The long tales of a tail/less ape

August 01, 2017 Tuesday

Bedtime Story

Tarski's Inductive Definition of Truth

Tarski too had come to this similar conclusion that in our natural language there is no way of deciding if a sentence is well formed.

Hence his Convention T would not be applicable to the natural languages.

The second reason why he considered the natural languages to be not capable of handling Convention T is that they are closed.

By closed, he meant that the natural languages are capable of describing the semantics of their own elements.

In this very paper Tarski gave his definitions of truth which is known as inductive definition of truth.

I am not sure why it is called inductive definition and whether this use of the word is same as implied in the use in inductive reasoning.

Let us quickly go through Tarski’s inductive definition of truth.

For a language L, that contains (not), (and), (or), (for all) and (there exists), truth definitions look like this:

(1) “A” is true if, and only if, A.

(2) “¬A” is true if, and only if, A is not true.

(3) “A ⋀ B” is true if, and only if, A and B.

(4) “A ⋁ B” is true if, and only if, A or B or (A and B).

(5) “∀xF(x)” is true if, and only if, every object x satisfies the sentential function F.

(6) “∃xF(x)” is true if, and only if, there is an object x which satisfies the sentential function F.

There seems to be nothing remarkable about these definitions.

All it seems that Tarski is done is to state something very obvious in terms of formal mathematical symbols.

Yet with the above truth definitions, one can reduce all truth conditions of complex sentences to the truth conditions of their basic constituents.

The simplest constituent of any sentence is the atomic sentence.

An atomic sentence is a declarative sentence that can either be true or false and which cannot be further broken down into any more simple sentence.

One can also call an atomic sentence as the simplest proposition.

A simple example is: I exist.

It is an atomic sentence of a natural language.

But if I say: I exist only to die.

This would already be a molecular sentence.

It is important to point out that in an atomic sentence, logic is not invoked.

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:

Tuesday, August 1, 2017