August
19, 2017 Saturday
Bedtime
Story
The Paradox of the
One
again have a look at the sentence “s” that we have also labeled under alphabet
[G].
[G]
The sentence printed in red on page 65 of the June 1969 issue of the Scientific
American is false.
Whether
“s” is true or false, it definitely is a sentence of English language.
In
that case we can apply the equivalence:
[D]
“p” is true if and only if p.
That
will give us the next statement [I].
[I]
“s” is true if and only if s.
If
you care to look up, you will see that “s” stands for the sentence [G].
So
we can replace the right hand side s of [I] with the sentence [G].
That
will give us the following sentence [J].
[J]
“s” is true if and only if the sentence printed in red on page 65 of the June
1969 issue of the Scientific American is false.
Now
compare the two sentences [I] and [J] and you will agree that we can draw the
following conclusion from it which we label as [K].
[K]
“s” is false if and only if “s” is true.
We
have thus arrived at an antinomy or more precisely, a self contradicting
statement.
This
is very similar to the Liar Paradox and was conceived of first by the Polish
logician Jan Łukasiewicz who was less of a mathematician and more of a
philosopher.
He
lived during the times of Tarski and even wrote a paper with him in 1930 on the
sentential calculus.
After
the World War II he emigrated to Ireland and joined the University College
Dublin.
He
stayed and worked with the University College Dublin till his death in 1956.
In
his younger days when he was at the University of Warsaw where he twice held
the post of rector, he along with Stanislaw Leśniewski had founded the
Lwow-Warsaw School of Logic.
It
got international fame thanks to Alfred Tarski.
Of
course, all this happened before 1940 when the evil of fascism had yet to take
firm grip over the continent.
Let
me digress not too much from Alfred Tarski’s paper Truth and Proof.
Tarski
then provides another example or rather another variation of the Liar Paradox
that is slightly more elaborate.
It
is worth going through.
I
shall take it up in the nights to come.
The
point that Tarski is making with all these paradoxes is that there is something
about the natural languages and inherent inappropriateness in its structure
that allow paradoxes to emerge.
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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