understand how the above “Six Great Ideas” can be understood
and held inside of us as part of us.
Also, in Volume II Mr. Parfitt in his section 113 Non-Metaphysical Cognitivism Chapter states that “Both
Platonists and Nominalists do not believe that number exist in space and time. But Platonists claim they
exist in some other way, or in some other partial reality. Nominalists reject this”. He then argues against
the Nominalist position, but it is too late, for he has already misstated the Platonist position.
Dr. Parfit does not give a reference for his statement about the reality or truth of numbers with respect
to what Platonist’s believe. But, he does with respect to what Nominalists believe. It is “Science without
Numbers” by Hartry Field. In this book Plato did believe that the concepts of numbers do not exist in
space or time. See the above discussion for what Plato believed about concepts. But, he also believe
that instantiations and the reality of numbers do exist in space and time and in us, as well as the
instantiations of how the concepts of what is good and right exist in us.
And, he, Plato, also believed that if we try to understand better how these concepts are instantiated in
us and become part of u that we, with God’s help, are able to “hold” them together inside of us and also
to hold in us a concept of how these concepts are held in us, this was his idea of who God is, how and
who holds the ideas of these concepts in us, and knows how we know them, even if we don’t most of
the time. For myself, as a Platonist I believe that not only the ideas of “goodness” and “virtue” can be
held by us in our minds and become part of us, but the ideas of “the Number One”, “the Number Two”,
the Number Three” can be held by us in our minds and become part of us.
“We hold these truths” as Dr. Mortimer Adler has claimed and told us he believes in a book title. Dr.
Field does indeed claim that “numbers do not exist in space and time” and he tries to justify this
statement philosophically. To support this claim he gives some arguments and new definitions of terms
in mathematical logic in order to demonstrate what he calls “a” Hilbert Representation Theorem” that
shows that there is a mapping, a “bridge” from numbers as he defines them to integers, rational
numbers, real numbers as they are normally defined using only tautological formulas and his definitions
from nominalistic logic. And, he argues for what he calls a “conservativeness principle” that says that “if
anything in physics or mathematics that is useful, can be proved equally well using this nominalistic
system then the nominalistic system is the system that we should use.” This does not prove or even
argue for, in my opinion, not using our currect definitions and systems of mathematical logic. Nor, does
it argue for or demonstrate in any way that numbers do not have truth in the sense of them not existing
in space and time.
In his book, “Truth and the Absence of Fact” Dr. Hartry discusses Alfred Tarski’s theory of Truth. He
points out that it is defined by instantiation of variables in 1st order logical functions and that there is an
object that the variable denotes if and only if the 1st order function is “true”. Of course, if you take this
as your way of defining the existence of mathematical objects, then which path in all the partial
variables unifications took in the logical predicates’ search to become the object have no effect on
whether it “exists” and therefore there is no “meaning” associated with the objects existence. Here is
the heart of the problem with this type of logical philosophy of mathematics.
In another essay, the next one, in the same book Dr. Hartry does try to argue for the importance of
“mental representations” as a way of explaining how we “believe” in things existence, but when he
names these representations only ”dispositions” and not “facts” or “evidence” I part company with his
dictionary of terms. Aren’t these “mental representations” actual “knowledge”? Where does what most
people believe exists and call “wisdom” fit into his scheme of conceptual understanding? Modern day
expert system logic programmers would call his “mental representations” the “evidence of things not
seen” when it exists in one slot of a 2nd order backward reasoned logical predicate. And they would call
it “facts”, the substance of things hoped for when it exists in the 1st slot of the 2nd order predicate.
When it exists in 2nd order object oriented forward chained logical predicates they would call it what he
refers in passing but does not discuss significantly as “structuralism” or “structured Platonist thought.”
It is not ridiculous to say that Plato “did not believe that number or numbers exist in space and time”. It
is just spiritual misleading and not justifiably philosophical except through tautologies. If he didn’t
believe it he wouldn’t have put them in patterns on the pages of his book Timeous in order to outlast his
own mind and help us 1000 years later illustrate how God might have created the Universe using them.
What we have to explain in order to explain how Platonist’s believe numbers exist in space and time is
how they believe that they exist both in the material world of space and time and in the mental world of
space and time inside of us. To take the Nominalist position that “numbers do not exist in space and
time” is equivalent to take the position that mathematics is not about reality, which most thoughtful
mathematical philosophers including Platonists reject. Not separating out Platonists from Nominalists is
the source of this “grave” ontological error. In terms of theology it is equivalent to saying that God does
not have an incarnated unique Son, which is the “Logos” or instantiated Rational Word of God.
In the reference quoted, “Platonism and Anti-Platonism” by Mark Balaguer quoted as a source of this
statement, Platonists do not believe that numbers exist in space and time” the author gives his
definition of what a “Platonist” and an “Anti-Platonist” is with respect to mathematical entities the
above statement is claimed to be the main part of the definition of what a Platonist is…ie one who
believes that numbers do not exist in space and time. With his definitions the author claims that “both
Platonism and Anti-Platonism are workable philosophies of mathematics.” But, I doubt that. He defines
what he calls “object Platonism” as the view that the mathematical realm is a system of abstract
mathematical objects such as numbers and sets, and that our mathematical theories, such as number
theory and set theory, describe these objects. Opposed to this he claims is the view structuralism, that
sees our mathematical theories not describing forms of particular systems of objects; they are
description of abstract “structures”, where a structure is something like a pattern, or an objectless
template. I guess here he is referring to what we now call in mathematics “categories” as the structures.
He relegates the dispute between “object platonists” and structuralists to an unimportant role in his
book. But, by not allowing “struuralism” into Platonism as a part of it I claim he has left out
mathematical reality itself. I do not think we ought to believe that the property of having only structured
properties is itself a non-structural property. And, I believe this because I do believe there is something
called the “meaning of meaning” and that it exists in itself independently using its properties as part of
its identity.
In his book Mark Balaguer lists several types of philosophy of mathematics conveniently leaving out the
one I believe Plato held. Under what he calls anti-realistic anti-platonism he includes “conventialism”
which Henri Poincare espoused and which holds that mathematical sentences in propositional logic
which are analytically true, such as 1+1=2, or truie only in virtue of their meaning, true and only
analytically true. I would call this anti-realistic, but not necessarily anti-platonistic.
He also lists “deductivism” which hold that there are such things as “mathematical truth” not just
“mathematical meanings” and that they can be stated in the forms of syllogistic rules such if A then T
where A is an axiom or conjunction of several axioms and T is a theorem provable form the axioms. I
would call this philosophy both “ realistic” and “platonistic” because Plato believed in syllogisms as
sources of truth.
And, he dicusses Hilberts “formalistic” philosophy of mathematics in which propositions and syllogisms
are “true” only in virtue of belonging to and provable in a particular formal symbolic system. So, Hilbert
would say that the analytic statement 1+1=2 is true not in virtue of the meaning of its symbols, but
because it is a theorem provable using the symbols of Peano Arithmetic. I agree with Balaguer in calling
this philosophy of mathematics “anti-realistic” and “anti-Platonist”.
