August
17, 2017 Thursday
Bedtime
Story
Constructing a True Sentence in Language L
If
you recall, last night we had constructed a language L comprising of 1000
sentences each of which we had labeled “s1”, “s2” and so on.
Following
this, for each sentence you would need to construct a partial definition of
truth.
Now
you know how easy it is to do that.
You
need to use the layout [D] and construct each partial truth in the format ‘“p”
is true if and only if p’.
In
the very end you will need to form the logical conjunction of all these partial
definitions.
This
is done by combining all of them into one statement by using the connective
“and” between two consecutive partial definitions.
The
final finishing touch that will have to be given to this long statement will be
to give it a different but logically equivalent form that would satisfy the
formal requirements that rules of logic impose on to definitions.
So
what will this land us with?
We
will end up with this following, almost bizarre, statement that we will label
as [F].
This
is how [F] will appear.
[F]
For every sentence x (in the language L), x is true if and only if either
s1
and x is identical to “s1”,
or
s2
and x is identical to “s2”,
or
s3
and x is identical to “s3”,
…
or
finally,
s1000
and x is identical to “s1000”.
This
sentence has all the desired requisites of general definition of truth.
It
is formally correct.
It
adequately satisfies the equivalences of the form [D] wherein “p” has been
replaced with the sentence of the language L.
Also
note that the sentence [F] definitely is a sentence that belongs to English
language but it is not a sentence of the language L.
It
cannot be so as it is made up of all the sentences of the language L and hence
it cannot be equal to any one of them.
You
will be right to argue that the procedure that we just carried out would not be
possible if we were considering the whole of English language.
There
are several difficulties one is likely to encounter if we decide to make a list
of English sentences.
It
is hard to determine when a given sentence can be called a sentence given the
flexibility allowed in the grammar of the English language.
A
specific exclamation may serve as a sentence in one instance but not in the
other.
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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