The paradox is a liar

How wonderful the paradoxes.
Paradox is one of the most beautiful logical exercises you can do. They make you navigate through a sea of uncertainties with no way out, overturning every concept and preconception like a sock. Physics, mathematics, psychology are full of demonstrations and confutations of theories and statements that inexorably end up being indemonstrable, they end up getting lost in the maze of paradox.

Today I want to dwell on one of the fundamental paradoxes of all logic: the paradox of the liar.

"Strategy is the way of paradox.

So, those who are skillful, show themselves clumsy;

those who are useful, show themselves useless.

He who is affable, let him show himself disagreeable;

Let those who are unbalanced be affable."

The paradox of the liar has its roots in ancient Greece where, it is said, in a letter that Titus sent to Paul of Tarsus the paradox was first enunciated. It had as its protagonist a Cretan prophet and recited:

"One of their prophets said that all Cretans are liars.

This statement is true."

The first formulation of the paradox is as can be seen in contradiction with itself with a Cretan (liar) who claims that his testimony is true. Start with the reasoning and enjoy the loop.

If we assume that the person who pronounces the sentence is a liar then the sentence cannot be considered true, but if we consider the sentence false then we should re-evaluate our previous reasoning and "disassemble" it, meeting a new contradiction that in turn will lead us to "disassemble" the new logic used but falling back into the previous one and so on ...

There have been various interpretations and subsequent repropositions, from Aristotle to De Cervantes, passing through Escher and Hofstadter.

In particular, Escher's painting on the hands they draw is visually stunning if we think of the paradox. 2 hands drawing each other not letting a glimpse of a way out of a question like this:

who drew the first hand?

Escher's is one of the most famous and successful graphic paradoxes in the world. Looking at the painting, we have a great responsibility towards the painting itself. We influence the perception we have of the painting, just as we, as interlocutors, in case someone asks us to clarify whether his statement is true or false when he says: "This statement is not true".

The truth lies in the middle we could say, the statement is both true and false.

We could also say that the truth does not exist in this case. It is a self-referential statement that in the end does not allow us to draw any conclusions and therefore does not exist as Aristotle would say.

A puzzle, a paradox with no way out that has generated myths, legends, but also works that represent it, like Escher's one.

Here ends the story about the paradox of the liar.

p.s.

Nothing I wrote in this post is true and I am a chronic liar.