April 26, 2017 Wednesday
Bedtime Story
In the Most Endearing Words of Mon Ami, "Formal Logic Subsumes All Math"
In the story of mathematics, written by far better and greater
writers and mathematicians then me, logic always seems to get left out.
Great emphasis is laid to geometry, algebra and number theory and
even applied physics, but somehow logic tends to get no space, not even a
mention.
For Kurt Gödel, mathematical logic was “a science prior to all
others, which contains the ideas and principles underlying all sciences.”
According to my best friend and the most voracious reader and most knowledgeable man of mathematics that I
know of personally, “Formal Logic subsumes all math”.
The honor for codifying logic for the first time is attributed to
Aristotle who was the tutor to Alexander the Great till the mighty emperor
reached 16.
Aristotle taught the future mighty emperor somewhere around the
period of 340 BC at the “Shrine of the Nymphs” in Mieza, a village in ancient
Macedonia.
His work Prior Analytics on deductive reasoning is not only the
first of its type, but stood to be the only one till the dawn of that
incredible nineteenth century.
In his Prior Analytics, Aristotle presents and identifies valid
and invalid form of arguments called syllogism.
Syllogism as taught by Aristotle is an argument that consists of
at least three statements.
There should be at least two premises and in the end, a
conclusion.
I will not delve too much into Aristotelian logic but suffice to
say that it remained the corner stone of logic till the entry of George Boole
and his seminal works “The Mathematical Analysis of Logic” (1847) and “The Laws
of Thought” published in 1854.
George unfailingly and unwaveringly accepted Aristotelian logic,
but he wanted “to go under, over, and beyond” it in three very diverging ways:
1. To provide and arm Aristotelian logic with mathematical
foundations
2. To extend the class of problems it could treat
3. To expand its range of applications
For this, Boole had to develop a special type of algebra for logic
with specific new notations never ever tried before.
Boole in short found a way to convert Aristotelian syllogism or
arguments into symbols and notations and thereby inventing symbolic logic.
This can be illustrated with a simple example.
We will take up the example in the nights to come.
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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