Balaguer concludes in his book that he doesn’t think we can ever discover epistemologically whether
mathematical objects fit into the sets or structural categories of thought associated with what he has
self-defined as Platonism and Anti-Platonism. I agree that right know I don’t think we know what we are
talking about when we talk about mathematical objects. But, I believes, like Plato says in his dialogue
Meno, that it is possible to set out searching to understand what concepts are and what the concepts of
mathematics are, even though at the start we don’t know this.
Did Plato believe that numbers can exist as “persons” inside of us. The answer is yes if you define a
“person” as someone who has an individual mind, either self-existent or existent with God’s help. This is
close to how most people would define angels, the bad angel persons are those who choose to create
themselves only through themselves. If you are a divine being whose name has a number in it you
cannot lose this part of you. For instance, if your name means #1 faith, or #1love, or #1 hope and you
lose yourself, just affirm to God inside of you what the atheist Betrand Russell used to like to say a lot
“No mind, no matter, no matter, no mind, I AM a spiritual being.” That part of the substance of your
being which is faith and the evidence of things not seen will recreate itself. Or, if you are a Christian
Jew you can affirm the Bible verse Jesus Christ taught, “Whosoever loses himself for my sake shall find
himself.”
How can God give angels ethics? This is the problem of how He can create their acts, their motions in
mind and in body, whether a spiritual or human body to match up with their acts. Not something that is
easy to do. Most of Plato dialogues are about the philosophical problems of understanding how to do
this. Plato was and still is a dualist, he believes both of our minds and our bodies exists separatedly,
possibly as separate substances and body. His writings indicate that Plato believed both that God,
divine ideas and angles and numbers could exist within himself in many different forms, but his books
do not support the idea that Plato believed they could exist as One God, as One indwelling Holy Spirit in
us. He believes in human Saints along with divine angels that exist separately, but possibly not as One
mind and act inside of a human divine spiritual combination of different substances.
Moses believed and still believes as a Saint in heaven that God can sanctify our acts to the point in
which we human become human vessels of God’s prophecy. Moses believed like Plato that God was
inside of himself, but he also believed something that Plato didn’t…. that God is a One inside of himself.
Perhaps that is why so many Jews and some Christians believe that he is a Saint in heaven nowadays.
There is a slightly different metaphysics which St. Paul believes in outlined in his New Testament letters
to fellow Christians, hence we have the current separation of the religions of Christianity and Judaism,
not because of anything God has done or willed, but because St. Paul and St. Moses have never have a
good enough dialogue with God’s help in order to help us all understand how this might happen. What I
am trying to do, through invoking St. Andrew’s and God’s help, is to get them, St.Paul and St. Moses to
talk to each other more in order that this may happenOf course to get this to happen we have to believe
first like I do that there is only one heaven up there for both Christians and Jews. It seems to me both
the Catholic and Protestant Churchs have failed us in not explaining this sound and rational theological
teaching to us up to this point.
.And, we can’t use any traditional belief that Moses is not a Saint to justify not doing this. For, most
Christians if not Jews need to believe that even if someone’s soul is only saved not completely
sanctified yet that it is possible to go back in time with God and Jesus Christ’s and the Holy Spirit’s help
to help them become one.
Even if you argue that Plato believed that the idea of Number, is only a metaphysical spiritual possibility,
Plato most certainly believed that this idea exists, in terms of being able to be “instantiated” from the
mental realms as a reality in the material and physical realms of “object oriented” ontology.
Computers and computer programs, for example, give a tremendously important example of how
knowing how that numbers have a reality in space and time can influence our lives. We didn’t
understand how to do this, how numbers are already encoded in nature by themselves, recursively,
aseitically, and how to encode numbers in nature ourselves, a thousand years ago. This is a pre-
requisite for understanding how they, themselves, are real. We used poorly thought methods of the
Roman and Greeks to represent them, add them, multiply them, divide them. We didn’t know how to use
zero as a place holder for decimal digits. We didn’t know how to connect the structural, object oriented
way we represented numbers in different base systems to the concept oriented algorithms to be used
to multiply, divine, add, subtract them. We didn’t understanding how knowing what limits of numbers
are themselves numbers gives us a calculus of numbers that encodes information about how electrons
in atoms moving in circuits can be magnetically move in order to store data, which is in”form”ation,
“form” held inside of “form, “idea” inside of an “idea”, “mind” inside of a “mind”, a concept held inside
of a concept, even as God is the “seed” that generates knowledge of himself inside of him or herself,
even as the number one, being being and non-being generates the number two, even as all of this is
knowledge, about numbers held together with numbers .
Otherwise we would have had digital computers back then. But, also, one recent discovery, other than
computers, that gives a factual reason based argument that numbers exist in space and time, is called
Benford’s Law. Benford’s Law gives the actual real probability distribution of integers and real numbers
if a random sample of them is drawn statistically. Just like the height of humans and the IQ of have a
certain probability distribution, so the set of integers occurring in reality has one. Here we have
appealed to the definition of reality that it is something that “kicks back” or in order words can be
sampled and questioned repeatedly giving similar results. Just like you assume if you conduct an
experiment repeatedly and it gives the same result, than you result has a “real” physical interpretation.
It was observed in many statistical tables occurring in different settings throughout the last century.
But, it wasn’t until recently that my fellow UC Berkeley Math. Dept. graduate Theodore Hill supplied a
proof of the law and gave some very practical examples of how to use it, ie to catch people fabricating
data in order to cheat on their income tax returns.
Another fascinating way that numbers are “encoded” in nature has to do with the subject area I wrote
my mathematics doctoral thesis on in 1974. It is the sub-subject area of mathematics called “number
theory” called the “geometry of numbers” invented by the German mathematician and predecessor of
Albert Einstein as a German mathematician, Hermann Minkowski. Einstein used the four-dimensional
space-time metric (+,+,+,-) that Minkowski and Lorentz studied in order to create and prove theorems
in the Special Theory of Relativity. I wrote a Phd thesis in 1974 at UC Berkeley on how the Russian
mathematician Georg Voronoi proved theorems about the denseness, and hence efficiently of higher
dimensional sphere packings using a way of looking at them in terms of deformations of lattices of
higher-dimensional polytopes.
In elementary geometry, a polytope is a geometric object with "flat" sides. It is a generalisation in any
number of dimensions, of the three-dimensional polyhedron. Polytopes may exist in any general number
of dimensions n as an n-dimensional polytope or n-polytope.
By considering these densest sphere packing we can come up with numerical codes that correct errors
in digital communication channels more efficiently and hence better to use to transmit signals over
longer distances.
My thesis is entitled:
“On Voronoi Reduction of Quadratic Forms”, UC Berkeley 1974
and you can access it online from our yhwhschofchrist.org website
http://www.yhwhschofchrist.org/5073/THESISPT1.pdf
http://www.yhwhschofchrist.org/5073/THESISPT2.pdf
http://www.yhwhschofchrist.org/5073/THESISPT3.pdf
"http://wThe ww.chofchrist.org/5073/THESISPT1.p5073/THESISPT
The “numbers” that are encoded in nature using these densest sphere packings are not only ordinary
integers, rational numbers, real numbers, but what are called “algebraic numbers”. What engineers and
physicists call Complex numbers are a special case of “algebraic numbers”. And, understanding and
using them mathematically to solve physical problems can be very useful to understanding and dealing
with nature.
