XPost: comp.theory, sci.logic

olcott <polcott2@gmail.com> wrote:

I will start simple with the most self-evident points

*Smart people can understand that*
"This sentence is not true."

is not true and that does not make is true because
if it was true then it would not be not true.

It is also not false. If it was false then it would not
be not true which would make it true. So smart people
understand that it is neither true nor false.

*Even smarter people can understand that when we ask*

Is this sentence (true or false): "This sentence is not true." ???<<<

That neither true nor false is a correct answer.

I will stop there until I have a good consensus.

The Tetralemma (Catuṣkoṭi) from Siddhartha Gautama is - as far as I know - the oldest idea for a proper answer, where also BOTH and NONE are possible values. Rudolf Kaehr has written a "diamond theory" about it - but of
course he had the best cybernetic "parents" like Norbert Wiener, Heinz von Foerster and Warren McCulloch, who already explored the self-references of
our nervous system - today we can understand the world as infinitely
complex system consisting of positive and negative feedbacks. And your
little "paradoxon" is just a binary version of it. Fortunatelly, Gotthard Guenther has learned us, how to look onto it from a new perspective by
leaving the one-dimensional true/false-logic.

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