CONSEQUENCES Of SOMETHING FROM NOTHING ABSTRACT In terms of logic, something-from-nothing is the equivalent of something and nothing).This is the equating of logical opposites. Accepting equivalent logical opposites in a system of inference always introduces a contradiction of the form: every formula is a theorem. This paper shows how some alias of every-formula-a-theorem, results when something-from-nothing, or any other equivalent opposite, is used in systems, which form conclusions based on inference. The paper extrapolates that parallel to the elements in the logic of a modal interpreted calculus, the derivation of number in mathematics, and the distinction between things, in mental reasoning. If something can come from nothing, inference in logic, calculation in mathematics, physical reality in science, and decision making in reasoning, all stop. All inference-based processes cease to work. The description of something is the same as the description of nothing. Nothing should now exist. Yet science and reasoning do work. You, I, and the universe do exist. Something can never come from nothing. Any challenge to this prohibition always refutes the very method used to prove that there is an alternative. The prohibition of equivalent opposites is always an axiom in analytical works of logic calculi. It must be extended to the rest of the sciences. KEY WORDS: Consistency, limitation theorems, interpreted modal calculus universe, cosmology, axiom, rules of 1
Transcript
CONSEQUENCES
Of
SOMETHING FROM NOTHING
ABSTRACT
In terms of logic, something-from-nothing is the equivalent of something and nothing).This is the equating of logical opposites. Accepting equivalent logical opposites in a system of inference always introduces a contradiction of the form: every formula is a theorem. This paper shows how some alias of every-formula-a-theorem,results when something-from-nothing, or any other equivalent opposite, is used in systems, which form conclusions based on inference. The paper extrapolates that parallel to the elements in the logic of a modal interpreted calculus, the derivation of number in mathematics, and the distinction between things, in mental reasoning. If something can come from nothing, inference in logic, calculation in mathematics, physical reality in science, and decision making in reasoning, all stop. All inference-based processescease to work. The description of something is the same as the description of nothing. Nothing should now exist.
Yet science and reasoning do work. You, I, and the universe do exist. Something can never come from nothing. Any challenge to this prohibition always refutes the very method used to prove that there is an alternative.
The prohibition of equivalent opposites is always an axiom in analytical works of logic calculi. It must be extended to the rest of the sciences.
Introduction Those who use analytical logic always assure consistency by inserting an axiom that prevents logical opposites from being derivable. This is fundamental to logic, but does not yet have a counterpart in the sciences. An example is the acceptance ofsomething-from-nothing in the study of the origin of the universe and quantum theory. In terms of logic, something-from-nothing is the equivalence of something and not-something (or something and nothing).This is the act of equating logical opposites. Accepting equivalent logical opposites ina system of inference always introduces a contradiction of the form: every formula is a theorem. This paper shows how some form of every-formula-a-theorem, results when something-from-nothing, or any other equivalent opposite, is used in systems, which form conclusions based on inference. The paper extrapolates that parallel to the elements in the logic of a modal interpreted calculus, the derivation of number in mathematics, and the distinction between things, in mental reasoning. The result: All inference-based processes cease to work. If something can come from nothing, inference in logic, calculation in mathematics, physical reality in science, and decision making in reasoning, all stop. The description of something is the same as the description of nothing. This paper shows that any process that admits equivalentopposites inserts a contradiction into any process that is
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used to establish conclusions. Because at that time, all opposites are equivalent, any challenge to the prohibition for using equivalent opposites always refutes the very method used to prove that there is an alternative. We see this by examining the consequences of equivalent opposites to logic,number/mathematics, science, reasoning, and something from nothing.
But if opposites are the same:Each of the seven steps is nullified. If the opposite of
each step is performed, no science is accomplished. This destroys the scientific method. All of Science disintegrates.
What follows are how and why this happens.
1. Consequences to Logic
Theorem 1: If opposites are equivalent, every formula is a theorem, every statement is derivable, and all inferences cease.
Proof:1.1 Contents of An Interpreted Modal CalculusClass containing the ordered pair: (I) Class of Logical Signs, (II) Class of Sentences, (III) Class of Descriptive Signs, (IV) Semantical rules and (V) Modality rules. [2] [3] [4] [5] [9] [16] [24]
(1) Logic Variables - Subjects, anything we can think about Or
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(2) Logic Constants - Properties, Predicates, descriptions Or
(3) Logic Axioms - Statements that accepted without proof
They are:
(4)Logic Statements - Combinations of variables and constants formed inaccordance with the restrictions imposed by formation rules. They are a combination of a subject (whatever we name) and a predicate (an expression about the subject).
They Obey:
(6)Logic Denial – Process for labeling variables, constants or statements as their opposites.
(7)Logic Formation Rules - Procedures for combining variables, constants, subjects, and predicates to create statements that have meaning.
(8)Logic Transformation Rules - Procedures for creating statements fromother statements. This procedure is also called inference.
(9)Logic Conclusions - Statements derived from other statements by application of the transformation rules.
