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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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In the beginning was LOGOS

and LOGOS was with Godand LOGOS was God.

...

Load{LOGOS}

...

Ergo, TODOS

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Contents

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

0.1 Tools and Resources . . . . . . . . . . . . . . . . . . . . . . . 80.1.1 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.1.2 Resources . . . . . . . . . . . . . . . . . . . . . . . . . 9

0.2 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1 Mathematical Foundations 121.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.0.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 131.0.2 Axioms and Assumptions . . . . . . . . . . . . . . . . 131.0.3 Philosophy and History of Math . . . . . . . . . . . . . 14

1.1 Sets and Relations . . . . . . . . . . . . . . . . . . . . . . . . 151.2 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.3 Operations and Groups . . . . . . . . . . . . . . . . . . . . . . 171.4 Building Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Logic 192.0 History and Use of Logic . . . . . . . . . . . . . . . . . . . . . 202.1 Foundation of Logic . . . . . . . . . . . . . . . . . . . . . . . . 212.2 Ways to Prove Something . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Direct Proof . . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 Indirect Proof . . . . . . . . . . . . . . . . . . . . . . . 222.2.3 Counter-Example . . . . . . . . . . . . . . . . . . . . . 22

2.3 Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

iii

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CONTENTS iv

3 The Theory of Everything (TOE) 25

3.0 Story of TOEs Creation . . . . . . . . . . . . . . . . . . . . . 263.1 Construction of the Theory . . . . . . . . . . . . . . . . . . . 273.2 Physical Space . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Quasi-Abstract and Abstract Spaces . . . . . . . . . . . . . . 293.4 Classification of Information . . . . . . . . . . . . . . . . . . . 303.5 The Supernatural Realm . . . . . . . . . . . . . . . . . . . . . 31

4 God and Persons 324.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1 Persons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Theories About God . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.1 God does not Exist . . . . . . . . . . . . . . . . . . . . 354.2.2 God Exists . . . . . . . . . . . . . . . . . . . . . . . . 354.3 Proofs of Gods Existence . . . . . . . . . . . . . . . . . . . . 364.4 The Story of God, the Point . . . . . . . . . . . . . . . . . . . 374.5 Perspectives of God and Gods Relation to the World . . . . . 38

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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.

Definition0.0.2: 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.

Definition 0.0.8: Given two things, X and Y, a conditionstates X Y.

Definition 0.0.9: 1. Given a condition, A, which states B C, not A (or A) B C, and thus...

2. Given a conjecture, Y, which states X Z, not Y (or Y) X Z.

A term word.

Assumption 3: Principle of Non-contradition

1. Given conjectures or conditions, X and Y, X is true X(not X) is false; and Y is true Y is false.

Definition0.0.10: An axiom is an assumption of the existenceof conditions, {X1, X2, ...}.
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Definition 0.0.11: Given X and Y are conditions, a conjecture

X implies Y means if X is satisfied, then so is Y, or Xs exis-tence constitutes the existence of Y. This can be stated Y is animplication of X.

Assumption 4: Logical Implications of Assumptions and Axioms

1. If an Axiom of a Theory asserts the existence of X, we mayassume that X exists.

2. If an Assumption of X, is made, X may be performed.

Definition 0.0.12: A conjecture is (1)a statement that canbe proven true or false. (2)Given sets of conditions, A and B,A B is a conjecture. (3)In general, for a set of conditions, A,and a conjecture, X, a conjecture would say A X. (4)Giventwo conjectures, X and Y, X Y is a conjecture.

Definition 0.0.13: A theorem is a conjecture logically impliedby assumptions and axioms that can be proven to be true.

Definition 0.0.14: A lemma is a theorem used to prove a partof the main theorem. Given a set of lemmas, L, and a main

theorem T, L T.

Definition 0.0.15: A corollary is a subsequent theorem logi-cally implied by the main theorem.

Assumption 5: Logical Implications of Theorems

1. Given conditions C := {X, Y,...} and given a conjecture, Z,if proven that {X,Y,...} imply Z (C Z) then when suppliedwith C ={X, Y,...} we may automatically assume Z. In otherwords, [(C Z) C] true Z true.

(a) This general theorem would read: Given {X, Y, ... }, Z, Let {X, Y,...} then Z, If {X, Y,...}, then Z,or {X, Y,...} Z. Making use of C, we would sayC Z.