The various scientific, philosophically versions written by logical positivists say that
“Number or numbers do not exist in space or time”. This is the same as to say to us that whenever we
read books and try to understand them, we should not pay any attention to the page numbers. Yet, they
claim that their philosophies are “rational”. Do they not understand that the word “rational” itself comes
from the thinking about “ratio” of two numbers, which is a new number, with a new reality, created by
God and us as we combine the “ratio” of two already existing thoughts about two older in God’s and our
human divine order of space-time created, pre-existing numbers?
I would agree that in Plato’s time numbers were thought of as existing in the mind more than in space
and time. But, nowadays, if they are any Platonists still alive, and I think they are, I don’t see how
anyone who lives and works with mathematics and computers all day, computers consisting basically of
physically hardwired representation of 0’s and 1’s in shift registers and disc memories could not but
believe that these 0’s and 1’s exist in space and time. Numbers, nowadays, play a tremendously more
significant part of the physical universe we live and work in today then they did 100 years ago and the
logical positivists, came up with their eccentric metaphysics claiming they “do not exist in space and
time” and don’t have anything to do with “what matters”, what “reality is”. Remember we are talking
about reality as what “kicks back” and “influences us”. And, computers and the numbers in space and
time inside of us them do influence us more than 100 years ago.
The solution to the dilemma that logical positivists pose to make us think mathematics is not about
reality, is contained in understanding more clearly how Plato thought about numbers. The dilemma is: “If
mathematics exists in a heavenly eternal condition and realm of forms or ideas which are separate from
everyday reality in our temporal lives, how can these ideas or forms participate eternally in the temporal
realm, when the logic, ontology, epistemology, the way we know it, understand it, eternal life, is
different from the way of everyday existence?
The solution is to understand that eternity, and the mathematics of it, is not a fixed structure, but what
remains the same inside of that divine and eternal structure of form eternally inside of the temporal
realm. And, this involves theology, not just natural science and physics. Plato believes in us, even
though it is a difficult task trying to understand how this unity exists inside of diversity, and not
excluding this part of the metaphysics and epistemology from our discussions. The dialogue Parminides
is his deepest attempt to try and help us “go there”.
If we think of Plato’s concepts as classification type expert systems, something Plato started out as a
process to undertake in his dialogue Theatetus, then the unification algoritm of our robot’s or human’s
compiler acts as the means of realizing eternal unity inside of diversity in our knowledge and
understanding and wisdom. We have explained above that there are two types of this eternal computer
mathematics unity…One comes as we run forward, “hopefully’, in an object-oriented, forward chained
data grabbing search…and One comes as we reason backward, in a goal-oriented backward chained
using “faith” or the instantiations not from “facts” and the partial metaphysical instantiations already
arrived at that we have “hoped” for
Our computer keeping its search up until it halts with the result it has been given to achieved or there
are no longer any possible instantiations for it to make.
Are both these ways of achieving “unity in diversity” the same? No, these are two different ways,
methods, that result in two different “ethics”. But, they can be “one” way, “one” truth if all the
assumptions and conclusions of the rule-base that the robot or human computer uses are both
“humanly” and “divinely” ordered by a topological sort in a finite knowledge network that has a finite
set of given ending and start nodes. Then we do not have to worry about the robot or human “stopping”
or halting in its questioning, getting answers from us and the environment, before it has exhausted all
its possible questions. Of, course, this assumes that the designer of the system, God, he who has
designed its concept of a concept that it uses to make new rules, has put enough of them, enough
questions for it to ask in its rule-base.
Human history, argues that we won’t be good enough to achieve this. But, the fact that we haven’t quit
trying argues that our faith and hope in the every improving “Totum Bonum” and the “Summan Bonun”
that what our ideas of God are, not our idea of the computer in us or the robot, and His or Her Name is
will keep us going forward and making a lot of progress.
How can it be that numbers exist in space and time in computers, and not in “us” inside our minds? We
are the people who created the computers using the already existing numbers inside of space and time
in our minds.
The reason that some philosopher who have lost their faith in God don’t people that numbers or the
idea of number exists in space and time is that it is so hard to understand how they exist there. That is
why it took us so long in order to figure out how to create computers. We had to understand Boolean
Logic, electricity and magnetism, the idea of a mathematical function or algorithm, before we had a
chance of doing this. And, these ideas are not self-evident, it took us thousands of years to understand
them. But, when we did, understand how God, the creator of knowledge, exists in numbers and numbers
exist in God our creator of knowledge, then the whole world we exist in took a quantum leap forward in
time in terms of what humans can be expected to know and to do and can be expected to do and know.
God without Number, is like God without Man, he still exists, for He is self-existent, but He is not in a
very rational or very good situation. Similarly, Numbers without a God and humans to create them would
not have come as far as they have dwelling in space and time and us.
Which philosopher’s would argue that animals understand what the number infinity means? If there are
any, we don’t want to study their books. Just knowing how to repeat an action without ever stopping, an
infinite number of times, is not understanding what the idea of infinity is. That is the definition of
insanity when you don’t know what you are doing. In the last few decades we have figured out how
robots can (ie understand the number infinity ) and that is frightening enough. It means robots are
higher up on the intelligence scale than animals, even if we haven’t figured out how to explain God and
ethics to them yet.
So, given that we believe it is important to try and understand both the concept of “God” and the
concept of “number” as part of “One Concept”, how can we know and Number and Numbers and then
know God, and better?
One way, starting off from Number and Numbers, is to study what Aristotle
Called their “Totum Bonum” and “Summa Bonum” starting off with the idea that “Bonum” or Good
means what exists for its own sake. If they do, and we have just given some reasons to argue for this,
then how do numbers exist for there own sake?
This was basically a problem of Boolean Logic asking how could a “recursive” or “regenerating”
“function” be defined to self-generate in terms of its data, its variables, and itself. At the beginning, in
writing the operating system for the computer, there was “One” such basic recursive function, and,
surprise, we call it the function “One.”, the “Number One”. Just, as in the beginning there was only
“One” Platonist. I mean here, in the beginning of Plato, there was only One Plato made by God in the
image and likeness of Himself and our friend Plato’s own past and with a divinely created Eternal soul.
But, now there are many different Platonists, and many different computers defining the number one
differently. it differently. And, the same computer can “boot up” various versions of itself in its
programs and operating system using different copies of this number ‘One’ function. Wouldn’t it be an
interesting question to try to understand philosophically how this mathematics affects the “ethics” or
robot and human societies? I think some of us have already started that task.
Most current philosophers understand that we are living in an “information age”. And, the key to
understanding that information, and understand how to represent knowledge of it is “numbers and
mathematics”.
Dr. Alain Badou’s books on metaphysics and ontology are focused on understanding, given that we
accept that “numbers” are important and real”, what kind of numbers are there? Which numbers are just
possible, if any, and which are real? Moreover, logical Truth, scientific Truth, religious Truth is consider
a clear enough type of entity that we can ask how it exists in an ontological sense. Anyone who has
written computer programs know that when they tell you something it is true in some sense. Also, a
scientist who conducts experiments in nature and not on a computer also understands that these
experiments give information about his theories which are truthful and have consequences about the
truth of the theories. An ordinary person living his or her life day to day has experiences that his or her
sense tell them that are “factual” and hence truthful in some sense. Most mathematicians nowadays
can give you different examples of different types of numbers, 1) positive integers, 2)rational, irrational,
negative integers, 3) what people who do Calculus call “real numbers” or those which are “limits’ of
sequence of numbers in parts 1) and2) , 4) what advanced mathematical symbolists call zeros of
polynomials with coefficients defined over a “field “algebraic numbers”, transcendental numbers or
those real but not algebraic. 5) the game theoretic numbers of Drs Conway and Knuth that were
discovered after the use of Boolean-Valued Mathematical Logics in order to to prove the independence
of the continuum hypothesis*.