1.2 Definitions
A=d Logical Signs All variables and logical constants
B =d Descriptive Signs Constants referring to objects, properties, relations, individuals, predicates, sentences
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G =d Class of Designators All Modal operators
A (a0….ai) =d Class of Logical Signs (Where ai are the elements of A, and i is a finite natural number)
B (b0….bi) =d Class of Descriptive Signs (Where bi are the elements of B, and i is a finite natural number)
S (s0….sj) =d Class of Sentences (Where sj are the elements of S, and j is a finite natural number)
G (g0….gv) =d Class of Designators (Where gj are the elements of G, and v is a finite natural number)
L (A, S,) =d Language L
E =d Expressions of Language L
E d AThe class of expressions of L is the class of all finite sequences whose members are elements of the class A.
Z =d Semantical Rules of Language LThe value assignment for the sentences S
L(A,B,S,Z,G) =d Interpreted Modal Language L
Z(sj,sm) =d sj is true if and only if sm is true
Dd=d Direct Derivability
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The relation between a sentence and a finite class of sentences Dd(sjk,sj,).
C (A,B,S,Z,Dd) =d Interpreted Modal Calculus C
1.3 AxiomsFor any class A and any class S, if (A,B,S,Z,G,Dd) is an interpreted modal calculus, then every element of Sis a finite sequence of elements of A, every element ofA occurs as a member of some element of S, and B is a subset of A.
Dd (sjk,sj,)Every second-place member of Dd is an element of class S, and every first-place member is a finite subclass of S such that sjk,
is directly derivable from sj,.
sj GThe class of sentences of S is the class of all finite sequences whose members are elements of the class of designators, G.
S (s0….sj) =sub G(g0….gv) The class of sentences of S is the subclass of all finite sequences whose members are elements of the class of designators, G.
B (b0….bi) =sub S(s0….sj)The class of descriptive signs of B are the subclass of the sentences of class S.
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1.4 Direct Derivability/Transformation Rules
(1) (p p) → p
(1a) (□ p □ p) → □ p
(2) p → (p q)
(2a) □ p → (□ p □ q)
(3) (p q) → (q p)
(3a) (□ p □ q) → (□ q □ p)
(4) (p → q) → [(r p) → (r q)]
(4a) (□ p → □ q) → [(□ r □ p) → (□ r □ q)]
1.5 Modus Ponens
If P is true, then Q is true
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Assume P is true
Therefore, Q is true
1.6 Modus Ponens with Necessitation
If □P is true, then □Q is true
Assume □P is true
Therefore, □Q is true
1.7 Substitution
Subst s (p q)
In sentence s substitute statement q for statement p
Statement s is not any other statement, so we can substitute not-s (¬ s) for those other statements:
For Transformation Rule (1):
(5) p p → p(5a) p = ¬ s(5b) ¬ s ¬ s → ¬ s
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By Modus Ponens:(5c) ¬ s ¬ s (5d) ¬ s (5e) Therefore ¬ s
But if (5f) s = ¬ s(5g) s
So, every formula is a theorem
(5h) ¬ s and s
For Transformation Rule (1a):
(5i) □ p □ p → □ p(5j) □ p = ¬ □ s(5k) ¬ □ s ¬ □ s → ¬ □ s
By Modus Ponens:(5l) ¬ □ s ¬ □ s (5m) ¬ □ s (5n) Therefore ¬ □ s
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But if :(5o) □ s = ¬ □ s(5p) s
So,(5q) ¬ □ s and □ s
Every formula is a theorem
(5r) ¬ s and s(5s) ¬ □ s and □ s
For Transformation Rule (2):
(6) p → (p q)(6a) p = ¬ s(6b) q = ¬ s(6c) ¬ s → (¬ s ¬ s)
By Modus Ponens:(6d) ¬ s (6e) (¬ s ¬ s)(6f) Therefore ¬ s
But if: (6g) s = ¬ s(6h) s
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So, very formula is a theorem
(6i) ¬ s and s
For Transformation Rule (2a):
(6j) □ p → (□ p □ q) (6k) □ p = ¬ □ s (6l) □ q = ¬ □ s (6m) ¬ □ s → (¬□ s ¬ □ s)
By Modus Ponens:(6n) ¬ □ s (6o) (¬□ s ¬ □ s)(6p) Therefore ¬ □ s
But if :(6q) □ s = ¬ □ s(6r) s
So,(6s) ¬ □ s and □ s
Every formula is a theorem
(6t) ¬ s and s
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(6u) ¬ □ s and □ s
For Transformation Rule (3):
(7a) (p q) → (q p)(7b) p = ¬ s(7c) q = ¬ s(7d) (¬ s ¬ s) → (¬ s ¬ s)
By Modus Ponens:(7e) ¬ s (7f) (¬ s ¬ s)(7g) s
But if (7h) s = ¬ s(7i) s
So, every formula is a theorem
(7j) ¬ s and s
For Transformation Rule (3a):
(7k) (□ p □ q) → (□ q □ p)(7m) □ p = ¬ □ s(7n) □ q = ¬ □ s
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(7p) (¬□ s ¬ □ s) → (¬□ s ¬ □s)
By Modus Ponens:(7q) ¬ □ s (7r) (¬□ s ¬ □ s)(7s) ¬ □ s
But if (7t) □ s = ¬ □ s(7u) s
