September
01, 2017 Friday
Bedtime
Story
Notion of Truth Using Object Language and Metalanguage
For
truth to be defined adequately in such a system of languages, any equivalent of
form [D] will work out.
Form
[D] if you recall is “p” is true if and only if p.
“p”
will be replaced on both sides by an arbitrary sentence of object language.
All
the formulations will be done in metalanguage which then obviously means that
all the possible sentences of the object language will be contained in the
metalanguage.
Metalanguage
will also contain the names for the sentences of the object language which you
will note must not be present in the object language.
Metalanguage
will be also having those extra terms and expressions that will allow it to
examine and discuss the object language.
Metalanguage
should also be allowed to handle the object language and use it or combine its
sentences.
Take
for instance something as simple as metalanguage being able to define a set of
some sentences of the object language or being able to add two or more
expressions of the object language to form new expressions.
Metalanguage
will be allowed to express relations between both the sentences and the objects
contained in the object language.
This
will allow metalanguage to express definitions in the matters of object
language with the use of semantic terms.
Thus
metalanguage with the help of semantic terms will be allowed to define truths
in the object language.
So
metalanguage has to far more bountiful than the object language and there is no
way that metalanguage can coincide with the object language.
If
the object language could be made to coincide with the metalanguage, then both
languages would turn out to be semantically universal and then the Liar Paradox
would once again regenerate in both of them.
Tarski
concludes that if all these conditions are met with, then truth would certainly
be definable without us landing up in logical mess.
Tarski
admits that the technicality of actually carrying out this operation is far
from simple.
No
doubt that given a statement of the object language, one will be able to create
a truth statement of the form [D].
But
look at the complication that pops up.
You
will agree that the set of all sentences in the object language would be
infinite.
And
we know that any one sentence, even if very long, is made up of finite length
of words or letters.
This
will prohibit us from coming to a general definition by forming logical
conjunction of all partial definitions.
It
will only bear a vague semblance to the hypothetical infinite conjunction.
I
know the last two sentences are cryptic and will not make sense unless an
example would be provided.
I
hope to clarify those last two sentences in the nights to come.
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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