Laws of Logic

1. LAWS OF LOGIC
AXIOMATIC TO MATHEMATICS - AHALLER
I. Law of Identity
II. Law of Non Contradiction
III. Law of the Excluded Middle
IV. Law of Rational Inference or
Coherency
The HolyTrinity of Logic
The Individual First Three Rely on the Fourth to Unify and
Transcend to Complete a Sound Syllogism

3. LAW OF IDENTITY
What is the definition? Whose dictionary are we using?
• Without clear definitions we cannot reason clearly.We have
word deconstruction
• “Who’s on first, what’s on Second, and “I don’t know is on
third” – Abbot and Costello
A equals A A = A 5 = 7-2

4. Definitions Have Consequences
WithoutThem We Have Confusion
Deconstruct Words People Can Rationalize Anything
LAW OF IDENTITY

5. LAW OF
NON CONTRADICTION
• A cannot equal Not A A≠ ~ A 5 ≠ 7
• Example – a book cannot be a book and not a book at the
same time
• If physically here at school, you cannot be physically
elsewhere at the same time at another location

6. LAW OF EXCLUDED MIDDLE
EITHER OR – NOT BOTH – BINOMINAL – P OR Q (~P)
NOTICE THE MATH SYMBOLS
▪ True
▪ Yes
▪ On
▪ Male (XX)
▪ Equal =
▪ LessThan <
▪ MoreThan >
▪ False
▪ No
▪ Off
▪ Female (XY)
▪ Not Equal ≠
▪ GreaterThan or Equal to >=
▪ LessThan or Equal to <=

7. Powerful Tools Available in Excel such as the
IF FUNCTION

8. LAW OF COHERENCY – RATIONAL INFERENCE
All information should create a unified whole – it should make
sense not nonsense – Coherency is the Glue that holds together
the first three laws – thus the holy trinity of logic Empirical
adequacy unified as a coherent whole
The Law of Rational Inference
If A is = to B.
and
If B is = to C
then
A is = to C

9. DEBATE AT OXFORD UNIVERSITY IN ENGLAND
 Skeptical Questioner: How dare you say truth is
exclusive!Word, words, there are nothing but
words formed and shaped by culture and time.
Why must there be a reason to everything?That
is aWestern idea. It is not Eastern!
 Why do you dogmatically insist things must be
coherent?
 Professor: Yes 1+ 2 is exclusively 3.That is the
nature of truth is the aspect of being exclusive. If I
am a member of the 4,5, and 6 inclusive club may
make me nicely sincere but sincerely mistaken.The
moment I say it is Monday it is Monday exclusively
it does not include the other six days of the week.
They are excluded.
 Regarding coherency – do you wish that from this
point forward I respond coherently or
incoherently?

10. POSTMODERN ERA
REACTION TO ESCAPE FROM REASON
 No Meaning
 No Truth
 No Certainty
 With logic it might be difficult or elusive,
but we can establish often and make
accurate predictions
 Meaning
 Truth
 Certainty

11. TESTS FOR TRUTH
AHALLER
 Meaning
 Certainty
 Empirical Adequacy: Does data exist in the real world through experimentation or historical documentation?
 Existential Relevancy: Some truths pass over into our lives and we experience the consequences. We hear of the
dangers of a tornado but do not appreciate it unless we personally experience one. Until then we must go on the
reports given us by others. Personal experience confirms matters.
 Logical Consistency: What I am observing does it make sense or nonsense? Anyone can have a theory.To discard
the spurious theories from the possible explanations make sense. The laws of identity, non contraction, and the
excluded middle become our compass.
 In a Post TruthWorld note as all measurements get jettisoned.
 Law of Identity – new definitions get deconstructed
 Law of Non-Contradiction gets rejected. A truth and its opposite have validity. We get uncertainty.
 Law of Exclude Middle gets rejected as narrow minded and bigoted for cultural, religious, or philosophical reasons
 Law of Coherency gets rejected. Everyone can have an opinion, but opinions are not necessarily certain and factual.

12. TESTS FOR TRUTH
AHALLER
 Example
 Empirical Adequacy: Does data exist in the real world through experimentation or historical documentation? Do I
have birth certificate or proof parents raised me as an Eskimo with photos?
 Existential Relevancy: Might be relevant if I need survival skills in an Artic surrounding. Personal experience
confirms matters.
 Logical Consistency: Do I look and dress like one would expect an Eskimo to be?
 In a Post TruthWorld note as all measurements get jettisoned.
 Law of Identity – new definitions get deconstructed – anyone can declare they are an Eskimo!
 Law of Non-Contradiction gets rejected. A truth and its opposite have validity. We get uncertainty. I am an Eskimo and
not an Eskimo at the same time?
 Law of Exclude Middle gets rejected as narrow minded and bigoted for cultural, religious, or philosophical reasons. How
dare you say you are an Eskimo and member of an exclusive class of people?
 Law of Coherency gets rejected. Everyone can have an opinion, but opinions are not necessarily certain and factual.
If I state I am an Eskimo, How do I establish truth?