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Logos

Steven Kowalski

2011

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i

Disclaimer: You may know how to rewrite something Ive written.

Please dont give me answers. I want to figure it out on my own. Myposting of these copies is a gift to you. If you wish to use my ideas, makesure to reference me. Furthermore, I am CLAIMING this thesis. If youhave any questions as to what I mean by that, read my Copyright Notice athttp://logos-logic.wikispaces.com/Index
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Contents

0 Principle Foundations 10.0 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

0.1 Tools and Resources . . . . . . . . . . . . . . . . . . . . . . . 50.1.1 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50.1.2 Resources . . . . . . . . . . . . . . . . . . . . . . . . . 6

0.2 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1 Mathematical Foundations 91.0 History and Philosophy of Mathematics . . . . . . . . . . . . . 101.1 Sets and Relations . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Operations and Groups . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Building Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Logic 152.0 History and Use of Logic . . . . . . . . . . . . . . . . . . . . . 162.1 Foundation of Logic . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Ways to Prove Something . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Direct Proof . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Indirect Proof . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Counter-Example . . . . . . . . . . . . . . . . . . . . . 18

2.3 Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 The Theory of Everything (TOE) 213.0 Story of TOEs Creation . . . . . . . . . . . . . . . . . . . . . 223.1 Construction of the Theory . . . . . . . . . . . . . . . . . . . 23

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CONTENTS iii

3.2 Physical Space . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Quasi-Abstract and Abstract Spaces . . . . . . . . . . . . . . 253.4 Classification of Information . . . . . . . . . . . . . . . . . . . 263.5 The Supernatural Realm . . . . . . . . . . . . . . . . . . . . . 27

4 God and Persons 284.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Persons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Theories About God . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.1 God does not Exist . . . . . . . . . . . . . . . . . . . . 314.2.2 God Exists . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3 Proofs of Gods Existence . . . . . . . . . . . . . . . . . . . . 32

4.4 The Story of God, the Point . . . . . . . . . . . . . . . . . . . 334.5 Perspectives of God and Gods Relation to the World . . . . . 34

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Chapter 0

Principle Foundations

1

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CHAPTER 0. PRINCIPLE FOUNDATIONS 2



0.0 Assumptions

Definition 0.0.1: A definition is an explicitly stated meaning

of a word, symbol, or variable.

Definition 0.0.2: An assumption ofX is an ability to performX.

Assumption 1: Assumptions Listed

1. Let us assume that assumptions exist and that those listed inSection 0.0: Assumptions are true throughout the book.

2. Assume the assumptions in each section.

Definition 0.0.3: A chiffre is a base unit of writing (e.g., c, ,, 3, etc.).

Definition 0.0.4: A letter is a chiffre used to spell words (allunits in the alphabet, if it exists).

Definition 0.0.5: A word is an un-spaced string ofletters that

has a meaning.

Definition 0.0.6: A symbol is a chiffre or inseparable combi-nation of chiffres (other than a word) that stands for an idea.
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Definition 0.0.7: A number is a symbol that stands for a

value.Assumption 2: Use of Words and Symbols

1. Assume the ability to use all words as defined in WebstersDictionary and in this book.

(a) If a word is defined in a different manner in Logos, assumethe Logos definition.

2. Assume (1)standard sentence structure in American English

and (2)structure of words and symbols defined in Logos.

3. Assume the symbols defined in the book.

Assumption 3: Principle of Non-contradition

1. Given conditions X and Y, if X is true, then X (not X) isfalse; and ifY is true, then Y is false.

Definition 0.0.8: An axiom is an assumption of the existenceofX.

Definition 0.0.9: Given Xand Y are conditions, X implies Ymeans ifX is satisfied, then so is Y, or Xs existence constitutesthe existence ofY. This can be stated Y is an implication ofX.

Assumption 4: Logical Implications of Assumptions and Axioms

1. If an Axiom of a Theory asserts the existence ofX and Y, wemay assume that X and Y exist.

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Definition 0.0.10: A conjecture is a statement that can be

proven true or false.Definition 0.0.11: A theorem is a conjecture logically impliedby assumptions and axioms.

Definition 0.0.12: A lemma is a theorem used to prove a partof the main theorem.

Definition 0.0.13: A corollary is a theorem logically impliedby the main theorem.

Assumption 5: Logical Implications of Theorems

1. Given conditions {X, Y,...} and given a conjecture, Z, if proventhat {X,Y,...} imply Z then when supplied with {X, Y,...} wemay automatically assume Z.

(a) This general theorem would read: Given X, Y,... , Z,Let {X, Y,...} then Z, If{X, Y,...}, then Z, or {X,Y,...} Z.

2. Given a theorem, W : {X, Y,...} Z and a theorem A :

Z

B,there is a new theorem, C : {X, Y,...}

B

Lemma 0.0.1: Given conjectures, X and Y, ifX Y is true X Y isfalse.

Proof. Let X and Y be conjectures and let Theorem A: X Y be true.Then X implies Y. Thus to state X does not imply Y would be false.Therefore A: X Y is false.

Lemma 0.0.2: Suppose an axiom asserts the existence ofX and a conjec-ture, A, states that X implies Y. IfY is false, then A is false.

