Liar's Paradox

When we call a statement true or false, we are saying that we have
compared that statement to a given fact or principle and either found
corraboration or contradiction. For example, if we say "All apples
are cubes that glow in the dark," we can only judge that statement as
being true or false by comparing the statement to what we know about
apples.

In the Liar's Paradox, we say "This very statement is false." The
alleged paradox is that if the statement is true, then it is false as
it claims, but if it is false as it claims, then it has stated the
truth and cannot be false, ad infinitum. Properly understood,
however, there is no paradox.

To judge the truth or falsity of "This very statement is false," we
must compare the statement not only to itself as explicitly required,
but also to what we know about finding the falsity of any general
statement. This is implied by the use of the term "false," much like
the term "apple" would require us to compare a statement to what we
know about apples. With the Liar's Paradox, the very fact of the
supposed paradox proves that the statement cannot be definitively
proven false. And as such, the statement is ultimately true because
it admits that it falsely asserts that it is provably false.

Similarly, in the Truth Teller, we say "This very statement is true."
Although there is no alleged paradox, the statement's self-reference
to its own veracity is not sufficient evidence for its truth. The
informal fallacy called petitio principii, or begging the question,
occurs where a questioned fact is called in as proof of that fact, and
such proofs are always illegitimate. However, we can go further here
and say that the statement is definately false because it falsely
claimed that it was provably true.

Very Respectfully,
Ray Donald Pratt
.

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