So,(7v) ¬ □ s and □ s
Every formula is a theorem
(7w) ¬ s and s(7x) ¬ □ s and □ s
For Transformation Rule (4):
(8a) (p → q) → [(r p) → (r q)](8b) p = ¬ s(8c) q = ¬ s(8d) r = ¬ s
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(8e) (¬ s → ¬ s) → [(¬ s ¬ s) → (¬ s ¬ s)]
By Modus Ponens:(8f) (¬ s → ¬ s)
Then(8g) [(¬ s ¬ s) → (¬ s ¬ s)]
By Modus Ponens applied again:(8h) (¬ s → ¬ s)
Then(8i) (¬ s ¬ s) (8j) ¬ sBut if (8k) s = ¬ s(8m) s
So, every formula is a theorem
(8n) ¬ s and s
For Transformation Rule (4a):
(8p) (□ p □ q) → [(□ r □ p) → (□ r □ q)](8q) □ p = ¬ □ s(8r) □ q = ¬ □ s
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(8s) □ r = ¬ □ s(8t) (¬□ s → ¬ □ s) → [(¬ □ s ¬ □s) → (¬ □ s ¬ □ s)]
By Modus Ponens:(8u) (¬ □ s → ¬ □ s)
Then(8v) [(¬□ s ¬ □ s) → (¬□ s ¬ □s)]
By Modus Ponens applied again:(8w) (¬□ s → ¬ □ s)
Then(8x) (¬□ s ¬ □ s) (8y) ¬ □ s
But if (8z) □ s = ¬ □ s(8aa) s
So,(8bb) ¬ □ s and □ s
Every formula is a theorem
(8cc) ¬ s and s
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(8dd) ¬ □ s and □ sFor each sentential formula, every formula is a theorem when: (8ee) ¬ s = s and ¬ □ s = □ s
When opposites are equivalent, every formula is a theorem, every statement is derivable, and all inferences cease.
2. Consequences to Number/Mathematics [2][4][5]
Theorem 2: If opposites are equivalent, every number is the same, equivalent to zero, and the capability to calculate ceases.
Proof:Two categories of numbers form the numbers with
which we are familiar. They are:(A) Numbers identifying some At least quantities
And(B) Numbers identifying some Exact quantity
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The structure for numbers we normally use is for exact quantities. That structure is comprised of a second structure for at least quantities.
2.1 At least Quantities
We explain the construction of the at least numbers first. Starting with the structure for zero, we give examples to number 3, and then generalize for any number N:
(2 - 1) 0@ (T) ↔ ¬ x1) Tx1
There are at least zero T’s if and only if there is no x1 such that x1 is a T.
(2 – 2) 1@ (T) ↔ x1) Tx1
There is at least one T if and only if there is an x1 such that x1 is a T.
(2 - 3) 2@ (T) ↔ x1) x2) Tx1 Λ Tx2} Λ J {Tx1 Λ Tx2}There are at least two T’s if and only if there is an x1 and anx2 such that x1 is a T and x2 is a T; and x1 and x2 are different.
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(2 - 4) 3@ (T) ↔ x1) x2) x3) Tx1 Λ Tx2 Λ Tx3} Λ J {Tx1 Λ Tx2 Λ Tx3} There are at least three T’s if and only if there is an x1, an x2, and an x3 such that x1 is a T, x2 is a T, and x3 is a T; and x2
and x3 are different.
In general the at least structure simplifies to:
There are at least N T’s if and only if there are N X’s such that the N X’s are T’s, and all of the N X’s, are different:
(2 - 5) N@ (T) ↔ x1) . . . xN)
Tx1 Λ . . . Λ TxN} Λ J {Tx1
Λ . . . Λ TxN}
Or simply(2 - 6) N@ (T) ↔{ x N) T(x N) Λ JN(x
N)}
2.2 Exact Quantities
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Now we consider the exact numbers. We generalizeto 6, give examples of 10 and 100, and then generalize to N:
(2 - 7) 0 (T) ↔ ¬ [1@ (T)]There are exactly zero T’s if and only if there is not at one least T.
(2 - 8) 1(T) ↔ 1@ (T) Λ ¬ [2@
(T)] There is exactly one T if and only if there at one least T, and there is not at least two T’s.
(2 - 2) 2(T) ↔ 2@ (T) Λ ¬ [3@ (T)]There are exactly two T’s if and only if there are at least twoT’s, and there is not at least three T’s.
(2 - 10) 3(T) ↔ 3@ (T) Λ ¬ [4@
(T)]There are exactly three T’s if and only if there are at least three T’s, and there is not at least four T’s.
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(2 -11) 4(T) ↔ 4@ (T) Λ ¬ [5@ (T)]There are exactly four T’s if and only if there are at least four T’s, and there is not at least five T’s.
(2 - 12) 5(T) ↔ 5@ (T) Λ ¬ [6@ (T)]There are exactly five T’s if and only if there are at least five T’s, and there is not at least six T’s.
(2 - 13) 6(T) ↔ 6@ (T) Λ ¬[7@ (T)]There are exactly six T’s if and only if there are at least six T’s, and there is not at least seven T’s.
(2 - 14) 10(T) ↔ 10@ (T) Λ¬ [11@ (T)]There are exactly ten T’s if and only if there are at least ten T’s, and there is not at least eleven T’s.
(2 - 15) 100(T) ↔ 100@
(T) Λ ¬ [101@ (T)]20
There are exactly one hundred T’s if and only if there are atleast one hundred T’s, and there is not at least one hundred and one T’s.
