July
30, 2017 Sunday
Bedtime
Story
The Concept of "Well-Formedness" in Natural Languages
You
may scoff at the banality of the Convention-T and it really does look overdone.
This
is so because both the object language and the metalanguage are the same; same as
in English language.
Now
have a look at this sentence.
“Roza
krasnaya” is true if, and only if, rose is red.
In
the above sentence where the object language is Russian and the metalanguage is
English perhaps it appears to our mind more sensible and meaningful.
Now
it must be made clear that when Tarski originally conceived of this idea, he
had meant to be applicable only to formal languages and not to natural
languages.
After
having discussed so much about formal calculus, you can surely guess what a
formal language would look like.
Yes,
exactly like the Principia Mathematica.
A
formal language is a set of strong of symbols along with very specific set of
rules.
It
needs to be emphasized that all such ideas of formalizing mathematics and
language has its origins in the Begriffsschrift, the book on logic penned down
by Gottlob Frege way back in 1879.
Though
the title of the book literally translates as “concept-script”, its more
descriptive name would be “a formula language, modeled that on arithmetic and
pure thought.”
Why
do you think Tarski thought his idea of Convention T was not applicable to the
natural languages?
Well,
for two very important reasons at least.
First,
there is no way of deciding if a sentence of a natural language is well formed.
You
may wonder what on earth is meant by “well formed” or rather what is
well-formedness.
Well,
in a natural language well-formedness refers to that quality when a clause
confirms to the grammar.
Clause
as you may know, but have forgotten, is the smallest grammatical unit that can
express a complete proposition.
And
what you may ask is a proposition?
A
proposition is a statement that expresses something that is either true or
false.
A
clause consists of a subject and a predicate.
Now
predicate is a complex term with multiple meanings.
It
is something that seems very familiar and yet strangely inexplicable.
We
have discussed time and again the meaning of predicate from the perspective of
mathematical logic.
Now
let us examine from the point of linguistics and grammar.
Within
linguistics and grammar, there are two competing views.
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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