So, in conclusion, to summarize the main argument of this review, mathematics is about reality,
therefore mathematics is about ethics, therefore Judaism, which is more about ethics than beliefs, can
be a part of our common Christian Jewish theology. Judaism which is about keeping faith with our
actions toward others, and Christianity which is about keeping faith with our faith toward others, can
help each other in this process. This hopefully will happen more if we make it clearer how computer
science and robotics enable this and we understand more how mathematics can be reality.
* For more introductory details on how to understand these different types of numbes we have the
reference “What Numbers are Real ?” Published by the Mathematical Assoication of America
So, contrary to what Dr. Parfitt says Plato believed, we mathematicians now have at least 4 different
mathematical logical ways in which numbers can instantiated themselves in space and time and exist.
One wonders whether it is a coincidence that space and time also has 4-dimensions or directions in
which it can instantiated itself in the world? To look at things this way of course you have to take a
spiritual view point from which to observe the matter and mind realities we are talking about.
REFERENCES:
On What Matters, Volume I and II by Derek Parfitt
Our Mathematical Universe, Max Tegmark.
Artificial Intelligence 3.0, Max Tegmark
The Importance of Quantum De-Coherence in Brain Processs, Max Tegmark, Science
Consciousness as a State of Matter, Chaos, Max Tegmark, Solitons & Fractals, March 2015.
What Numbers are Real, Michael Henle, MAA
The Nature of Mathematical Knowledge, by Philip Kitcher, 1984, Oxford University Press
Number and Numbers, Being and Event Alain Badiou
Philosophy of Mathematics, Structure and Ontology, Stewart Shapiro
Phi: A Voyage from the Brain to the Soul, Giulio Tononi
Consciousness as Integrated Information: A Provisional Manifesto, giulio Tononi
Integrated Information in Discrete Dynamical systems: Motivation and Theoretical Franework, Giulio
Tononi
Sefer Yetirizah,The Book of Creation by Aryeh Kaplan
Andrew Harrell, "Implementing Mixed Chaining in a Classification Type Expert System", Proceedings
11th U.S.Army Conference on Applied Mathematics and Computing, Carnegie Institute of Technology,
Pittsburg, Pennsylvania, 1993.
Andrew Harrell, ‘Concept of a Concept, Parts I & II” discussion board science and religion
subdirectory, yhwhschofchrist.org, 1982
Andrew Harrell, “On Voronoi Reduction of Quadratic Forms”, Phd Thesis UC Berkeley, 1974
Science Without Numbers, Dr. Hartly Field
Truth and the Absence of Fact, Dr. Hartly Field
Platonism and Non-Platonism Mark Baleguer
Six Great Ideas, Adler, Dr. Mortimer
Parmenides, Plato
Surreal Numbers, D.E. Knuth
The Republic, Plato
The Meno, Plato
The Amplified Bible, YHWH
Article #333Add/Reply to this discussion board posting
Subject: Can Robots Repent?
Author: Andrew W. Harrell
Posted: 10/19/2017 10:07:03 PM
Once we understand how to give robots the capability for ethics, we have the theological problem of
how to give them the capability to repent.
How is repentance possible in the scheme of Robotic/Human Intelligence that we have outlined the
beginnings of?
Is it, in fact, possible for a robot to repent?
We certainly don’t understand how to do this now.
In his recent article for the Jewish Review of Books Abrahm Soker briefly outlines the two main
philosophical positions with respect to trying to define repentence as something philosophic, and hence
ethical, and hence more than just something theological.
He discusses a theory of repentance either as the Jewish philosopher and theological Moses
Maimonides has explained as having to do with the restaining of the will through obedience to habitual
rules and ordinances, with the power to accomplish it coming from our higher power, God.
Or, there is an Aristotelian system of natural ethics which presupposes the development of a human
ability which helps God to help us accomplish this. Christians normally call this “helper”, an indwelling
Divine Holy Spirit, and believe it has Oneness and Truth and “Goodness” in its instantiation in our souls.
As we have started to explain in this book, our ethical acts can be understood as an artificial
intelligence forward chaining robotic production. Considering the dichotomy of individual non human
helpers available to Christian human agents as divided up into robots and angels. Angels, being only
messengers are not available to assist us much with the action part of our ethics. So, robots should be
able to be useful here.
Beliefs can be understood as a logical 2nd order part of our and robots ethics which are backward-
chained from an always faithful adherence to our starting goals.
The axioms of a logical system inside of us or the robots are only a 1st order primary part of the
knowledge production system which provide 1st order rules and ordinary are used to satisfy the 1st part
of logical syllogisms, or back up subsequent invocations of assumptions in the secondary parts of the
syllogisms.
For Abraham Soker, repentance happens when we close the gates of alternate directions in our prayer
meditations, thinking.
One way of understanding this philosophic viewpoint about how repentance happens is outlined in the
Buddhist scripture, “A Better Way to Catch a Snake”. If you think of our souls as birds caught inside of a
house, or as Plato envisioned inside of a system of paths in a cave, and God inside of our souls as the
owner of the house then one way to help the poor birds escape from the house or cave is my closing all
the doors or passageways that don’t provide the best route into the outdoors which is open and full of
bright sunlight. If we provide our robot with search rules that allow it to investigate only ethical
solutions to its problems, then when it fails to reach the goal with one search pathway, it must “repent”
or with God’s (the particular unification algorithms of the robot’s computer compiler that we have
installed) go back to the next level of beginnings in its thought, using other already existing facts in its
database in order to be able to finally solve and provide all the alternate possible ethical solutions to its
environment and progressively betterment of its and our situation.
In contrast to this approach there is a Christian Science type of theological and ethical way of thinking
and repentance that alternatively affirms and denies possible search pathways using our own human
transcendental faithful natures, a Son of God inside of the unification algorithm of our’s or the
computers uniquely experienced spiritual thoughts and abilities.
Article #334Add/Reply to this discussion board posting
Subject: You should do the right thing
Author: Andrew W. Harrell
Posted: 10/23/2017 01:24:25 PM
So, to summarize again,:
Saying "You should do the right thing, you should believe in God and listen to Him, saying it to humans,
humans and humans, robots and humans" Is not where religion goes wrong,
but when and where it is in the right.
Article #335Add/Reply to this discussion board posting
Subject: future book out of this discussion?
Author: Andrew W. Harrell
Posted: 11/26/2017 02:36:24 PM
The above notes and comments hopefully are the preliminary part of a short book which hope to edit and
publish in about year.
Any thoughts and comments on this important and interesting topic of discussion from others would be
greatly appreciated and incorporated in the finished text.of the book.
