April 27, 2017 Thursday
Bedtime Story
George Boole Coverts Aristotelian Syllogism Into Notations
Here is an example how Boole converted Aristotelian syllogism into
symbols and notations, thereby revolutionizing logic.
Aristotelian syllogism applies deductive reasoning to arrive at a
conclusion based on two or more propositions.
So here we have two propositions followed by an Aristotelian
conclusion.
Only some men find mathematics interesting.
No woman finds mathematics interesting.
Conclusion: Nobody interested in mathematics can be a woman (Mind
you, this is not an absolute truth but a conclusion based on the top two propositions).
In Boolean symbolism, this can be written as:
M ⊂
W ⊂
The dash represents the negated relationship.
There is another way of this Boolean symbolism wherein the two
characteristics can be combined.
Let me show how that goes.
M-(ma) = 0 (the group that does
not love mathematics and has men does not exist). Here an assumption is being
made that all men love mathematics.
Wma = 0 (the group that has women and loves mathematics does not
exist)
The above two examples should give you quite a fair idea what
Boole was trying.
What George Boole started and never completed fully was brought to
its grand finale in 1910 by Whitehead and Russell through their chef d’oeuvre
Principia Mathematica.
This first “complete” work of true and pure mathematical logic attempted
and nearly-successfully demonstrated, (and thereby making it a very tedious
book), that all number-theoretical notions can be expressed and defined in
terms of pure logic.
It made a bold claim that all the axioms of number theory can be
derived from very few propositions that can be given the label of logical
truths.
Hence Principia Mathematica was almost Hilbert’s dream come true;
it had reduced the problem of consistency of mathematics, particularly the
consistency of number theory to the consistency of formal logic.
So now all that remained for the absolute proof of the consistency
of the axioms of number theory was to show that the axioms of logic were
consistent.
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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