August
15, 2017 Tuesday
Bedtime
Story
What Happens if the Word "True" Features in the Definiendum
Tarski’s
method of stating a truth surely is simple and has many advantages but it also
poses certain difficulties that were posed last night, namely the repetition
and thus the notion of vicious cycle.
So
let see another method of naming the expressions using a letter-by-letter
description of the expression.
It
is lengthy and may sound absurd, but please I beg you to continue to humor me.
[C]
The string of three words, the first of which is the string of letters K, O, A
and El, the second is the string of letters I and Es, and the third is the
string of letters Ba, La, Ae, Ac, Ak, is a true sentence, if and only if, coal
is black.
Formulation
[C] hardly differs from [A] in its meaning.
In
fact, one can consider [A] to be a miniature version of [C].
You
can see that the new formulation is hardly sagacious but in it no one claim
that it is creating a vicious cycle as it does not even has a appearance of it.
This
formulation, can in principle, be done for any sentence.
Thus,
the formulation of this type will have the appearance:
[D]
“p” is true if and only if p.
I
request you to commit this statement [D] and its form in your memory as we will
keep referring back to it in the future bedtime stories.
The
only difference in the version [C] as compared to that of [A] is that it so elaborate
that it will never be accused of generating a logical vicious cycle.
It
has to be stated clearly that any statement that would be placed in the place
of p if it contains the word “true” as its syntactical part needs to be treated
differently.
In
those cases vicious cycle will once again manifest.
Even
then, [C] would be a meaningful sentence in terms of the classical
understanding of truth.
Consider
for instance this sentence that you happened to come across while reading a
book:
[E]
Not every sentence in this book is true.
Let’s
apply Aristotelian understanding of truth to it.
In
that case, [E] would be true if, in fact, not every sentence in the book is
true and [E] would be false otherwise.
The
equivalence of [D] can be used here by substituting [E] for p.
So
what do we get if we actually carry out the substitution?
“Not
every sentence in this book is true” is true if and only if not every sentence
in the book is true.
Now
this sentence makes sense but does not give the truth value of the phrase.
To
really get the truth value of [E], one will have to read the book very
carefully and verify each sentence.
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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