July
17, 2017 Monday
Bedtime
story
Liar's Paradox
Alfred
Tarski. By the time he published his paper “Truth and Proof” in 1969 had
comfortably settled himself in the Mathematics Department at the University of
California, Berkeley (since 1942).
Over
there he had built quite a formidable reputation for himself as a teacher.
His
seminars at Berkeley had become legendary, especially those dealing with formal
logic.
With
this little bit of extra background on the personal life of Tarski, let us
begin to examine his work on logic more closely.
We
will begin with the paradox that that was not invented by Tarski but goes back
to the dawn of civilization.
My
guess is that any intelligent ape of any civilization would have been quick to
grasp on to this paradox.
There
are several version of this paradox, but we will consider the most elementary
one.
“This
statement is false.”
We
shall label this statement as Statement 1.
Now
you see that grammatically and semantically, this is a perfectly straight
forward sentence.
The
problem arises when you assign a truth value to it.
Logically,
Statement 1 can either be true or false.
So
let us assign the truth value true to Statement 1 and see what we get.
If
Statement 1 is true, then “This statement is false” is true.
In
that case, Statement 1 must be false.
Which
means that our hypothesis that Statement 1 is true leads to the conclusion that
Statement 1 is false, which is a contradiction.
Now
let us assign the truth value false to Statement 1 and see what we get.
If
Statement 1 is false, the “This statement is false” is false.
In
that case, Statement 1 turns out to be true.
Which
means that our hypothesis that Statement 1 is false leads to the conclusion
that Statement 1 is true, which once again is a contradiction.
So
in the end, we land up with Statement 1 being both true and false which is a
paradox.
Many
have tried various ways to resolve this paradox.
Some
claim that the Statement 1 “is neither true nor false”.
By
this claim, the debaters are discarding the most fundamental tenant of logic:
the principle of bivalence.
The
semantic principle of bivalence is one of the cornerstones of logic which
states that every declarative sentence expressing a proposition (of a theory
under proposition) has exactly one truth value, either true or false.
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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