July
27, 2017 Thursday
Bedtime
Story
Tarski Offers a Solution to the Liar Paradox
If
you ask me from where I got all this material that dates back centuries, that
would be a very valid question and I would be obliged to answer.
Since
it is generally a one way correspondence, I will assume that the question was
raised and hence I will force myself to reveal my sources.
I
got the material for my recent bedtime stories from a paper published in 2009
by two scholars, Ahmed Alwishah of Stanford University and David Sanson of Ohio
State University in the journal Vivarium.
I
think it is important to give some reference even in writing something as banal
and as unimportant as bedtime stories.
Now
we shall come back to Alfred Tarski and see what he had to say on the centuries
old Liar Paradox.
Tarski
saw the whole paradox as an outcome of the structure of language.
While
Tusi too had found the origin of the Liar Paradox in the self-referential
structure of the language, he really could come out with no solution to its
resolution.
Tusi
got over the problem by simply pronouncing that such self-referential declarative
sentences are not deserving of being assigned truth values.
Tarski,
on the other hand, offered a solution to this long-standing vexing conundrum.
He
recommended that whenever one needs to assign truth-value to a sentence, one
needs to consider language to be made up of different levels or hierarchy.
He
says that the Liar Paradox arises because our language is “semantically
closed.”
In
a closed language like ours it is possible for one sentence to state the truth
or falsity of another sentence or even itself.
This
can be avoided only if we assign the idea of hierarchy in languages.
Then
within it, only the sentences of languages at higher levels be allowed to
predicate truth level to sentences in lower levels of language.
In
such a case, the sentence to which the truth (or false) value is being assigned
would be the “object language” whereas the sentence which is referring or
assigning these values would be a part of a “meta-language”.
In
such a system of “languages”, it would be permissible for sentences in the
higher semantic hierarchy to assign truth values to sentences lower in the
semantic hierarchy, but not the other way around.
This
will prevent the paradox from arising as it will prevent the system from
becoming self-referential.
This
is a brilliant thought mon ami, isn’t it no matter how unrealistic may be its
applicability.
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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