September
04, 2017 Monday
Bedtime
Story
Establishing Truth
Since
the definition of truth does not provide us with the truthfulness of any
statement or a definition and since the search for the truth is the very
essence of all scientific enterprise, we need to develop some other criteria
for truth.
There
is need to establish procedures that will help identify truthful statements
from false ones.
Even
if complete truthfulness cannot established, at least probabilistic truth needs
to be hammered out.
Most
sciences have now a well-established method for finding out the truth about any
statement.
Physics,
for example, is based primary on the outcome of experiments.
Theoretical
physicists make predictions on the basis of deductive mathematics following
which experimental physicists think and devise experiments to seek out if the
predictions actually work out.
The
experimental outcomes are a feedback loop for the theoretical scientists who
either develop their ideas further or change their hypotheses (sometimes even
forced to out rightly reject them) depending on the outcome of the experiments.
Hence
experiments are the gold standard in physics.
In
my own field of medical sciences, we have a system known as Randomized
Controlled Trials to establish the truth of a statement when someone makes a
claim that some treatment works.
The
proof system in mathematics is purely deductive starting from axioms and going
step by step using the rules of the game to arrive at something.
In
this specific paper Tarski limits the notion of truth only to this deductive
science that is applied to perfection in mathematics.
The
whole method is called the axiomatic method and about which I have written a
lot in my previous bedtime stories when I was laying the groundwork for Gödel’s
theorems and writing about the foundations of mathematics that mostly took
place in the late nineteenth and early twentieth century.
It
is a great story to tell how the notion of proof developed in the axiomatic
system.
The
historical perspective is essential to our understanding of the notion of
proof, the topic of our current discussion.
Mathematics,
in the very beginning, was just a collection of sentences about a group of
objects (say geometrical figures) or maybe phenomena (perhaps speed or rate or
some stuff like that).
These
sentences were framed using certain cache of words and they were accepted as
being true.
These
sentences were neither cohesive nor had any order nor any structure.
Can
you guess why these statements were considered true?
I
think you very well can because we humans do most things in life using
intuition or heuristics.
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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