Article #349Add/Reply to this discussion board posting
Subject: Review of the Book “Wittgenstein’s Lectures on the Foundations of Mathematics”
Author: Andrew W. Harrell
Posted: 6/7/2018 01:53:45 PM
Review of the Book “Wittgenstein’s Lectures on the Foundations of Mathematics” Cambridge 1939
Edited by Cora Diamond
As Wittengstein says in these books have to do with trying to understand what it means to see
something as something. He was especially interested in trying to “recognize this thing as a
proposition” with signs as a part of our human discourse and language. He claimed in part of the books
that these recognitions should lead to most of the questions philosophers have usually asked. He
didn’t want us to use an ideal language but an improved more exact one. He claimed that our ordinary
use of language conforms to an acceptable degree of exactness only in rare cases. I don’t agree.
Wittengstein does not believe in considering the meaning inside of meaning to be a part of reality. For
him concepts are empirical language games which are verified in a transcendental and logical world
which is not empirical. They are verified using rules of language,but there is common set of language
rules for all of human kind. This has consequences which conflict with what Plato and I believe, that
there is a common set of language rules that define what great ideas like goodness and mercy mean as
we all try to understand them.
Modern advances in the artificial intelligence of neural networks used as, feed forward and feed
backward perceptions, tend to support his approach. This is because this software, these machines do
use symbolic representations of what they recognize, but recognize them in a cross wired encoded
system of non-conceptual neuronic physical matter.
But, even more recent advances in this software have demonstrated the important of “deep”
intermediate layers between the input and output encoding and decoding of the symbolic
representations. These “conceptrons” have quantum consciousness tensored high information ,high
entropy content learning and operating inside their own recurrent structures. Cf Buduma and Locascio.
In order to have this we first have to have a common set of rules that define what the concept of
number is. Do these rules define uniquely what number is? No. And, we know, for instance, that
currently there are many different types of rules which define many different types of numbers, all of
which we would like to think are real.
Wittenstein says in these two short books of his lectures that he is proposing to talk about the
foundation of mathematics in as much as it deals with the manipulation of mathematical symbols.
Occasionally, he says, he will come up with new interpretations of what he is talking about, not that the
new ones are not equally arbitrary as the old ones. He will only deal with puzzles that arise from words,
such as proof, number, order, series. To understand a phrase, he says, is to understand its use. But, yet,
he has already said, that he does not believe that mathematics is connected to reality, or useful. What a
paradox? The word proof changes its meaning as the rules used change. To this I agree. It also changes
its meaning as the order that we apply these rules are changed. But, Wittengstein omits consideration
of some ways of ordering the rules that determine how we are to think, I think. He does not explain how
we can think backward with his rules in order to faith in what we have not yet understood to be
ultimately understandable.
Plato already understood this, as anyone who studies and understands his famous dialogue Parmenides
can see. It is concerned with what common rules we need to understand what the concept of Oneness
is. When Wittgenstein was giving his lectures at Cambridge it was just the beginning of the age of
computers and information. And, computer languages were just beginning to be written. Those that
wrote the first ones came to understand how important it is to understand how languages “unify” and
“instantiation” variables in a particular way that defines the Oneness that the computer uses to come to
progress forward in using its intelligence and reason to prove theorems, do procedures, map variables
using using variable arguments in 1st and 2nd order logical and arithmetical functions, in order to
complete the work of its programs.
Wittengstein, in his lectures on the foundation of mathematics objects to how Frege defined number.
He didn’t want to think about number as being defined by the property of a property. He only wanted to
think about it like the atheist Bertrand Russell did as the number of objects in a set being determined by
the sum total of
All the properties determining the elements in the set, not the properties of the properties determing
the elements. He gives the argument, suppose we have a set of objects, real numbers for instance that
we want to determine the number of.
Cardinal numbers? Is it endless? He wouldn’t say so, even if it is impossible to do Calculus without using
this as a axiom. He would have to consider such a fact, outside mathematics if he was to use it. And, in
fact, this is an enormous claim he is making here that in effect declares mathematics not to be about
reality if you don’t use it or admit it for use.
If we talk of an experiential proposition, or a word, we can as Wittengstein say a reality corresponds to
it. What reality corresponds to the word, “One”. Philosophers and mathematicians who are philosophers
and theologicans have been trying to figure this out for several thousand years now. And, we have made
some progress, haven’t we. We have fallen short when we try to define the concept of it as a set, an
object, as a structure, but not I claim if we try to understand it as a category of thought, which is a goal
to reason backward in wisdom and understanding of our experience in order to understand and know.
Let’s keep on trying.
d
Communicating the meaning of numbers and words to others, understanding the logical definition of
the terms we use and hence being able to communicate that meaning back through them to us is
important. The reality of the environment of which world, which context, the definition of our numbers
and our geometric object exists must play a part in the way we construct there existence and this
existence must be constructed in a way that takes into consideration all the different ways we might
construct them in these environments. At least this must happen if we want to be able to say we are
understanding them the way God is. But, the way God seems to see them is a viewpoint that is
constantly expanding as we humans understand more and proceed into a bright future with Him or Her.
Is it better to give up and say we shall never be able to understand all of this rationally. Or, is it better to
keep on going like we are going, changing for the better as we understand and learn more? I hope you
are in the later camp, or at least admit the possibility of ending up in it if you aren’t in it now.
To not use this fact and claim that we don’t need it is in effect to claim that human knowledge as far as
mathematics is concerned doesn’t need it. It is to claim that our present form of logical systems used
by mathematicians can solve any problem they are faced with that humans can. But, thanks to
Professor Godel we now know both Wittengstein, Russell were wrong about this fundamental assertion
of logical positivism which says that what mathematics is talking about nowadays and in the past is not
reality and that numbers are only constructed out of knowledge that is made up of logical tautologies
and there is no why, no meaning that we can understand about their usefulness to us only to trust in the
accuracy of the experts in logic in order to evaluate the correctness of our mathematical conclusions. It
is to say that we can’t expect divine help in understanding mathematics, because God is not a
mathematician, and in effect to say that because he isn’t a mathematician he doesn’t exist. I AM humbly
but firmly called to differ with them about this, for I believe He dwells in , Andrew W. Harrell, as a Holy
Spirit, and He is a mathematician.
Oneness for Wittgenstein is what all the different “instances” in a logical formula or sentence about
empirical data have in common. For Plato, Oneness, is also a kind of Truth that can hold in a world of
divine ideas as well as on earth. And, for Plato, even Aristotle, Oneness when it exists independently in
us or the World, independently , of outside influences to the nature of its existence or non-existence, is
beautiful and Good in itself.
For us humans as well as some computers this former type of Oneness can exist faithfully or reasoned
backward logically toward and from a goal. Or, it can exist hopefully or reasoned forward from current
facts, chained together in a series of logical variable instantiations in procedures and axioms.
How did Wittengstein and the logical positivists believe that mind and matter are instantiated together
in us individual and collective human intelligence? This is one of the greatest problems not only of
modern philosophy, but also of ancient philosophy. Many philosopher ancient and recent believe that we
cannot understand how we know things in a forward or backward chained together manner both our
minds and our physical body simultaneously. But, some of us recent philosophers believe that it is
possible to have what Kant called “synthetic a priori knowledge” that is not just “tautological” or what
we would want to call “essentially trivial.”, having no practical use that can be demonstrated beforehand.
