August
13, 2017 Sunday
Bedtime
Story
Tarski uses Form of Logical Equivalence
Tonight
let us see how Tarski in this paper tried to formulate a more precise
definition of truth, an improvement over the Aristotelian one yet keeping its
basic tenets the same.
Tarski
starts with a very simple non-controversial sentence.
“Coal
is black.”
He
labels this sentence as “S”.
Then
he raises the following question: What do we mean by saying that S is true or
that it is false.
The
answer is not difficult if you go by Aristotelian definition of true statement.
If
S is true it implies coal is black.
If
S is false it implies coal is not black.
Now
if we eliminate S, we will end up with the following two formulations:
[A]
“Coal is black” is true if and only if coal is black.
[B]
“Coal is black” is false if and only if coal is not black.
Thus
[A] and [B] provide a satisfying explanation of the words “true” and “false” as
far as the sentence “coal is black” is concerned.
Since
the explanation of the words “true” and “false” is restricted to one particular
sentence “coal is black”, we can consider these definitions of “true” and
“false” to be partial.
Yet,
it is interesting to note that the two definitions that we got have a form that
follows the rule of logic, namely the form of logical equivalence.
A
logical statement that has the form of logical equivalence has two parts that
are joined by the connective “if and only if”.
The
left side is called the definiendum and the right side the definiens.
The
definiendum is the sentence whose truth value is under consideration.
In
simple words, definiendum is the term that is being defined by a definition.
Definiens
is the phrase that provided the explanation.
In
short, it defines the definition of the definiendum.
So
in our example, the phrase:
“coal
is black” is true
is
the definiendum.
And
the second phrase:
coal
is black
is
the definiens.
So
far so good.
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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