We can generalize to any N for exact quantities, by induction:
(2 -16) N (T) ↔ N@ (T) Λ¬ [{N+1} @ (T)]There are exactly N T’s if and only if there at N least N T’s, and there are not at least (N+1) T’s.
And we can generalize to any N for at least quantities, by induction:
(2 -17) N@ (T) ↔{ x N) T (x N) Λ JN(x N)}There is at least N T’s if and only if there are N X’s such that N X’s are T’s, and all of the N X’s, are different.
2.3 Equivalent Opposite Exact Quantities
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When opposites can be equivalent, the following is the consequence when we equate exact quantities:
(2 -18) N (T) = ¬ [N (T)]Exactly N T’s are equivalent to what are not exactly N T’s
(2 -19) N (T) = [0
(T)]Exactly N T’s are equivalent to what are exactly zero T’s
(2 -20) N@ (T) Λ ¬ [N@ (T)] {N+1}@
(T) = ¬ [1@ (T)]Exactly N T’s and not at least (N+1) T’s, is equivalent to not at least one T.orExactly N is equivalent to exactly zero.
When the logical opposites of exact quantities are equal to each other, every numberis the same, and also equivalent to zero.
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When opposites can be equivalent, the following is the consequence when we equate at least quantities:
(2 -21) N@ (T) = ¬ [N@ (T)]There is at least N T’s equivalent to not at least N T’s.
(2 -22) [0@ (T)] = ¬ [N@
(T)]At least zero T’s are equivalent to not at least N T’s
(2 -23) ¬ [1@ (T)] = ¬ [N@
(T)]Not at least one T’s are equivalent to not at least N T’s
(2 -24) N@ (T) = ¬ [1@
(T)]At least N T’s are equivalent to not at least one T. At least N T’s are equivalent to at least zero T’s.
When the logical opposites of at least quantities are equal to each other, every quantity of things is the same, and also equivalentto zero.
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3. Consequences to Reason
Theorem 3: If opposites are equivalent, every description is the same, and the capability to make decisions ceases.
Proof:
Descriptions are lists of attributes. Attributes are statements. Descriptions are indexed lists, row matrices composed of statements. Different lists of attributes allow us to distinguish one description from another. [1] [4] [13] [14] [17] [21] [22]
3.1 Indexed ListsEach indexed item (d) is an attribute in the
list. The structure of the list is an r x s matrix. That is, it is an array that has r rows and s columns, D r x s
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The description list is composed of attributesin the form of statements:
(3-1) [d ij]Because it is a list, s is always 1. This
makes it a column matrix:
(3-2) D = [d ij] = [d i1]
Assume two lists:(3-3) A r x s and B t x u
A and B are equal if:(3-4) r = t and s = u,
And(3-5) [a i1] = [b i1]
Since these are column matrixes, (3-6) s = u = 1
But since no descriptions are the same, the total collection of attributes[a i1] can never equal the total collection of attributes [b i1]:
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(3-7) [a i1] not equal to [b i1]
The indexed list for descriptions will always have different total numbers ofattributes and/or different names of attributes. This list is called the Complete Descriptions List of Attributes.
3.2 Complete or Partial Lists The explication for sameness lies with descriptions. We identify things by their Complete Description List. It is different for each thing. Because attributes are different in the complete list of attributes for any two things, their lists are always different. Each list however is a linear combination of some other list. That’s why we compare a description of one or more things to describe a thing we have difficulty describing. We use terms such as, “It’s like....” or “Think of....” or “Compare it to....” For that reason, one or more attributes can be the same when comparing two description lists, but only when at least one list is a Partial Description List. That is, at least one list has less attributes than is necessary to distinguish the thing from any other thing. If one partial list has the same attributes as another partial or a complete list, the things we’re comparing have the same
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description. That is, they have the same description in terms of those common attributes only. They, however, cannot be distinguished from each other in terms ofthose attributes.
For instance, a palm tree and willow tree have tree in both their attribute lists. For that attribute, they are the same. If we say “name the one that is a tree”, they cannot be distinguished. They have the same description unless other attributes in their description lists are identified. The total description list for each tree is sufficiently different that the two trees can be distinguished.
3.3 Things [4] [18]Things have different descriptions.
Things are identified by descriptions. Multiple attributes make up those descriptions. By this, we are able to determine multiples of things. Thus, there isa direct correlation between things, descriptions, andattributes with number.
Assume these definitions:
THG =d thing
DSC=d description
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3.4 AT LEAST Things
(3-8) 0@ (THG) ↔ ~ DSC 1)THG (DSC 1)There are at least zero Things if and only if there is no Description1 such that Description1 is a Thing.
(3-9) 1@ (THG) ↔ DSC 1) THG (DSC 1)There is at least one Thing if and only if there is a Description1 such that Description1 is a Thing.
(3-10) 2@ (THG) ↔ DSC 1) DSC 2) Thing (DSC 1) Λ THG(DSC 2)} Λ J {DSC 1 Λ DSC 2}There are at least 2 Things if and only if there is a Description1 and a Description2 such that Description1 is a Thing and Description2 is a Thing; and each description is different.
There are at least 3 Things if and only if there is a Description1 and a Description2 and a Description3 such that Description1 is a Thing and Description2 is a Thing and Description3 is a Thing; and each description is different.
