I have come across something quite interesting, this being the Liar Paradox. Which is this in its simplest form:
Or to avoid self reference (a logical not):
Before we can address the Liar Paradox, some simple foundation for logic have to be laid down, I will give the widely accepted axioms for classical logic as presented by Leibniz:
1) Everything is identical with itself.
2) No statement is both true and false at the same time.
3) Every statement is either true or false.
These are the three most important ones (concerning the paradox).
This paradox seems to invalidate our most basic and foundational axioms from which we base many ideas, discoveries, philosophies and logics on.
The question being then, is this an issue with logic, or with language? Is logic at fault here and our classical logic needs re-evaluating? Or is it simply semantic limitations? However, seeing as language is supposed to function "constructively" upon logical predicates and modifiers, then does this mean (if either logic or language is in danger) that both are in danger? What does this mean then for our highly prided upon system of logic and foundations for many theories concerning metaphysical truths (or lack of) and philosophies?
This sentence is false
Or to avoid self reference (a logical not):
Before we can address the Liar Paradox, some simple foundation for logic have to be laid down, I will give the widely accepted axioms for classical logic as presented by Leibniz:
1) Everything is identical with itself.
2) No statement is both true and false at the same time.
3) Every statement is either true or false.
These are the three most important ones (concerning the paradox).
This paradox seems to invalidate our most basic and foundational axioms from which we base many ideas, discoveries, philosophies and logics on.
The question being then, is this an issue with logic, or with language? Is logic at fault here and our classical logic needs re-evaluating? Or is it simply semantic limitations? However, seeing as language is supposed to function "constructively" upon logical predicates and modifiers, then does this mean (if either logic or language is in danger) that both are in danger? What does this mean then for our highly prided upon system of logic and foundations for many theories concerning metaphysical truths (or lack of) and philosophies?