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2. Given a theorem, A := C Z and a theorem B := Z W,

there is a new theorem, D := C W

3. Given a condition, X, X X

Theorem 0.0.1: For true statements, X, Y, Z, we see that [X Y Z X] [X Y Z]

Proof. Two parts () Let [X Y Z X]. X Z and Z X soX Z. Furthermore, since Z X and X Y, Z Y. Thus Y Z.Since Y Z and Z X, Y X. Therefore, [X Y Z]. ()Let [X Y Z]. Since Z Y and Y X, Z X. Therefore,

[X Y Z X].

Theorem 0.0.2: Given conjectures, X and Y, if X Y is true X Y isfalse.

Proof. Let X and Y be conjectures and let Theorem A:= X Y be true.Then A= X Y is false.

Theorem 0.0.3: X is true (X) is true.

Proof. Two-part proof() Let X be true. Then X:=Y is false. Since Y is false, Y is true. ThusY=(X) is true.() Let (X) be true and let Y := X. Then (X)=Y is true. ThusY =X is false. Therefore, since X is false, X is true.

Definition 0.0.16: Let X1, X2, ... , Xn be conjectures. X1 X2 ... Xn (X1 or X2 or ... or Xn) forms a new conjecture A;thus, A is either (1)true or (2)false.

1. X1

X2

...Xn

is true an m between 1 and n inclusiveXm is true.

2. X1 X2 ... Xn is false m {1, 2,...,n}, Xm is false.

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Definition 0.0.17: Let X1, X2, ... , Xn be conjectures. X1

X2

... Xn

(X1

and X2

and ... and Xn

) forms another conjec-ture, A, which must be either (1)true or (2)false, and so we willdefine and as:

1. X1 X2 ... Xn is true m {1, 2,...,n}, Xm is true.

2. X1X2...Xn is false an m between 1 and n inclusiveXm is false.

Theorem 0.0.4: Given a conjecture, Y, [Y Y] is false.

Proof. Y is a conjecture, so it is (1)true or (2)false. Case 1: Y is true.Then Y is false. Thus by definition of and, YY is false. Case 2: Y

is false. Then Y is true. So, by the reasoning in the first case, YY isfalse. Therefore, for any conjecture, Y, it would be false to make a claimthat states that both Y and Y are true.

Lemma 0.0.5: Given a true conjecture, X, and any conjecture, Y, only oneof the following can be true: X Y or XY.

Proof. Y is (1)true or (2)false. So, (1) suppose Y is true. Then X Y istrue; and since Y is false, XY is false. And, (2) ifY is false, so is X Y.Furthermore, Y is true, so XY is as well. Therefore, since for both casesthe implication holds true, either XY is true, or X Y is true.

Lemma 0.0.6: Given X logically follows from a set of axioms, [X Y]being a theorem [X (X Y)] is a theorem.

Proof. () X Y is true. By assumption of X, X is true. Hence, X Xis true as well. So, X both X and Y. So, X [X Y].() [X (X Y)] is true. So, X X is true, and X Y is true andtherefore a theorem.

Lemma 0.0.7: [X Y] is a theorem [(X Y) Y] is a theorem.

Proof. Let X Y be a theorem. Y Y is also a theorem. Thus X and Y

both imply Y. Therefore, it is true to say that [(X Y) Y].

Theorem 0.0.8: Let X, Y, Z be true. Then, A := [X Y Z] true B := [(X Y) Z] true C := [X (Y Z)] true.

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Proof. Three-part: (A B) [X Y Z] is true. So, D := (X Y) is true

and so is D Z. Thus [(X Y) Z] is true.(B C) [(X Y) Z] is true. So(C A)

Lemma 0.0.9: X Y and XZ are theorems. X is true implies XZYis true.

Proof. Two part () Suppose X Y and XZ are true. Then A := XZis true. Since X Y, we know that Y is true as well. Thus X Z Y istrue.

Theorem 0.0.10: Suppose X is true and a conjecture, A, states that Ximplies Y. If Y is false, then A is false.

Proof. Let X be true and let a conjecture, A := X Y. Suppose Y isfalse. Then Y is true. We know that X is true, so XY is true. Thus[[X Y] X] [X Y: A] is false (WRONG!!! REDO!).

Indirect Proofs: If were given a conjecture, X Y based on condi-tions C, then there are two ways to prove: directly and indirectly. To prove

something directly based on the assumed C, we assume X C and provethat Y is a logical consequence. We can also prove something indirectly.Two ways to do this is by proving that the contrapositive of a statement istrue and by using a proof by contradiction.

