February 02, 2017 Thursday
Bedtime Story
Logic Goes a Long Way Back
Let us see what each of the four property of a logical system
stands for.
Consistency in a system refers to the notion that one statement or
a theorem of the system should not contradict the other.
Validity in a system means that starting from true premises and
processing on it will never lead to false outcomes.
Completeness refers to provability.
This means all statements within the system can be proved by using
the arguments that are within it.
So essentially all theorems of the system are provable.
Soundness is the reverse of completeness.
It means that all the statements or the theorems within a logical
system are true.
It is difficult to find a perfectly logical system even in
mathematics.
As I plan to discuss this in future, it was proved that
sufficiently complex formal systems of mathematics cannot be consistent and
complete.
Reminds me of Heisenberg uncertainty principle, almost dooming us
to live in a “flawed” universe of uncertainty and inconsistency.
Yet, no matter how disquieting and disheartening it may sound,
logic is the basis of rationality.
From the logical reasoning, flows the deductive reasoning that is
the foundation of mathematics.
Before I enter the realms of mathematical logic, it is interesting
to know that just as Greeks were discussing logic in and around 300 BC, a Hindu
school of logic arose somewhere around that time.
The school went by the name of Nyaya and many of its beliefs on
the human sufferings and misery was based on Buddhism.
Remember mon ami, suffering is neither new nor recent as many
modern day gurus, spiritualists and religious zealots would have you believe.
It was always there since life, more specifically sentient life came
to be.
Sentience is a minimalistic way of defining consciousness.
Many life forms may not and surely do not have the human- ape form
of consciousness yet they certainly possess qualia, the ability to experience
subjective perceptual experience.
The Nyaya School despite having some influence from Buddhism went
much further, proposing some very novel views on epistemology, logic, inference
and perception.
The word Nyaya is a
Sanskrit word for method or rule, but more specifically a collection of general
rules.
The men in these schools discussed questions like what is
knowledge and what is it to know?
The branch that dealt with knowledge went by the name of Pramana, a Sanskrit word that literally
stands for “means of knowledge”.
They took immense pain to stress upon the correct means of acquiring
knowledge and upon its validity and reliability.
It is worth digressing into this Hindu school of knowledge and
logic in nights to come before we switch over to the modern formal mathematical
logic.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
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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