In general:There are at least N Things if and only if there are N Descriptions such that each Description is a Thing and each Description is different.
(3-12) N@ (THG) ↔ DSC 1) . . . DSC N)
THG (DSC 1) Λ . . . Λ THG (DSC N)} Λ
JN {DSC 1 Λ . . . Λ DSC N}
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Or simply
(3-13) N@ (THG) ↔ { DSCN) THG (DSCN) Λ JN (DSCN)}
3.5 EXACT Things
(3-14) 0 (THG) ↔ ¬ 1@ (THG)There are exactly zero Things if and only if there is not at least one Thing.
(3-15) 1(THG) ↔ 1@ (THG) Λ ¬ 2@ (THG)There is exactly one Thing if and only if there at least one Thing, and there are not at least two Things.
(3-16) 2(THG) ↔ 2@ (THG)Λ ¬ 3@ (THG)There are exactly two Things if and only if there are at leasttwo Things, and there are not at least three Things.
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(3-17) 3(THG) ↔ 3@ (THG) Λ¬ 4@ (THG)There are exactly three Things if and only if there are at least three Things, and there are not at least four Things.
In general:
(3-18) N (THG) ↔ N@ (THG) Λ ¬ {N+1}@ (THG)There are exactly N Things if and only if there at least N Things, and there are not at least (N+1) Things.
3.6 Equivalent Opposite Exact Things
When opposites can be equivalent, the following is the consequence when we equate exact numbers of things:
(3-19) N (THG) = ¬ [N(THG)]Exactly N Things are equivalent to what are not exactly N Things.
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(3-20) N (THG) = ¬ [0
(THG)]Exactly N Things are equivalent to what are not exactly zero Things
(3-21) N@ (T) Λ ¬ {N+1}@
(T) = ¬ 1@ (T)Exactly N Things and not at least (N+1) things, is equivalent to not at least one Thing.orExactly N things are equivalent to exactly zero things.
When the logical opposites of exact quantities are equal to each other, every numberis the same, and also equivalent to zero.
When opposites are equivalent, the following is the consequence when we equate at least number of things:
(3-22) N@ (THG) = ¬ [N@ (THG)]
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There are at least N Things is not equivalent to at least N
Things.
(3-23) [0@ (THG)] = ¬ [N@ (THG)]At least zero things are equivalent to not at least N things.
(3-24) ¬ 1@ (THG) = ¬N@ (THG)Not at least one thing is equivalent to not at least N
things.
(3-25) N@ (THG) = ¬ 1@
(THG)At least N things are equivalent to not at least one thing. At least N things are equivalent to at least zero things.
When the logical opposites of at least quantities of things are equal to each other, every quantity of things is the same, and every quantity of things is equivalent to zero quantity of things.
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3.7 Equivalent Opposites When the Thing is You
Equivalent opposites can be ‘you’ and ‘not-you’. They have different descriptions. ‘Not-you’ has amongits members, sunlight, mountains, and waterfalls. Their attributes describe ‘Not-you’. They are all thethings you are not. They are ‘not-you’. ‘You’ have among its members, person, human, and reader. Their attributes describe ‘You’. ‘Not-you’ and ‘You’ can never be the same. If ‘Not-you’ and ‘You’ are ever the same, they have the same attributes, the same description. Everything has that same description. When something and nothing are equivalent, everything has the same description.
4. Consequences to Science
Theorem 4: If opposites are equivalent, every physical model is the same, and the capability to determine physical reality ceases.
4.1 The Scientific Method [10] [23]
Science is the process of obtaining knowledge about the origin and operation of the universe, as well as the things in it.
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Science does this through the scientific method, satisfying seven principle actions:
(4-1) (I) Observation
Form a question about some event
(4-2) (II) Hypothesis
Make an educated guess about the answer to the question
(4-3) (III) Prediction
Establish a set of conditions that result if the educated guess is true, orEstablish a set of conditions that result if the educated guessis false
(4-4) (IV) Test
Create tests designed to prove the educated guess trueor Create tests designed to disprove, the educated guess
(4-5) (V) Check for Consistency
Compare the test results to see if they prove the educated guesstrue, or
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Compare the test results to see if they disprove the educated guess
(4-6) (VI) Form Conclusions If tests were to establish the educated guess true, and the tests establish the educated guess true, the method is finished If tests were to establish the educated guess false, and; the tests establish the educated guess false, the method is
finished However,
If tests do not coincide with either planned conclusion for the educated guess
That is:If tests were to establish the educated guess true, and the
tests establish the educated guess falseOr
If tests were to establish the educated guess false, and the tests establish the educated guess true
Then:More observations must be made and/or the educated guess must be changed.
AndStart again with (II) prediction, and proceed again with steps
(III) through (VI).
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(4-7) (VII) Form Contrary Tests
This makes the Conclusion falsifiable. Forming contrary tests means:It must be possible to structure some test that proves ourConclusion false, if this contrary test is successful
When the contrary test cannot yield a result that falsifies the conclusion, the educated guess becomes a scientific theory, an idea that continues to show credibility after repeated tests.
When opposites are equivalent, satisfying the opposites of the seven principle actions of the scientific method, is the scientific method. The opposite of any conclusion is true and all contrarytests are valid. Science, as we know it, cannot be performed.It completely breaks down.