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0.1 Tools and Resources

Definition 0.1.1: A tool, X, is something used to create a

product, Y.

0.1.1 Tools

Suppose Y is Logos. There are three general tools I shall use: X1: my mind,X2: my body, and X3: my computer.

My mind To create or recreate ideas, I must use the components of mymind. Generally stated, these include my sense of imagination and sense ofreason which base themselves on my memory. These components are relatedto my brain and hence my body. Thus,...

My body I use verbal communication (mouth and voice), body movement,sense of hearing (ears), and sense of vision (eyes) to create a resource basedon memory, which forms itself by expressing and witnessing ideas and actionswith/of others and myself (REWRITE!!!). I use my vision to read words andadd to the aforementioned resource. And, in typing, I use my manual digits(movement) to record information as well as my sense of vision to read whatI type.

My computer To create the words, equations, and diagrams in this book,

I shall use the hardware of the computer (i.e. keyboard, mouse, monitor,etc.). In addition, I shall use LATEX, a program used to create documents,which uses packages that provide the capability to type information, cre-ate equations, and include diagrams. The diagrams will be created usingMicrosoft Office or Adobe Illustrator.
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Definition0.1.2

:A resource,

X, of a product,

Y, is a rawsupply used to create Y.

0.1.2 Resources

The resources I shall use in creating this work are: words, symbols, depic-tions, and mind content.

Words To express ideas, I choose to use words in the English language andin other languages. For the foreign and focal words I use, I shall supply adefinition.

Symbols For recurring concepts (such as an imply), broad concepts(such as plus (see Section 1.3)), and relative concepts (such as variables),I may wish to use a symbol. I will define the symbols used.

Depictions Sometimes depictions, such as diagrams, express a conceptbetter than words and symbols. In addition, diagrams aid in a personscomprehension of an idea expressed using these words and symbols. Thus,as a visual aid, I will supply diagrams to help in this area.

Mind Content Its possible to put together a random configuration ofwords and symbols and to include an irrelevant drawing. However, my goal isto use these three resources to express my knowledge database of information.This database is a product of my experience in learning concepts and ideasof others. In addition to this personal experience, I have developed conceptsand theories of my own making using my senses of reason and imagination.All of these concepts, theories, and ideas are either recorded in my memory orto be developed through writing this dissertation. Therefore, in [THE PARTON RECOGNITION], I will recognize key minds and products of minds usedto develop this work.
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0.2 Format

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0.3 Introduction

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Chapter 1

Mathematical Foundations

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CHAPTER 1. MATHEMATICAL FOUNDATIONS 10

1.0 History and Philosophy of Mathematics

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1.1 Sets and Relations

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1.2 Functions

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1.3 Operations and Groups

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1.4 Building Arithmetic

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Chapter 2

Logic

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CHAPTER 2. LOGIC 16

2.0 History and Use of Logic

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CHAPTER 2. LOGIC 17

2.1 Foundation of Logic

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CHAPTER 2. LOGIC 18

2.2 Ways to Prove Something

2.2.1 Direct Proof

Deduction

Induction

2.2.2 Indirect Proof

Proof by Contradiction

Proof by Contraposition

2.2.3 Counter-Example

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CHAPTER 2. LOGIC 19

2.3 Theories

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CHAPTER 2. LOGIC 20

2.4 Systems

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Chapter 3

The Theory of Everything(TOE)

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CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 22

3.0 Story of TOEs Creation

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3.1 Construction of the Theory

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3.2 Physical Space

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3.3 Quasi-Abstract and Abstract Spaces

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3.4 Classification of Information

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3.5 The Supernatural Realm

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Chapter 4

God and Persons

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CHAPTER 4. GOD AND PERSONS 29

4.0 Introduction

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4.1 Persons

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4.2 Theories About God

4.2.1 God does not Exist

Our existence is a process of haphazard occurrences. These occurrencesstem from a source that spontaneously and haphazardly brought them about.But wait... That cant happen! For this source must have also been caused bya source. And this pre-existing source from which all sources stem would haveto have spontaneously created them... meaning this source has either beenprogrammed to function this way by itself or by some intentional systemwith the ability to program the source, which would imply a creative andintelligent minds existence before the time everything was set into motion.Sounds too much like God.

OK... Everything was just mysteriously here ever since the beginning oftime; and time started... by some haphazard occurrence...

Alright, third times a charm. There was no beginning. There is no end.Everything that exists has always just existed from time extended from neg-ative infinity to the present. There is no reason for our existence. Objects inmotion have always been in motion. It is only by the principle of serendipi-tous chance that life exists, that I am capable of reason, and that Math, the

product of pure logic, is parallel to the Laws of Physics. My sense of reason isprobably askew, but theres no way of knowing this because I am confined tomy mind, an alternative reality serendipitously created by neurons firing, andthese neurons fire from some serendipitous neuron firing mechanism whichstems from... neurons firing (among other things). Oh how grateful I am,dear Serendipity!

4.2.2 God Exists

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4.3 Proofs of Gods Existence

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4.4 The Story of God, the Point

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4.5 Perspectives of God and Gods Relation

to the World

Documents

Logos - Book (11-15-11 0316)