Checking proofs and arguments.

[sigurdV]

Here is an argument I want to get checked.

I first posted it in Philosophy since its immediate concequences are probably most of philosophical interest.

But now ,on second thought, I decided that Philosophers lacks the necessary qualifications:

They dont usually show any logic ability. Their forte is NOT checking proofs

The question of Paradoxes is of some Mathematical interest:

It is known how to remove them (preventing self reference) ,

but then they can no longer be derived,analysed and solved.

So Dear Mathematician: Is there an error somewhere in the argument below?

(Ahem...I did not intend underlining everything above, and neither this line...sigh)

Definition:

y is a Liar Identity if and only if y is of the form: x = "x is not true", and if y is true then x is a Liar Sentence defined by y.

 

No liar identity is Logically true.

Proof (Based on: (a=b) implies (Ta<-->Tb)

 

1. Suppose x="x is not true" (assumption)

2. Then x is true if and only if "x is not true" is true (from 1)

3. And we get: x is true if and only if x is not true (from 2)

4. This contradicts the assumption. (QED)

The logical form of the Liar Paradox:

 

1. x is not true.

2. x = "x is not true".

Some values for x makes the Liar Identity Empirically true:

 

1. Sentence 1 is not true.

2. Sentence 1 = " Sentence 1 is not true."

 

To get to the paradox one must produce

 

"3. Sentence 1 is true." from sentences 1 and 2.

 

But since sentence 2 is BOTH Empirically true and Logically false it can not be a well formed sentence!

Therefore no paradox can be derived from sentence 1.

 

Any comment this far?

Edited June 27, 2012 by sigurdV