July
25, 2017 Tuesday
Bedtime
Story
Tusi Gets the Crux of Liar Paradox
Tusi
after thinking deeply on the Liar Paradox came to the conclusion that a paradox
is generated when a declarative sentence declares something about itself.
This
does not always happen in all instances of declarative sentences declaring
something about themselves but in special circumstances as in the Liar Paradox.
Consider
the example of the last night.
When
the D1 declared something about D2, there was no paradox even if the statement
D2 had been something about falsity.
For
better illustration consider these statements:
[S1]
S2 is false
[S2]
This statement is false
Notice
here that if you consider the statement [S2] by itself, then the Liar Paradox
arises.
But
when both [S1] and [S2] are taken together, the paradox disappears.
If
the statement D1 declares itself falsely to be not D1, then this false
declaration self-referring itself to be ‘false’ generates a paradox.
The
key point is the self-reference and Tusi’s genius lay in grasping that pith of
the entire paradox.
Let
us see how Tusi stated it some 800 years ago:
“Moreover,
if the first declarative statement declares itself to be false, then [both] its
being true, insofar as it is a declarative sentence, and its being false,
insofar as it is that-about-which-something-is-declared, are concomitant.
Thus
the following paradox can be generated: The first declarative sentence, which
is a declaration about itself, namely that is false, is either false or true.
If
it is true, then it must be false, because it declares itself to be false.
If
it is false, then it must be true, because if it is said falsely, then it will
become true, which is absurd.”
These
lines are astounding brilliant and the kind of thinking displayed in them is a
landmark in the history of the Liar Paradox.
Tusi
makes three brilliant analytical points that were totally novel at that time.
[1]
The liar sentence is singular wherein the subject is itself.
[2]
He clearly invokes the idea of self-reference.
[3]
He has pin pointed out the crucial assumption that is guilty of creating the
whole problem – the assumption that a declarative sentence, by its very own
nature, can declare something about anything.
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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