July 08, 2019 Monday
Bedtime Story
Disturbing Non-Logical Axioms
All these axioms (commonly referred to as ZFC)
on which several systems of mathematics are based upon belong to the class of
non-logical axioms and this should come as a surprise to most thinking apes.
It actually disturbed me in a manner that I
find hard to put down in words since it really has no consequence on my
everyday working life or to my cellular biochemistry or to my banal existence as
an ophthalmologist.
But to see the most fundamental of our
operating system on which the world of theoretical physics or mathematical
physics operates is based on non-logical axioms (though it is almost never put
explicitly that way) is deeply unnerving.
This, of course, does not demean the
physical explanations since unlike mathematics physical theories and laws are
not totally deductive but based on induction reasoning and backed by constant
experimental verifications.
Experimental testing is perhaps crucial
BECAUSE of the fact that scientists understand the pit falls of pure deductive
reasoning and perhaps to some extent that not all mathematical derivations need
either be “true” or “meaningful”.
List of mathematical proofs and theorems is
probably infinitely large and only a fraction of them find application in
mathematical and experimental physics.
This is the reason why some believe that
mathematical proofs are psychological or mental objects though Leibniz, Gottlob
Frege and Rudolf Carnap (a member of the Vienna Circle) strongly contest such a
stance.
Axioms thus are best considered as a
starting point from which other statements/theorems are derived logically and
deductively.
Are these axioms meaningful?
If at all these axioms are meaningful, then
what do they mean?
Are axioms really “true”?
All these questions are beyond mathematics
and enter the realm of philosophy of mathematics that men Wittgenstein try to
question and seek answers to.
The core five beliefs of the Protestantism
perhaps can be seen as non-logical axioms that are applicable to
Protestantism-accepting True-Believers.
They are then not absolute truths and are
not applicable to areas that have nothing to do with Protestant-specific
religion.
And yet for the True-Believers their
religions are absolute and apparently applicable to all the facets of reality
and if any evidence or experimental facts contradict the core axioms of
Protestantism then it is just too bad for those evidences.
The evidence need to be discarded or turned
a blind eye at the altar of faith and True-Belief.
Once you have understood the axiomatic
system of mathematics then perhaps it allows one to see the parallel between it
and the case with the True-Believers in a more objective and perhaps reconcilable
manner.
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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