September
03, 2017 Sunday
Bedtime
Story
Beginning of - The Notion of Proof
Tonight
I shall begin with the second part of Tarski’s paper – The Notion of Proof.
Throughout
the first part we saw an incredible effort from Tarski to develop an adequate
and satisfactory definition of truth.
The
satisfaction implied was that such a definition of truth with all the rigorous
conditions set up for the definition would not allow paradoxes such as Liar to
generate.
Whether
it was achieved or not may be arguable.
But
even assuming that we did manage to achieve this feat, it still does not
guarantee in any way the truthfulness of any particular sentence.
In
fact the whole exercise was never designed for that purpose.
Consider
the following mathematical statements or sentences regarding triangle.
“An
angle bisector of a triangle is a straight line through a vertex that cuts the
corresponding angle in half.
The
three angle bisectors meet at a single point that is known as the incenter
which is also the center of triangle’s incircle.”
To
know the truthfulness of the statement, our definition of truth will be of no
aid.
All
our definition of truth will help us is to confirm that that these two
sentences within quotation marks are true only if the angle bisector cuts a
vertex into half and if these three bisectors meet at the incenter.
The
statements in the quotation marks will be false if the three bisectors do not
always meet at the incenter.
To
establish the truth of these two sentences, we will have to explore the
Euclidean geometry and establish the proof.
The
same will hold true not only for mathematics but also for the other spheres of
science.
To
get to the truth of any scientific statement, it will need the rigors of
scientific method to establish or refute it.
Logic
or the theory of truth does not serve any purpose in establishing the veracity
of any statement.
There
are some isolated few who will reject any definition that does not fall under
the notion of truth that was put up by Tarski earlier.
We
all know very well that neither in the sciences nor in mathematics has there
any serious attempt made to formulate truth in the manner we have been
discussing.
In
fact, if it was so attempted, most of the stuff of mathematics and theoretical
physics, chemistry and biology would have to be got rid of.
Definitions
of some of the most elementary objects of science such as atom, electrons,
protons, genes, cells or even life does not comply to the notion of truth that
we have been discussing.
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.
Advertisements
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:
No comments:
Post a Comment