August
20, 2017 Sunday
Bedtime
Story
Tarski's "Antinomial Book"
Today
let me take you through yet another version of Liar Paradox which is more
serpentine yet equally illuminating.
Consider
a book that has 100 pages.
Each
page has only one sentence written on it.
On
page 1 the sentence reads:
“The
sentence printed on page 2 of this book is true.”
On
page 2 the sentence reads:
“The
sentence printed on page 3 of this book is true.”
This
keeps on happening monotonously as you keep turning pages until you reach page
99.
However,
as we turn the page 99 and go over to the 100, to our surprise and disbelief it
says:
“The
sentence printed on page 1 of this book is false.”
Now
mon ami, pray close your eyes and sit back to consider what this strange book
means.
Assume
for a moment that what was written on the page 1 was indeed false.
Then
if you turn page by page and leaf over the entire book, and you reach the last
page, you will be forced to come to the conclusion that your assumption on what
was written on page 1 was wrong.
Then
go for the other option.
Start
with the assumption that the sentence written on page 1 was true.
In
this case, the moment you reach the 100th page, you will be forced
to accept that your assumption of the sentence on page 1 was wrong yet again.
So
mon ami, once again we have a paradox or an antinomy just like the Liar
Paradox.
Tarski
calls a book like this an “antinomial book”.
I
do not think there exists any such word “antinomial” or a pronoun in any
English dictionary and it was probably coined by Tarski.
Something
akin to how Asimov had coined the word “robotics” from the already established
word “robot” back in 1941 in his short science fiction story “Liar”.
If
you think there is something unique or special about this specific 100-paged
“antinomial book”, you would be mistaken.
Tarski
goes on to explain that any number of such “antinomial books” can be created if
you care to apply your mind a little.
All
such books need to have just one sentence per page with the following format:
The
sentence printed on page 00 of this book is XX.
The
“XX” in each of the books need to be replaced with either “true” or “false”.
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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