On the Liar Paradox.

[sigurdV]

A new approach to Paradoxes.

 

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?

PS To the moderator: I decided to ask the Mathematicians for checking my argument, since I believe they are better equipped for checking arguments. If one thread must be closed so close this one. I will then later return to Philosophy to continue on its philosophical consequences once its verified that my argument does not contain any errors.

Edited June 27, 2012 by sigurdV