logos - book 11-19-11 2035

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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

    http://-/?-http://-/?-
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    ii

    In the beginning was LOGOS

    and LOGOS was with Godand LOGOS was God.

    ...

    Load{LOGOS}

    ...

    Ergo, TODOS

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    CONTENTS iv

    3 The Theory of Everything (TOE) 24

    3.0 Story of TOEs Creation . . . . . . . . . . . . . . . . . . . . . 253.1 Construction of the Theory . . . . . . . . . . . . . . . . . . . 263.2 Physical Space . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Quasi-Abstract and Abstract Spaces . . . . . . . . . . . . . . 283.4 Classification of Information . . . . . . . . . . . . . . . . . . . 293.5 The Supernatural Realm . . . . . . . . . . . . . . . . . . . . . 30

    4 God and Persons 314.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1 Persons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Theories About God . . . . . . . . . . . . . . . . . . . . . . . 34

    4.2.1 God does not Exist . . . . . . . . . . . . . . . . . . . . 344.2.2 God Exists . . . . . . . . . . . . . . . . . . . . . . . . 344.3 Proofs of Gods Existence . . . . . . . . . . . . . . . . . . . . 354.4 The Story of God, the Point . . . . . . . . . . . . . . . . . . . 364.5 Perspectives of God and Gods Relation to the World . . . . . 37

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    Chapter 0

    Principle Foundations

    1

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    CHAPTER 0. PRINCIPLE FOUNDATIONS 2

    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

    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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    CHAPTER 0. PRINCIPLE FOUNDATIONS 3

    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, X is true X (not X) is false;and Y is true Y is false.

    Definition 0.0.8: An axiom is an assumption of the existenceof X.

    Definition 0.0.9: Given X and Y are conditions, X implies Ymeans ifX is satisfied, then so is Y, or Xs existence constitutesthe existence of Y. 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 of X and Y, wemay assume that X and Y exist.

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

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    CHAPTER 0. PRINCIPLE FOUNDATIONS 4

    Definition0.0.10

    :A conjecture is a statement that can beproven 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, if X 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: 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)=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.

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    CHAPTER 0. PRINCIPLE FOUNDATIONS 5

    Definition0.0.14

    :Let X and Y be conjectures. XY (X orY) forms a new conjecture A; thus, A is either (1)true or (2)false.

    1. XY is true One of the following is true: (a)Both: (i)Xis true, (ii)Y is false; (b)Both: (i)Y is true, (ii)X is false;(c)Both: (i)Y is true, (ii)X is true.

    2. X Y is false Both of the following are true: (a)X isfalse, (b)Y is false.

    Definition 0.0.15: Let Y and X be conjectures. YX (Y andX) forms another conjecture, A, which must be either (1)true or

    (2)false, and so we will define and as:1. Y X is true Both: (a)Y is true, (b)X is true.

    2. Y X is false Either: (a)Y is false or (b)X is false.

    Theorem 0.0.3: 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: Yis 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 claim

    that states that both Y and

    Y are true.Lemma 0.0.4: 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 XY.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 0.0.5: 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 X being true, we know that X is true. Hence,X X. So, X both X and Y. So, X [X Y].() X (X Y). So, X X and X Y.

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    CHAPTER 0. PRINCIPLE FOUNDATIONS 6

    Theorem 0.0.6: Suppose an axiom asserts the existence of X and a con-

    jecture, A, states that X implies Y. If Y is false, then A is false.Proof. Let X be a conjecture implied by a set of axioms and let Y be aconjecture. Suppose A := X Y and suppose Y is false by the implicationsof the same axioms used to supply X. Then Y is true. We know that Xis true, so XY is true. Thus [[X Y] X] [X Y: A] is false(WRONG!!! REDO!).

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    CHAPTER 0. PRINCIPLE FOUNDATIONS 7

    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

    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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    CHAPTER 0. PRINCIPLE FOUNDATIONS 8

    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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    CHAPTER 0. PRINCIPLE FOUNDATIONS 9

    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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    CHAPTER 0. PRINCIPLE FOUNDATIONS 10

    0.3 Introduction

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    Chapter 1

    Mathematical Foundations

    11

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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 12

    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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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 13

    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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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 14

    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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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 15

    1.2 Functions

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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 16

    1.3 Operations and Groups

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    CHAPTER 1. MATHEMATICAL FOUNDATIONS 17

    1.4 Building Arithmetic

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    Chapter 2

    Logic

    18

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    CHAPTER 2. LOGIC 19

    2.0 History and Use of Logic

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    CHAPTER 2. LOGIC 20

    2.1 Foundation of Logic

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    CHAPTER 2. LOGIC 21

    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 22

    2.3 Theories

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    CHAPTER 2. LOGIC 23

    2.4 Systems

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    Chapter 3

    The Theory of Everything(TOE)

    24

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 25

    3.0 Story of TOEs Creation

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 26

    3.1 Construction of the Theory

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 27

    3.2 Physical Space

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 28

    3.3 Quasi-Abstract and Abstract Spaces

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 29

    3.4 Classification of Information

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    CHAPTER 3. THE THEORY OF EVERYTHING (TOE) 30

    3.5 The Supernatural Realm

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    Chapter 4

    God and Persons

    31

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    CHAPTER 4. GOD AND PERSONS 32

    4.0 Introduction

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    CHAPTER 4. GOD AND PERSONS 33

    4.1 Persons

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    CHAPTER 4. GOD AND PERSONS 34

    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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    CHAPTER 4. GOD AND PERSONS 35

    4.3 Proofs of Gods Existence

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    CHAPTER 4. GOD AND PERSONS 36

    4.4 The Story of God, the Point

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    CHAPTER 4. GOD AND PERSONS 37

    4.5 Perspectives of God and Gods Relation

    to the World