4.2 Micro-Physics [12] [15] [25] [26]
Quantum Theory
Tracking a chain of particles, Z
The capability to observe the movement, collision, and breakup of particles if vital to theany science associated with quantum theory.
This can be shown through the following, based onRudolf Carnap’s axiom system for physics [3]:
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(4-8) Jnd (ze, zg) ↔Trkd (ze, zg)Particle ze is joined to particle zg if and only if they can be tracked from particle ze to particle zg
Particle z1 can be tracked to particle z7 if and only if particle z1 is earlier than particle z2 and particle z2 is coincident with particle z3 and particle z3 is earlier than particle z4 and particle z4 is coincident with particle z5 and particle z5 is earlier than particle z6 and particle z6 is coincident with particle z7
But if:
(4-10) EThn = ¬ EThn, and Cdnt = ¬ Cdnt
This admits an equivalent opposite that inserts a contradiction.
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By DeMorgan’s Rule, particle tracking cannot be done:
(4-11) ¬ Trkd (z1, z7) ↔ ¬ EThn (z1, z2)v ¬ Cdnt (z2, z3) v ¬ EThn (z3, z4) v ¬ Cdnt (z4, z5) v ¬ EThn (z5, z6) v ¬ Cdnt (z6, z7) Particle z1 cannot be tracked to particle z7 if and only if particle z1 isnot earlier than particle z2 and particle z2 is not coincident with particle z3 and particle z3 is not earlier than particle z4 and particle z4 is not coincident with particle z5 and particle z5 is not earlier thanparticle z6 and particle z6 is not coincident with particle z7
When opposites are equivalent, particle behavior cannot be tracked.
4.3 Macro-Physics [6] [7] [20]
Laws of Physics
Predictions are based on physical laws being the same everywhere
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Physics depends on the capability to predict a finite number of value measurements (such as charge, temperature, mass, etc.) to establish a specific state at a one location, by inference based on the values ofthose measurements (charge, temperature, mass, etc.) done atother locations previously.
This can be represented by the following which isbased on Rudolf Carnap’s axiom system for physics [3]:
The state at a specific location can be predictedby states determined at a different group of locations.
(4-12) Prct L (S) ↔ Det K {[Lj (Sj)]} Λ L (S) K {[Lj (Sj)]There is a non-empty finite class S, a finite number of measurementsdefining the state at location L with respect to S, determined by the state with respect to Sj at a class K of locations Lj. And location L is not in the class K of locations Lj.
But if opposites are equivalent, we can by substitution, change from:
(4-13) K {[Lj (Sj)]} = ¬ L (S)
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To:
(4-14) L (S) = K {[Lj (Sj)]}
The result is insertion of a contradiction:
(4-15) Prct L (S) ↔ Det L (S) Λ L (S) L (S)There is a non-empty finite class S, a finite number of measurementsdefining the state at location L with respect to S, determined by the state at location L with respect to S. And location L is not at location L
When opposites are equivalent, no predictions of states can be made in physics.
Evolution Theory
Biological Transition of one organism to another [8] [12] [18]
This can be represented by the following, based on Rudolf Carnap’s axiom system for biology [3]:
The organic unit ‘A’ is transformed into the organic unit ‘B’ if and only if ‘r’ is an end slice of ‘A’ and ‘w’ is an initial slice of ‘B’, and either ‘r’ is a part of ‘w’ or ‘w’ is a part of ‘r’ and ‘r’ and‘w’ are different.
But if opposites are equivalent, by DeMorgan’s Rule:
(4-17) ¬ Trfm [Org (A), Org (B)] ↔ ¬ ESli (r, A) v ¬ ISli (w,B) v ¬ [Prt (r, w) Λ Prt (w, r)]v I (r, w)
Also, if opposites are equivalent: ¬ Trfm [Org (A), Org (B)] = Trfm [Org (A), Org (B)] So:(4-18) Trfm [Org (A), Org (B)] ↔ ¬ ESli (r, A) v ¬ ISli (w,B) v ¬ [Prt (r, w) Λ Prt (w, r)]v I (r, w)
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The organic unit ‘A’ is transformed into the organic unit ‘B’ if and only if ‘r’ is not an end slice of ‘A’ and ‘w’ is not an initial slice of ‘B’, and ‘r’ is not a part of ‘w’ and ‘w’ is not a part of ‘r’and ‘r’ and ‘w’ are identical.
When opposites are equivalent, transformationof one organism to another cannot be determined.
5. Consequences to Something from Nothing
Theorem 5: If opposites are equivalent, the definitions for something and nothing are the same, each thing is the same as nothing, and nothing should now exist.
Proof:
Definition of Nothing Figure 5-1 gives a set of sources and
definitions for the word “nothing”. The left
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of the figure is the dictionary that is the source for the definition. The right is the definition from that source.
SOURCE of DefinitionM iriam -W ebster OnlineThe Free Dictionary By FarlexYawiktionary.comOnline M edical DictionaryDictionary.die.netGoogleW ikiAnswers.com
Not anything; no thingno thing; not any thing
DEFINITIONDictionary Definitions for the word 'nothing'
not any thing; no thingNo thing; not anythingNot any thing; no thingNot anything; no thingNot anything; no thing
FIGURE 5-1
In Figure 5-1, note that all of the definitions for nothing are in terms of zero things. The definition of zero (0), in terms
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of things, is the same definition as that forthe word nothing.
