July 04, 2019 Thursday
Bedtime Story
Attempt to Try Logic Behind a Mind of True-Believer
To a brain endowed with the traits of
True-Believer evidences are violations of its axiomatic system around which it
has build up its entire “meaningful” existence and without which it will simply
“crash” (speaking in the language of machine).
I have put those two terms “meaningful” and
“crash” within quotation marks because they are ill-defined concepts in the arena
of artificial general intelligence, the Psi theory and the MicroPsi
Architecture of Dietrich Dörner and Joscha Bach.
Just consider the first axiom of Euclid
which states ‘Things which are equal to the same thing are also equal to one
another.’
It would be very difficult or almost
impossible for a mathematician to get rid of this axiom or to alter it because
axiom comes from the Greek word “worthy” and axiom in some sense is thought to
be strongly self-evident.
An axiom is the starting premise for all
further reasoning or argument.
Mind you that it was the genius of Euclid
to differentiate an axiom from a postulate.
While axiom was thought to be strongly
self-evident a postulate was simply an assertion proposed in a manner of “let
this be true” giving no assurance that the postulate in fact is true in any meaningful
way.
Euclid’s first postulate was: To draw a
line from any point to any point.
This postulate asserts that a straight line
segment can be drawn joining any two points which though seemingly obvious was
not treated as an axiom but a postulate.
These examples of the first axiom and the
first postulate of Euclid give us a fair idea of the crucial difference between
the two.
If you think that a Protestant’s axiom of
Sola Scriptura or Sola Fide is illogical you might be surprised to know that
even in mathematics there are two categories of axioms that are known as
logical axioms and non-logical axioms.
Logical axioms are found in the world of
mathematical logic or propositional logic where only symbols and the most
primitive connectives are used such as equal or negation.
For instance let us consider the most basic
logical axiom which is the axiom of equality found in first-order logic of a
first-order language.
It says that let
be the first order language.
For each variable x, the formula x = x is
universally valid.
This implies that for any variable symbol
x, the formula x = x can be regarded as an axiom.
There are several other examples of logical
axioms but we shall limit ourselves to this one.
The most important to understand about
logical axioms is that they are tautologies.
Tautologies are powerful true statements that
hold true in every possible interpretation.
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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