August
24, 2017 Thursday
Bedtime
Story
Unwanted Consequence of Nihilistic Approach
To
show the unwanted consequence of taking nihilistic approach to the word “true”
Tarski gave the following example.
Consider
for a moment an ancient mathematician who is long since dead has published lots
of serious papers.
In
all his work there is one certain term that keeps repeating that is open to
different interpretations in different places.
Now
there is a mathematician existing in the present who also happens to be a
historian who comes across the works of this great guy who is long since gone.
After
studying all the works assiduously, the historian mathematician comes to the
conclusion that under one of the interpretations of that term, all the theorems
worked out by the past mathematician turn out to be true.
This
means that all the proofs turn out to be valid.
Now
it is obvious that this historian mathematician would consider this
interpretation of that specific term as true.
In
that case he might even stick his neck out and make a claim that any future
mathematician who uses this term in its same interpretation would also
eventually end up in proving his theorems.
Yet
if our historian mathematician wants to be very formal and adopts his new
nihilistic approach, then he would not allow himself to make this conjecture.
So
what has this truth-theoretical nihilism has unwittingly done?
It
has alienated the very conceptual notion of truth from our mind.
So
we are back to our old quandary.
There
has to be a solution to the problem of notion of truth such that it will not
rock the classical concept of truth and yet not allow such paradoxes such as
Liar to arise.
For
this to happen, there has to applied some restrictions on the notion of truth
yet at the same time keeping it available for the purpose of intellectual
discussions.
We
need to go back once again to the Liar Paradox and examine it closely.
What
is it that actually generates the paradox?
To
be more precise, what is or are the features of common natural language that
gives origin to the antinomy.
Tarski
says that one feature that starkly stands out of the natural languages is their
universality.
The
all tend to be all-comprehensive and that is exactly the basic intent of any
common natural language.
It
is the very medium that allows to express anything and everything that is
capable of being expressed.
To
fulfill this requirement, its vocabulary is constantly expanding.
A
natural language has linguistic objects and semantic terms.
Stay tuned to the voice of an average story storytelling
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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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