July
24, 2017 Monday
Bedtime
Story
Tusi is not Impressed with Abhari's Reasoning
Abhari
in his solution to the Liar Paradox is invoking the negation of conjunction
which you will get now if you read back his lines:
“To
solve the paradox we should not concede that if it is false then one of his
sentences is true.
For
its being true is taken to be the conjugation of its being true and being
false.
Therefore
its being false necessitates the non conjunction of its being true and being
false.
And
the non-conjunction of its being true and being false does not necessitate its
being true.”
The
only problem in his argument is that in some cases negation of a conjunction
does merit negation of conjunct.
This
is so when the conjuncts are logically equivalent.
Logical
equivalence means when one follows from the other or vice versa.
Since
the two statements:
“The
Liar sentence is true” and
“The
Liar sentence is false” are logically equivalent, negation of a conjunction can
allow negation of conjunct.
So
Abhari’s solution though very painfully thoughtful does fall apart under
detailed scrutiny of modern logic.
Tusi
himself was hardly convinced with Abhari’s reasoning of the liar paradox.
Tusi
argued that no matter what truth condition (conjunction or conditional) Abhari
wishes to associate with the Liar Paradox, it does not matter.
It
can be argued directly that its being false entails the negation of its being
false, and so entails its being true.
Tusi
then proposed his own solution to this great paradox.
He
wrote, “If a declarative sentence, by its nature, can declare-something-about
anything, then it is possible that it itself can declare-something-about
another declarative sentence.”
Tusi
is saying that nothing can prevent one declarative sentence to declare
something about another declarative sentence.
Consider
the following two declarative sentences D1 and D2.
D1.
“It is false”
D2.
“Abhari is fasting”
D1
can declare D2 to be false.
Meaning
“It is false that Abhari is fasting”
There
is no paradox being generated here simple because both the declarative
sentences have two different subjects.
A
paradox is generated when a declarative sentence declares something about
itself.
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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