Now, through the tremendous advances in understand how computers and us can think there are many
ways to explain how this can happen. I hope to explain a few of them in this paper.
Modern schemes of computer learning through perceptrons, in the 1960s, 70s, 80s, and 90s can been
augmented now by computer learning through what I would call “conceptrons” for the reason that the
neural networks they use have a “deep learning” part involving meaning inside of meaning, and which
can result in ways of understanding things which we should “call” concepts because of this new
capability. In the input to the neural network there is a 1st level part that understands how to recognize
what it is seeing or hearing, then there is a intermediate deep level part that has what we call “recurrent
neural network” learning inside of itself before the final output level of the thinking nework is reached in
which the conclusion of our thoughts are encoded back inside another symbolic representation in the
network of what we are talking about, in order for it to be referred to in other “thoughts” of a larger
knowledge network of mental concepts and thoughts.
In these “conceptrons”, the middle layer can be simplified from a matrix to a row of vectors, then a
“tensor product” of the vectors constructed in order to create enough entropy in the information
content of the middle layer. This matches up with the new Qauntum theory of consciousness which also
uses tensor products to create and break down the analyzing of the networks. We already know from
study the tensor products that occur in the matrix representations of our Quantum theory of atoms that
this approach is already studied and well understood mathematically.
These new conceptual neural networks have meaning inside of meaning stored in them and hence can
be used to try and understand how humans think about, perceive, remember, understand, self-create
great ideas like “goodness”, “justice”, “truth”. “God”. “Love” and how these great ideas affect our
emotions, of fear, pain, anger, etc. And, using these new conceptual structures as a way to understand
consciousness we will undoubtably we able to understand better how we self-identify with ourselves
and others.
If mathematics is only made up of tautologies for axioms, then it is just the “invariance under change of
notation.”
I believe, in order for numbers to be defined as a reality in us and the world, they must be defined in a
structure of how we understand what consciousness is.
We must understand how they become an existence, how they “matter” to us and the world and others.
And, this, I think requires the use of a mathematical theory of conceptual structures and how these
structures, or objects, can be stored and remembered in our minds along with the logical functions and
procedures in our consciousness that our minds use to store, recall, and manipulate, add to, subtract
from them.
Once we do this, we will be able to understand and control and use our humans emotions, through
thinking, meditating, self-realizing or self-instantiating them better than we now can. We will be able to
understand how we can be “touched by angels”, and how we can better communicate with God, and
even “self-create these mental angelic beings as part of us and the World around us”.
Wherever there is “fullness of understanding in Christ”, there will be change and movement in objects
and things around us. And, wherever there is change in one of us, there is often also change in others
of us, living with us and around us. This change and mental movement in Christ can be impersonal and
also personal. How does it happen? One way we know is through study, hearing, putting to use, and
understanding of God’
When we can better understand how God and angels can touch us in our bodies and minds, We will
better be able to share an understanding of joy, compassion, understanding, loving kindness,
equanimity with ourselves and each other.
Words, through faith and hope, that appear in the Bible and elsewhere in us and around us. But, why
should we Christians also be prohibited from trying to understand how it happens in us, starting and
continuing in us, as well a happening starting and continuing in God.
When we can better understand how God and angels can touch us in our bodies and minds, We will
better be able to share an understanding of joy, compassion, understanding, loving kindness,
equanimity with ourselves and each other.
Dear God, Day by Day, help us to understand you better…in order that we can love you more dearly,
follow you a little more nearly. This is my prayer, St. Augustine’s and mine.
Please say Amen.
References
Ludwig Wittenstein, The Blue and Brown Books
“Wittgenstein’s Lectures on the Foundations of Mathematics” Cambridge 1939 Edited by Cora Diamond
Budema and Locascio, “Fundamentals of Deep Learning”
Article #350Add/Reply to this discussion board posting
Subject: more thoughts on this subject
Author: Andrew W. Harrell
Posted: 7/9/2018 06:27:44 PM
SCIENTIFIC HOPE VERSUS INTUITIVE FAITH AS A BASIS FOR ETHICS
I believe in order to have a philosophic system of ethics:..human, divine, robotic, your ontology ,or your
definition of reality, has to be monistic.
There has to be a way in which things are either good or evil in a “real or instantiated” sense. The
instantiation can be natural or material , psychological or logical.
And, your theory of knowledge or epistemology has to have the capability to be “dualistic” in the sense
that your knowledge system of instantiation has to be able to know whether things are “true” or “false”,
but not necessarily logical. For Truth is not necessarily the same as ethical “Goodness”.
Also, the ground reality of your epistemological truth has to be factual in the sense of a rational
propositional fact. The instantiation is usually material, empirical or natural, reasoning forwardly or
hopefully. But. You also have to have the capability to instantiate facts or postulates in a non-material
non-natural sense working backwards, faithfully.
As an example of a theory of ethics which has only “natural facts” which can be instantiated is
Spinozas. In his he starts off with natural and scientifically knowable facts and reasons “backward”
faithfully, and not forward, hopefully.
I claim that Spinoza’s ethics is “God’s ethics” while the more common form we were talking about
before it is “human ethics”.
“Spinoza makes intellectual purification an important goal in pursuit of human happiness.” For him the
question of “What is Truth” in our intellect is the only goal worth pursuing. To understand this, he
postulates 4 modes of cognition.
1) indirect hearsay information
2) random or vague sense experience
3) causal inference
4) essential intuitive knowledge
Spinoza, like Plato, believes that we have an innate intuitive intellectual instrument that is self-evidently
knowable
Virtue is knowledge knowable as power and not as value itself, as Aristotle believed.
Will and Intellect are the same thing, the same reality.
Goodness is not value in itself, but that which we know to be useful.
A “free man” is one who lives solely by reason. And, reason is the way, the free man with God’s help,
sets himself free.
God is the first cause and the origin and the source of nature.
In order to define things we need to
1) be particular as possible, ie not abstract
2) formulate the rules of definition in a way that the essences of things are evident.
3) These essences are either of created (defined in terms of proximate causes) or uncreated (defined
in terms of itself or themselves0 things
Both, Spinoza, and also Descartes are “dualist” in the sense that they believe in “intuitive knowledge”.
But, for Descartes and Spinoza “intuitive knowledge” is based on what is called “a priori synthetic
knowledge” by Kant, later “noetic knowledge by parapsyhics. For, Hume these type of interior facts are
called “qualia” not “a priori”. For Spinoza they may or may not be.
Spinoza believed in a scientific faith, which was not to be doubted, and not intuitive but self-generated,
which formed the beginning of his knowledge. Pascal and Descartes believed in a scientific hope which
supposedly cannot be based on intuition either. For Descartes it could be self-generated, for Pascal it
was more of a religiously generated existential knowledge.
Is it possible to construct a three-fold Trinitarin classification of how these philosophers’ teaching could
relate ontology to epistemology and to theology? All three believed in God, Spinoza constructed what
he considered a rational proof of God’s existence onotologically taking it basically from St. Thomas
Aquinas. Pascal believed in the importance of faith in understanding God so his reasoning about God
was more existential. Leibnitz also believed he has a rational proof of a more spiritual God. So, I would
say Spinoza falls in the Father position the first part of an Aristotelian threefold syllogistic truth, Pascal
is in the second position of the syllogism, and Descartes the rational truth part of the third proposition
of Aristotle’s system of logical truth.
