July
16, 2017 Sunday
Bedtime
Story
Tarski and Gödel
As
I was saying, some of the greatest have argued that mathematics and logic are
identical.
The
book ‘The Principles of Mathematics’ that Bertrand Russell wrote in 1903 and
deals essentially with the foundations of mathematics has 59 chapters broadly
divided into seven parts: indefinables in mathematics, number, quantity, order,
infinity and continuity, space, matter and motion.
In
the book there is this crucial sentence in the very first chapter “Definition
of Pure Mathematics” that relates to our story on Tarski.
“The
fact that all mathematics is Symbolic Logic is one of the greatest discoveries
of our age; and when this fact has been established, the remainder of the
principles of mathematics consists in the analysis of Symbolic Logic itself.”
So
to Bertrand Russell, it was a given that any pure mathematician by default has
to be a logician.
By
the way, this book “The Principles of Mathematics” in the words of the great
man himself was only “a crude and rather immature draft of the subsequent work”
to his magnum opus that would follow suit.
That
magnum opus was, as now you are well aware, was the Principia Mathematica that
would form the nutrient agar on which the fertile mind of Gödel would weave his
remarkable incompleteness theorems.
Tarski
and Gödel were born close to each other, both temporally and spatially.
Tarski
was born in 1901 and Gödel in 1906 (Poland and Austria-Hungary respectively)
and both would leave for America almost at the same time around 1939 and
eventually both would end up becoming U.S. citizens.
Tarski
met Gödel twice in his life, once in 1930 when he went for a lecture at the
Karl Menger colloquium, University of Vienna.
The
other encounter was in the United States in the haloed grounds of the Institute
of Advanced Study in Princeton in 1942 where he had got a position as a
short-term research fellow.
But
it seems to me that it was more the impact of the work of Gödel (besides the
other logicians) than these two encounters that must have had a strong
influence on Tarski in his contributions to formal logic.
I
will try to study Tarski’s work on logic under the following headlines:
(i)
Liar Paradox
(ii)
The Concept of Truth in Formalized Language
In
1933, Tarski had published a lengthy paper in his native language Polish trying
to establish a mathematical definition of truth for formal languages.
(iii)
Tarski’s Undefinability Theorem
(iv)
Truth and Proof
“Truth
and Proof” is the title of the famous paper that Tarski had published in 1969.
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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