August
31, 2017 Thursday
Bedtime
Story
Constructing Tarski's Formal Restricted Language
Just
look at this interesting temporal deixis “tomorrow”.
We
all know that “tomorrow” defines the consecutive next day after every day.
Yet
“tomorrow” of the day when I was hospitalized last year would certainly be
different from the “tomorrow” of the Sunday that is going to come next.
The
point that Tarski was making was that such ambiguous words have no place in the
vocabulary of our language.
Formalized
languages are those languages that satisfy these conditions with supreme rigor.
What
is unique about such formalized languages is that there remains nothing to
distinguish in expressions that have the same form used in different places.
They
mean exactly the same not having any bearing to the context they were said or
written.
Tarski
says that on some occasions this technique is also used by linguistics while
discussing natural languages that have not been formalized.
This
is done to avoid any confusion.
Tarski
admits that once a language is so formalized, they are fully geared up for theorizing
on logic and mathematics.
He
recommends that the other sciences too should get rid of the usage of natural
languages and switch over to naturalized languages.
He
once again wished to make it clear that when he speaks about formalized
languages, he does not wish the formal language to be like the formalized
mathematics of Principia Mathematica, comprising solely of untried weird
symbols.
Nor
do the formalized languages need to be diametrically opposite to that of the
natural languages.
Au
contraire, he feels that the formalized languages would only be interesting if
they consist of fragments of natural languages.
The
fragmented language would still have the complete vocabulary that will allow
everything to be expressed clearly along with extremely precise syntactical
rules.
There
are some other conditions that are to be complied with in order to rationally
use the word “true” in the languages without ending up in paradoxes like that
of the Liar.
One
is that a sharp demarcation has to be made between the language which is under
discussion about which something is being said and the language that is being
used in defining the former.
This
point was already brought up in my previous bedtime stories.
The
former, as you will recall, is known as the object language and the later the
metalanguage.
The
metalanguage obviously will be more copious than the object and will encompass
it as well.
For
truth to be defined adequately in such a system of languages, any equivalent of
form [D] will work out.
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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