A contrapositive proof is a direct proof of the negated and flipped state-ment. This type of proof is different from the proof by contradiction. Proofby contradiction assumes the conditions, C, the hypothesis, X, and thenegated, Y. And by the assumption of Y, a contradiction of C or Xmust be drawn to prove that Y follows from X.

Theorem 0.0.11: Non-Contradiction of theorems Given a theorem, X Yand supplied with X, (1)(X Y) is true and (2)X Y is false.

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Proof. Two parts:

A := X Y is a theorem. So there exists a set of conditions, C, whichexist as implied by the axioms such that C A. Let C be satisfied. Then,X Y is true. So, given X, X Y is true. Thus XY is not true. Thusto state X Y := B would be false (proved (2)) and since B is false,B = X Y is true.

Theorem 0.0.12: Equivalence of Theorems and their Contrapositives!!! [X Y] is true [(Y X)] is true.

Proof. Two part:() X Y is true based on conditions C. Let C be satisfied. Then, C

and X Y are both true. So, supplied with X, (X Y) would yieldY, making X Y true. Given our conditions and theorem, suppose Y isassumed. We know that X Y is false, thus X Y is false, meaningthat since Y is assumed true, X is false, making X true. Thus, YXis true. If you look at what has been done, youll see that by supposition ofY, X is yielded. Therefore, rewritten, Y X.() Y X is true based upon conditions, C. Assume X is supplied. Weknow that Y X is false. So, Y X is false. Thus, since X is true,Y is false, making Y true. Therefore, supplied with X, we get Y; usingsymbols, weve proven X Y. Q.E. friggen D.

Theorem 0.0.13: Given conditions C, a conjecture Z := [X Y] is theo-rem because (Y C X is false.

Proof. content...

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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

Given a Unit of Information [book, chapter, section], the unit composesitself with subunits of information [chapter, section, subsection]. Thus, forstructure, we shall make a given Unit of Information, X: [Unit] [m] (m isnon-existent for book) submit itself to the following outline.

1. Subunit m.0 (m 0)

Outline of the Unit

Assumptions in the Unit

Introduction to the Unit

A Philosophical and Historical Overview of the Unit

2. Subunit [m.(n + 1)] for the most previous n {n : n Zandn 0}

Definitions used in Assumptions

Axioms and Assumptions

General Definitions

Theorems

Paragraphs and Proofs

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0.3 Introduction

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Chapter 1

Mathematical Foundations

13

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CHAPTER 1. MATHEMATICAL FOUNDATIONS 14

1.0 Introduction

1.0.1 Outline

1.0.2 Axioms and Assumptions

Symbol Meaning/ through symbol is or does not

Logic:= is defined as A A implies itself

implies because is logically equivalent toiff if and only if (same as ) for all there exist(s)s.t. (or ) such that not (i.e. the exact opposite of) and or

Sets: where{x : x is [attribute(s)]} The set containing all elements with [attribute(s)] [is/are] (an) element(s) contained in contain(s) the element(s) (or ) is (strictly) a subset of (or ) is a set containing all elements of (but is not the same as) complement\ minus= is exactly the same set as

united with (union) intersected with (intersection)(A, B) {(a, b) : a A and b B}

Relations

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Logic , ,

Sets , , =, , , , =Functions same as setsArithmetic =, , >, , a, b A, a b, a b : A (A,, ) Group A under operations and , where A =< A;, >

1.0.3 Philosophy and History of Math

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1.1 Sets and Relations

Definition 1.1.1: A set is a collection of whatever denoted as a listingbetween a { and a }, separated by a comma, with no repeated elements.

Axioms 1.1: There exist sets.

Definition 1.1.2: Given two elements, X and Y, the relation, , of X toY, if one exists, is the ordering principle between the two elements (e.g. =,=, , ). We write X Y to denote that X relates to Y.

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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

20

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CHAPTER 2. LOGIC 21

2.0 History and Use of Logic

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CHAPTER 2. LOGIC 22

2.1 Foundation of Logic

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CHAPTER 2. LOGIC 23

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 24

2.3 Theories

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CHAPTER 2. LOGIC 25

2.4 Systems

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Chapter 3

The Theory of Everything(TOE)

26

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CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 27

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

33

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CHAPTER 4. GOD AND PERSONS 34

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 (11-21-11 (0505))