Tuesday, November 5, 2013

Self-Referential Sentences such as the Liar Paradox

I appear to have a novel solution.

In mathematics, some numbers may be consistently defined recursively, though they must pass convergence tests. In logic, it seems convergence is impossible.

Let f(x) = 0 represent 'this statement is false.' To resolve what it means, I must substitute the statement, 'this statement is false' into 'this statement,' or f( f(x) ) = 0. Trying resolve this new statement, I get f( f( f(x) )) = 0. And so on.

The liar paradox is not a statement. It is nonsense. It can be neither true nor false.

As I've mentioned before, I should not be able to outflank the whole of professional philosophy. Their combined brainpower should find all the solutions my single brain can, just by chance. Their mistakes alone should outweigh my contribution, even if they had systematic bias against it.

Considering that both Godel's incompleteness theorems and the halting problem proof depend on these kinds of non-resolvable statements, I expected scholars to at least address the objection in passing. I expected to find I took the idea more seriously, not that I am apparently the first it has occurred to.

Explaining this bungle demands some strange ideas. Do I have superhuman insight, or are professional philosophers capable of seeing the real solution well enough to avoid it?


J. Jeffers said...


Alrenous said...

Can a statement be simultaneously true and false? That might seem like sheer nonsense to you -- but not to certain modern logicians.
It's sheer nonsense. While good scholarship is often counter-intuitive, the obverse is not true. Usually it's simply wrong.