July
21, 2017 Friday
Bedtime
Story
Abhari and the Negation of Conjunction
Abhari
took the following sentence into consideration while analyzing the Liar
Paradox:
“All
that I say at this moment is false.”
Before
giving the solution, or what he considered a solution, he gave the following
analysis of the paradox.
“This
statement is either true or false.
If
it is indeed true, then it must be both true and false.
And
if it is not true, then it is necessary that one of his sentences at this
moment is true, as long as he utters something.
But
he says nothing at this moment other than this sentence.
Thus
this sentence is necessarily both true and false.”
Abhari
offered the following solution to the Liar paradox:
“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.”
I
know it does not make much sense.
Abhari
is invoking here some of the fundamental laws of logic that in modern days go under
the name of negation of conjunction and negation of disjunction.
Anybody
who has done a basic course on Boolean Algebra or propositional logic would
know of De Morgan’s laws.
Let
me state these laws before we discuss them.
Negation
of conjunction is the disjunction of the negations.
Another
way of stating it in the terms of set theory is that the complement of the
union of two sets is the same as the intersection of their complements.
In
more formal language, the negation of conjunction would appear like this:
¬(P ⋀
(¬P) ⋁
(¬Q)
where
P and Q are two propositions.
The
other symbols are all too familiar to the readers of bedtime stories.
I
will deal with the negation of disjunctions in the nights to come.
You
might think all this too theoretical.
The
fact is that these simple logical rules form the basis of the devises that you
are holding in your hands.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
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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