The Figure 5-1 effectively defines nothing asthe absence of things. That definition is the definition for zero below:
(5-1) 0@ (THG) ↔ ¬ { DSC1) THG (DSC1)}There are at least zero Things if and only if there is no Description1 such that Description1 is a Thing.
(5-1) 0 (THG) ↔ ¬ 1@ (THG)There are exactly zero Things if and only if there is not at least one Thing.
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Definition of SomethingFigure 5-2 gives a set of sources and
definitions for the word “something”. The left of the figure is the dictionary that is the source for the definition. The right is the definition from that source. The definition for nothing is the opposite of that for something. All of the definitions for something are in terms of at least one existing thing.
SOURCE of DefinitionGoogle a thing of some kindThe Free Dictionary By Farlex An undeterm ined or unspecified thingW ordReference.com a thing of som e kindM iriam -W ebster Online som e indeterm inate or unspecified thing
a thing that is not definitely known;Your Dictionary.com Som e underm ined thing;
Som e thing definite but unspecified
DEFINITIONDictionary Definitions for the word 'something'
FIGURE 5-2
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Figure 5-2 defines something in terms of one or more things. That matches the definitions for: at least one thing, at leastN things, exactly one thing, and exactly N things below:
At least one thing(5-1) 1@ (THG) ↔ DSC1) THG (DSC1)There is at least one Thing if and only if there is a Description1 such that Description1 is a Thing.
At least N things(5-2) N@ (THG) ↔ { DSCN) THG (DSCN) Λ JN
(DSCN) } There are at least N Things if and only if there are N Descriptions such that each Description is a Thing and each Description is different. Exactly one thing(5-3) 1(THG) ↔ 1@ (THG) Λ ¬ 2@ (THG)
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There is exactly one Thing if and only if there at least one Thing, and there are not at least two Things.
Exactly N things(5-4) N (THG) ↔ N@ (THG) Λ ¬ {N+1}@ (THG)There are exactly N Things if and only if there at least N Things, and there are not at least (N+1) Things.
The definition of at least zero things, at least one thing and at least N things, all refer to existence:
At least zero things
(5-5) 0@ (THG) ↔ ~ { DSC): THG (DSC)}There are at least zero Things if and only if there is no description such that the description is a Thing.
At least one thing
(5-6) 1@ (THG) ↔ DSC): THG (DSC)
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There is at least one Thing if and only if there is a Description1 such that Description1 is a Thing.
At least N things
(5-7) N@ (THG) ↔ { DSCN): THG (DSCN) Λ
JN (DSCN)} There are at least N Things if and only if there are N Descriptions such that each Description is a Thing and each Description is different.
From these definitions, we can establish the definition of non-existence, existence, noting, and something:
NON-EXISTENCE
At least zero things exist. No things exist.
(5-8) 0@ (THG) ↔ ¬ { DSC 1) THG (DSC 1)}There are at least zero Things if and only if there is no Description1 such that Description1 is a Thing.
At least one thing
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(5-9) 1@ (THG) ↔ DSC 1) THG (DSC
1)There is at least one Thing if and only if there is a Description1 such that Description1 is a Thing.
At least zero things are just the negation ofat least one thing:
(5-10) 0@ (THG) ↔ ¬ {1@ (THG)}There are at least zero things if and only ifthere is not at least one thing.
or
(5-11) ¬ DSC 1) THG (DSC 1) ↔ ¬ [¬ { DSC 1)
THG (DSC 1)}]
EXISTENCE
At least one thing exists.
(5-12) 1@ (THG) ↔ DSC 1) THG (DSC
1)
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There is at least one Thing if and only if there is a Description1 such that Description1 is a Thing.
(5-13) 1 (THG) ↔1@ (THG) Λ ¬ 2@
(THG)There is exactly one Thing if and only if there at one least Thing, and there are not at least two Things.
NOTHING
(5-14) 0@ (THG) ↔ ¬ DSC) THG (DSC)There are at least zero Things if and only ifthere is no description such that a description is a Thing.
(5-15) 0 (THG) ↔ ¬ 1@ (THG)
There are exactly zero Things if and only if there is not at one least Thing.
SOMETHING
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(5-16) 1@ (THG) ↔ DSC) THG (DSC)There is at least one thing if and only if there is a description such that the description is a thing.
(5-17) 1 (THG) ↔1@ (THG) Λ ¬ 2@
(THG)There is exactly one thing if and only if there at one least Thing, and there are not at least two Things.
When something and nothing are equivalent, the following contradictions occur as the conclusion:
(5-18) 1@ (THG) = ¬ [1@ (THG)]Something is not something
(5-19) 1@ (THG) = 0@ (THG)At least one thing is at least zero things
(5-20) DSC) THG (DSC) = ¬ { DSC)
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THG (DSC)}There is some description such that the description is a thing and that description does not exist
(5-21) 1 (THG) = 0 (THG)Exactly one thing is exactly zero things
(5-22) 1@ (THG) Λ ~ 2@ (THG) = ¬ 1@
(THG)At least one thing, and not at least two things, is not at least one thing
(5-23) { DSCN) THG (DSCN) Λ JN
(DSCN)} = ¬ { DSCN) THG (DSCN) Λ
JN (DSCN)}At least N Things are not equivalent to at least N things.