In his essay “On Geometrical Demonstration (on the Geometrical Mind) included later in the Great
Books volume Pascal explains his ideas about some fascinating theories of mathematical proof and
definition.
We can compare this essay on Pascal’s intuitive, non-deductive, mathematical method of discovery and
proof and his intuitive existential way of defining erms, with Descartes, Spinoza, and later even
Poincare’s. But, that is a more difficult discussion. I will just mention some of his aphorisms and
assertions here:
“We must give definition to the defined. [in order to discovery new truths]”
Rules for definition:
1) do not attempt to define any of those things so well known in themselves that we have no clearer
terms to explain them by.
2) Do not leave undefined any terms that are at all obscure or ambiguous
3) Use in the definitions of terms only words perfectly well known or already explained.
Rules for axioms:
1) Do not fail to ask that each of the necessary principles be granted, however clear and evident it may
be.
2) Ask only that perfectly self-evident things be granted as axioms 3) “Time is [defined as] the motion
of a created thing”
“The three fundamental concepts of science and mathematics are:
1) motion
2) number
3) space
Descartes deductive, intuitive method of discovering knowledge can be stated as an injunction. It was:
“[N]ever to accept anything as true if I did not have evident knowledge of its truth: that is, carefully to
avoid precipitate conclusions and preconceptions, and to include nothing more in my judgments than
what presented itself to my mind so clearly and so distinctly that I had no occasion to doubt it.”
Discourse on Method
DO WE EVEN NEED TO WORRY ABOUT GIVING ROBOTS FREE WILL?
Leibnitz’s wondelful philosophic systems explains how a rational conscious being, assuming certain
logical principles and postulates can have free will. For the purposes of this discussion we will assume
that we have already figured out how to give our robots rational consciousness using the type of logical
functions and predicates that Leibnitz considered in his writings.
Is it even possible for our robots, if we give them free will but don’t give them ethics to be evil? Do we
even need to consider this possibly, that they have free will and become evil before we design them/
Such beings would be artificially created, out of material objects, that is by us, with intelligence, but not
necessarily with all the ethical capabilities, such as being able to believe in God as us.
Paradoxically, the best philosopher to study to understand that the answer to this question is yes, I
believe, is Dr. Gottfried (God’s Peace in English) Willhelm (Will I AM in English) Leibnitz.
Leibnitz did not talk to much about ethics in his writings because he had come to the conclusion from
study the theory of philosophioc reality (ontology) and philosophic knowledge (epistotomology) that
“This World is the Best of all Possible World. And, if everything is only goodness, then what does it
matter what we do or what our ethics concerning what we do are? Most of us understand that this is in
fact not the case, therefore, using Leibnitz’s philosophic beliefs to design ethical robots shouldn’t work.
But, maybe if we discuss them and try to understanding why these beliefs do work in giving the robots
free will but don’t work in giving them ethics we will be better able to design ethical robots.
HOW DOES LEIBNITZ DEFINE THE NUMBER ONE, AND HOW DOES THIS RELATE TO HIS MONADIC
THEOLOGY?
a
Because Leibnitz’s monads, or viewpoints, using his 2nd order logical predicates in which he define
integer and integer arithmetic in terms of, are real combined empirical and mental substances, not
logical constructs like Wittengstein’s, or 1st order empirical predicates like Russell’s type theory, he
believes that the number one is an individual instantiated real conscious viewpoint containing within
itself the mental definitions of all other integers, fractions, and real and complex numbers. A monadic
viewpoint carrys with it a completed essence and a reality of itself and all the completed essence and
reality of the environment in which it is defined. Because his monadic system is predicated essentially
on an assumption which believes in a most perfect being, God, Leibnit’s numbers have the means to
self-define all the completed infinities and limits involved in defining complex, algebraic, real numbers in
term of finite rational ones.
In fact one of Leibnitz main accomplisments was helping to argue philosophically for the possibily of
using “infinitesimals”in calculus in order to compute the integrals and derivatives of the different
algebraic and transcendental functions that Descartes and Isaac Newton used. In order to do this you
need, like Leibnitz postulated in his arguments the existence of a “perfect” or “completed” being to give
a “reality” to the substance of limits of integer and rational numbers and to fill in all the gapa in the one-
dimensional continuum of real numbers which define the coordinate axes of Descartes’ analytical
geometry and Newton geometry of absolute space.
HOW DOES LEIBNITZ’S SOLUTION OF DESCARTES MIND BODY PROBLEM THROUGH PRE-
ESTABLISHED HARMONY AFFECT ROBOT METAPHYSICS
AND, IF IT DOES, HOW DOES LEIBNITZ’S PHILOSOPHY TELL US HOW TO GIVE, ROBOTS AND
ANIMALS AND US, WITH GOD’S HELP, SOULS, WHICH BELIEVE IN FINAL CAUSES , BUT NOT ETHICAL
ONES.
Leibnitz had inherited Descartes celebrated mind body problem in metaphysics. The problem briefly is
this: if mind is essentially thought (and nothing else), and body is essentially extension, then how can
mind and body interact or forma unity as we know from experience they must. Or how can a thinking
substance and extended substance unite in the substance of a human being. Leibnitz believed in a
philosophical definition of substance than included both empirical extended bodies or objects and also
mental, non-extended, intentional thoughts in its definition or “thisness”. This definition or “thisnsess
according to Leibnitz have to have a unity in order to be a defined uniquesly determined thisness. This
unity is not necessarily only an instantiated logically propositionally determined unification of variables
in terms with facts like we have explained above but must be a combination of a “real or instantiated
unity in itself” and a “phenomenial or aggregated unity”. For Leibnitz such a unity provides a “well-
founded phenomena” grounded in experience and not simply phenomena as in Bishop Berkeley’s
idealistic philosophy. And, for Leibnitz such an ontologically and logically determined substance has
the capability to be active as a Cartesian substance which only has its essence in a material body or
extensive object doesn’t’
According to Leibnitz the fact that primitive simple substances are “essentially active” means they are
endowed with forces for acting and being acted upon using both primitive passive and active powers.
The primitive active force is a “rule or inherent law” like a rule asking questions or determining when an
expert system or robot is going to act or understand something. Since we believe in the existence of a
perfect spiritual being overseeing our artificial or human or robotic intelligence this action can be
considered to be a kind of “divine decree.”that controls the law of unfolding of the human or divine
simple substance we are involved with as a mind body system.
As we will explain further in the paper a knowledge network that can “give definition to the defined” like
Pascal believed we need in order to understand the things we are talking about involves logical 1st and
2nd order predicates and a set of rules or questions that an expert expert system compiler asks in order
to pin down and record for future questions a compiler or deep neural network might want to ask to
indentify the term for future deductive and inductive reasoning, even ethical conclusions. It can have
strivings by which it passes from perception to perception in accordance to this law of its human or
divine or robotic nature. And, these different substances inside of different beings can have different
modifications and representations of these natures and they can be “harmonized” if the laws or rules
are fit together in terms of their assumptions and conclusions in a way that these laws ask all the
questions, before it acts or doesn’t act, in order to achieve a goal, or stops asking questions,
completely its learning and understanding needed in order to completely learn how to do something or
understand an object or idea or concept.
