August
21, 2017 Monday
Bedtime
Story
Examining These Paradoxes
As
I was saying last night, any number of such “antinomial books” can be created
if you care to apply your mind a little.
The
“00” in any of such books that we create will be replaced by one of the numbers
from 1 to 100.
It
is allowed for the same numbers to appear in many different pages.
It
is true that not every variant of the original book will result in an antinomial
book.
Let
me explain it with certain specific examples.
Suppose
in one of our 100-paged book that we have constructed, in some page 50 it says
that the sentence on page 60 is true whereas in page 59 it says that the
sentence on page 60 is false.
This
will give rise to a discrepancy but not a paradox; it would merely suggest that
the sentence either on pages 50 or 59 are false.
The
antinomy will only be established when it can be shown that one of the sentences
in the book is both true and false, regardless of the assumptions of the truth
values of the other sentences.
Tarski
then in the paper delves a little bit in the history of Liar Paradox.
Like
a typical West-European-American writer, he writes about the Greeks but chooses
to completely ignore the contributions made by the Islamic mathematicians.
But
we can forgive him for this display of trifle unfairness as he may genuinely
not be aware of the contributions made by other civilizations to mathematics.
Not
everybody takes keen interest in the history of their subject.
Mathematics
is one science, if you can call it so, that actually developed and progressed
gradually right from the origin of humans.
Experimental
sciences, on the other hand, came much later and were very alien to
civilizations before the Enlightened Europe.
Experimental
science genuinely does have a history prior to seventeenth or at the earliest
sixteenth century.
Besides
Liar Paradox, there have been several other such paradoxes that have occupied
the minds of greatest minds for centuries.
Bertrand
Russell was probably the last of the greats to come with a version of his.
But
no matter whether of recent or antique, paradoxes like Liar’s and Russell’s
have played a great role in the development of modern mathematical logic.
Historically,
such paradoxes have been viewed in two manner of thinking.
The
first one and perhaps the most common approach is to consider such paradoxes as
clever tricks devised by sharp witted men for amusement and to be lightly
dismissed.
The
other way of looking and approaching these paradoxes is that taken by men like
Abhari and Tusi.
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