(5-24) ¬ { DSC1) Thing (DSC1)} = ¬{ DSCN) THG (DSCN) Λ JN (DSCN)}At least zero things are equivalent to not at least N things.
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(5-25) { DSCN) THG (DSCN) Λ JN
(DSCN)} = ¬ { DSC1) Thing (DSC1)}There are N Descriptions such that each description is a thing and each description is different, is equivalent toThere is no description1 such that description1 is a thing
OrAt least N Things are equivalent to at least zero things.
When the logical opposites, something and nothing, are equivalent to each other, every description of things is the same, and they are the description of zero things.
6. Summary We have examined the consequences of equivalent opposites to logic, number/mathematics, science, reasoning, and something from nothing. Thefollowing theorems were proved:
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Theorem 1-Consequences to Logic: If opposites are equivalent, every formula is a theorem, every statement is derivable, and all inferences cease.
Theorem 2-Consequences to Number/Mathematics:If opposites are equivalent, every number is the same, equivalent to zero, and the capability to calculate ceases.
Theorem 3-Consequences to Reason: If opposites are equivalent, every description is the same, and the capability to make decisions ceases.
Theorem 4-Consequences to Science: If opposites are equivalent, every physical model is the same, and the capability to determine physical reality ceases.
Theorem 5-Consequences to Something from Nothing: If opposites are equivalent, the definitions for something and nothing are the same, each thing is the sameas nothing, and nothing should now exist.
The result:
If something can come from nothing, all equivalentopposites are true. The description of something is thenthe same as the description of nothing. And, all inference-based processes cease to work. When something from nothing is true, inference in logic,
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calculation in mathematics, physical reality in science, and decision making in reasoning, all stop. Any process that admits equivalent opposites inserts a contradiction into any process that is used to establish conclusions. Because at that time, all opposites are equivalent, any challenge to the prohibitionfor using equivalent opposites always refutes the very method used to prove that there is an alternative method.
The prohibition of equivalent opposites is always madeas an axiom in analytical works of logic calculi. It must be extended to the rest of the sciences.
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REFERENCES
[1] Bara, Bruno G. (1995) Cognitive Science - A Developmental Approach to the Simulationof the Mind, Lawrence Erlbaum Associates, Hove UK
[2] Beyer, William H; Editor. (1287), Handbook of Mathematical Sciences, 6th Edition, CRC Press, Florida
[3] Boolos, George (1226), The Logic of Provability, Cambridge University Press, United Kingdom
[4] Carnap, R. (1258), Introduction to Symbolic Logic, Dover Publications, Inc., New York
[5] Dedekind, R. (1201) Essays on the Theory of Numbers, Open Court Publishing Company, Illinois
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[6] Feynman, Richard; Leighton, Robert; Sands, Matthew (1989) Feynman Lectures on Physics. Addison-Wesley, New York
[7] Feynman, Richard (1994) Character of Physical Law Random House, New York
[18] Mayr, E. (2001) What Evolution Is, Basic Books, New York
[19] Norman, Donald (1988) The Design of Everyday Things, Doubleday New York
[20] Penrose, R. (2004) The Road To Reality:A Complete Guide to the Laws of the Universe.Random House, London
[21] Rogers, Yvonne, Rutherford, Andrew, and Bibby, Peter (Ed.) (1992) Models In the Mind - Theory, Perspective, and Application, Academic Press, London
[22] Seber, George A. F. (2007), A Matrix Handbook for Statisticians, Wiley-Interscience, New York.
[23] Shimony, A. (1993), Scientific Method and Epistemology, Vol. 2, Cambridge University Press, Cambridge, United Kingdom
On Oct 20, 2010, at 11:42 AM, Thomas Lindley wrote:
Dr. Erich Reck,
As logicians, we assure consistency by always inserting an axiomthat prevents logical opposites from being derivable. Although this isfundamental to logic, it has not yet extended to most of the other sciences. The acceptance of something-from-nothing in the studyof the origin of the universe and quantum theory are examples. I am submitting this article, The Consequences of Something from Nothing, for The Bulletin of Symbolic Logic, to show that there areunacceptable consequences for accepting equivalent opposites.
After consulting with the other editors at the Bulletin, we have come to the conclusion that your paper is not suitable for further review by us.There are a number of reasons for this decision.Let me mention a few:
First, the paper is not well written, even at a grammatical level, and clearly does not conform to BSL's standards in that respect.
Second, the presentation of the technical material in it is highly non-standard and, again, not up to BSL standards or those of similar journals.
Third, the paper contains a whole number of statements about logic that are simply incorrect orat least highly misleading (e.g., the claim that "analytic logic always assures consistency by inserting an axiom that prevents logical opposites from being derivable"). Apart from that,
Fourth, the logic presented in the paper, to the degree to which it is correct, is fairly trivial, again compared to BSL standards, thus not warranting publication in that respect as well.
Fifth, the paper is much too sweeping overall, i.e., more like a popular science essay than anything a technical journal such as BSL publishes.
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Overall, there is no chance the paper could be published by us so that sending it to outside reviewers would be pointless. I am sorry if this judgment sounds harsh; but I wanted to let you knowabout the decision without further delay.
