Re: How about Self-Inconsistency
Rob and Yang,
Paradoxes of self reference have been known
for millennia. The oldest known example is
Zeno's paradox about lying Cretans:
Epimenides said "All Cretans are liars."
Epimenides was a Cretan.
Was Epimenides lying or telling the truth?
You can construct related examples with
a single statement:
This sentence is false.
Russell's paradox is about the set of all
sets that are not members of themselves.
(This paradox was actually discovered by
Zermelo, who designed his axioms in such
a way that this set does not exist.)
In any case, this paradox is not about self
reference, but about self membership, which
is not, in itself, contradictory.
Gödel's famous theorem constructs a formula in
arithmetic that can be interpreted as saying,
This formula is not provable.
If this statement is true, then there are true
statements that are not provable. If it is
false, then arithmetic is inconsistent because
there are provable statements that are false.
Since the second alternative is undesirable,
most people assume the former.
John Sowa