September
02, 2017 Saturday
Bedtime
Story
Conclusion of First Part "The Notion of Truth"
Tarski
then outlines the procedure how this operation can tried out, the operation
being construction of the notion of truth as envisaged by him.
Perhaps
once you see Tarski’s construction of the notion of truth in object and
metalanguage, those last two sentences of last night’s bedtime story might
become more clear.
First,
he says, take the simplest sentences that do not contain other sentences as
part.
For
them truth can be defined directly using the same form that we had discussed
earlier.
Then
use syntactical rules that allow formation of compound sentences from simple
sentences and extend the definition to them.
Here
we will need to apply recursion, a well established mathematical technique.
The
definition thus created can be used to develop the entire theory of truth.
This
theory of truth will have many truths of the logical equivalence form [D].
Besides
these, it will also generate some famous general laws such law of contradiction
and law of excluded middle.
Law
of contradiction or sometimes also known as the law of non-contradiction is the
second of the three classical laws of thought.
It
says that two contradictory statements cannot both be true at the same time in
the same sense.
For
instance take the two propositions:
“A
is B” and
“A
is not B”.
These
two propositions cannot simultaneously be true and hence are mutually
exclusive.
The
law of excluded middle was discussed earlier and it forms the third of the
three classical laws of thought.
It
states that for any proposition, either the proposition is true or its negation
is true.
So
Tarski says that with his system of object and metalanguage and using the
logical equivalence of the form [D] for framing the truths, even these laws can
be derived.
With
this Tarski ends the first part of his fascinating paper, The Notion of Truth.
Now
we shall move on to the second part of Tarski’s paper which is titled:
The
Notion of Proof
It
would, I think, make sense if I take it up in the nights to come.
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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