Such an idealistic and logical definition of what substance is allowed Leibnitz to define what he called
“monads”capable of occupying points in geometrical space and time with individual viewpoints and
casually pre-determined, a-priori and also a-posteriori determined characteristics. These monads can
be created on a computer nowadays using 2nd order logical predicate function with environments that
are passed along in function calls and can be logically added to and subtracted from using predicate
variable and fact compiler unification identifications and instantiations.
In Descartes philosophy, he postulated a particular gland, the pineal gland, as the mechanism for
enabling, through hormones or ortherwise, a cranial cognitive interaction of our minds with the physical
neural thoughts in our brains and the physical neural activating circuits in the whole central nervous
system. But, Leibnitz, being an idealist, and somewhat of a dualist like Plato and Descartes, postulates
that the logical connections and order between neural activations of phenomenial impressions or cranial
physical neural circuit which represent the physical rules based neural networks in us might be meta-
physical in a logical sense as a substance self-existing in a spiritual logical world outside the mental or
bodily parts of us. What a wondelful possibility? If they existed in God’s mind then they would be divine
hopeful and faithful knowledge, to augment our own knowledge neworks, wouldn’t they?
He presented a five-step argument to prove this possibility logically, using certain postulates and
axioms.
He took several principles for his logic.
Principle of the Best
Or, what is to say the same thing, there exists an absolutely self-determined perfect being, This being,
being what we will call a monad or individual spiritual substance, will be and have omnipresence and be
self-generated. Since power and knowledge are perfections they will exist as omniscience and
omnipotence in such a Being and not have limits in such a Being. Lets call Him or Her, God.
Predicate-in-Notion Principle (PIN)
“In every true affirmative proposition, whether necessary or contingent, universal or particular, the
notion of the predicate is in some way include din that of the subject, otherwise I do not know what
truth is.”
PC Principle of Contradiction, This notion of Truth goes back to Aristotle’s Posterior Analytics: “A
proposition cannot be both true and not true at the same time”
We know by studying and creating what are called “modal logics” nowadays that by delaying the
determination of the falsehood or truth of a proposition until more empirically determined facts become
available we can better represent “ethical questions”to “monads” or artificially created individual
“robots”.
Principle of Sufficient Reason (PSR), “There is no effect without a cause”, or “,basically, that is to say
everything is rationally determined. And, our intellects and minds, will determine our ethics.
Principle of Identity of Indescernibles (PII)
“It is not true that two substances can resemble each other completely and differ only in number. In
order words if they share all properties they are identical… in the form of a template for logical
propositions F with variables x,y (for all F) (Fx iff Fy) implies x=y.
Principle of the Indiscenibility of Identicals
If two things are identical, then they share all properties or in terms of a template for logical
propositions F with variables x,y x=y implies (for all F) (Fx iff Fy).
In the Discourse on Metaphysics we are told that these postulates imply the following conclusions :
1) No two sutstannces can resemble each other completely and be distinct.
2) A substance can only being in creation and end in annihilation
3) A substance is not divisible
4) One substance cannot be constructed from two
5) The number of substances does not naturally increase and decrease
6) Every substance is like a complete world and like a mirror of God or of the whole universe, which
each expresses in its own way.
Assume God exists and that:
1) There is no real influence of one substance on another.
So, assume that when one created substance acts on another, the fundamental laws of its inherent
nature are not changed for a while.
2)Assume God originally created the souls (and any other real unity) in such a way that everything
must arise from it for its own needs depends, only, through a perfect spontaneity relative to itself, and
yet with a perfect conformity relative to external things..
3) “This is what makes every substance represent the whole universe exactly and in its own way, from
a certain point of view, and makes the perceptions or expressions of external things occur in the soul at
a given time, in virture of its own laws, as if if in aworld apart, and as if there existed only God and
itself.”
4) “The organized mass, in which the point of view of the soul lies, bering expressed more closely by
the soul, is in turn ready to act by itself, following the laws of these corporeal machines, at the moment
when the soul wills it to act, without disturbing the laws of the other -- the spirits and blood then
having exactly the notions that they need to respond to the passions and percetpions of the soul.”
5) “It is this mutual relation, regulated in advance in each substance of the universe which produces
what we call their communication, and which alone brings about the union of the body and the soul.”
Article #351Add/Reply to this discussion board posting
Subject: How Ethical and Metaphysical Oneness can exist Eternally in us
Author: Andrew W. Harrell
Posted: 7/10/2018 11:26:10 AM
PARABLE OF THE FRIEND WHO IS GLORIFIED TO BE MORE BEAUTIFUL THAN A TREE OR FLOWER
Question asked to God, "Our Creator in Heaven, what is more beautiful to you a flower or a tree?"
"Why are the glorified souls of our prayer friends during this lifetime more beautiful than a flower or a
tree."
God answered:
"A Tree is more beautiful than a flower. Why?” "Because Pretty[Beautiful} is as Pretty[Beautiful] is and
as Pretty[Beautiful]does." The answer to this question is also why its better to be a living person than a
Saint or Angel
More
Why is a tree more beautiful than a flower? Some reasons: "Because it doesn't need as much care, puts
down deep roots, and often can bear good fruit."
added 7/8/18: "A tree is more beautiful than a flower because it lives with us, some longer than us, in
our lives here on earth, as a 'living witness' to the life around it. The birds that build nests in its
branches are supported on its branches and witnessed by the tree and in return when they fly around
the area they take its seeds to plant a new tree like itself and pieces of its branches in order to build
more nests."
"The tree, in order to be a living witness for us, and if one such kind of tree is a living witness for us,
they all are, must be a Unity, a number one for us. But, not just any kind of number one, it must be a
number one that last not just inside of the present moment unifying collecting everything around it as a
unity, but it must be a unity inside of time, long term, surviving, being reborn eternally for us.
And, if that tree is going to be that kind of number one being and essence and witness of everything
around it and us for that long of a time, it must be what we call in ontology, epistemology, metaphysics
a
"One Presence and a One Power, eternally". It is a One presence because its being is a Oneness
surviving over time, and it is a One Power because its life participating and giving vitality survives also
with its One Presence over that long of a period of time. Wow that means a tree is really beautiful in that
it is that special and unique in that way."
"So, to sum up, to whosoever is listening to this, God...Me inside of that Tree is a Wonderful Oneness
that exists Eternally and beautiful, because of these special and unique things we know about it. It is a
Oneness inside of Multiplicity as we look at it and experience it in the present moment, but more than
that and a Multiplicity and a Oneness as it continues to exist Eternally in time. Wow, no wonder now that
we know why it is so wonderful."
“But, then Our Creator in Heaven said, "A friend can be even more beautiful than a tree. Why?” "A
friend can walk with us until the Son of God always shines in both of us, where the Son of God, the
Word of God always shines as a One goodness, a One special unique, self-existing Oneness extending
back into our past, living now in our present more, and we can be assured (if we are faithful) that we
and our friend, knowing all of this and believing that God will help us keep knowing it project an
instantiation , a presence, of ourselves and God and each other forward into our future, inward inside of
us and outward from us, outside of us, hating what is evil [loath all ungodliness, turn in horror from
wickedness], but holding fast to that which is good… rejoicing with those of us who rejoice
by sharing joy, weeping with those of us who weep.”