Re: The Reasoned Death of the Liar's Paradox
- From: translogi <wilemien@xxxxxxxxxxxxxx>
- Date: Thu, 02 Aug 2007 10:55:37 -0000
On Aug 1, 11:10 pm, raydpratt <raydpr...@xxxxxxxxx> wrote:
The Liar's Paradox arises from statements like "This very statement is
a false proposition." As the argument pointing out the paradox goes,
if such a statement is taken as true, then it must be false as it
claims; but, if it is false as it claims, then it has made a truthful
statement about its falsity and must be taken as true, and thus the
argument begins anew, ad infinitum.
Normally, as a matter of logic, a statement declared to be true or
false is a statement that was compared to some referent fact or
concept and either found to match or not to match.
Thus, when we say that a statement is true or false, we imply or show
that such a comparative process can be and has been carried out.
With the correct process in mind for how to comparatively find a
statement to be true or false, let us look closer at the exact meaning
of a statement that gives rise to the Liar's Paradox:
"This very statement is a false proposition."
This statement ascribes to itself the predicate-class quality of being
a statement that can be proven false by comparison to a referent fact
or concept.
what is a "a predicate-class quality"?
What do you mean by "proven"?
where do you compare it with?
?????
In judging the truth value of the statement, we need only compare the
attributes of the subject class -- here the statement itself -- with
the attributes of the predicate class -- here the comparative process
of how we find statements to be true or false.
The subject class of the statement declares itself to be false, ipse
dexit, but this is at variance with the predicate class which requires
that statements be proven true or false by comparison to a referent
fact or concept.
So, the statement has made a provably false proposition, and thus itIs your proof sound?
correctly states that it makes a false proposition, and thus its final
outside truth value is true.
Conversely, to clarify the point, the opposite statement that "This
very statement is a true proposition," would have a final outside
truth value of false because the statement asserts itself to be true
rather than being found true. The subject class -- the statement
itself -- falsely ascribes to itself the predicate-class quality of
being found true by comparison to a referent fact or concept.
Someone will urge, of course, that we have not dispensed with thethe positive version is quite an other cattle of fish i believe.
Liar's Paradox because we must change our final outside truth value
because it is contradicted by the self-assigned truth value of the
statement itself -- whether it be the positive version or the negative
version of the statement (which gets the most press).
I am more of the Popperian/ intuitionistic school,
Somethings can be formaly proven to lead to an absurdity (and are
therefore FALSE)
Being True is something very ungraspable.
We should counter, of course, that the self-assigned truth values ofWhat is practical about the death of the liar paradox?
either the positive or negative versions of the statement were a part
of the very matter that we judged with a correct, comparative process
for determining the truth or falsity of propositions. Thus, we may
reject as unsound the argument that we must change our final outside
truth values based solely on the contradictory truth values alleged in
the statements themselves.
Specifically, with the little-discussed positive version of the
statement, we have simply and correctly disagreed that it states a
true proposition.
Likewise, with the negative version of the statement, we have come to
correctly understand the statement and have agreed with its assertion
that it makes a false proposition -- thus, there is either no
contradiction in giving the statement a final outside truth value of
true or, at the very least, we have correctly disagreed with the
statement's self-asserted final outside truth value of being false.
In short, we prefer a sound process for determining the truth or
falsity of propositions, not an unsound rule that changes our final
judgments with a simple decree of disagreement.
This should be the logical death of the Liar's Paradox, and a very
welcome death for those of us who value logic as a practical matter.
Many of us have been doubtlessly tortured by the endless sing-songnot practical either
chants of "if true, then false, and if false, then true," etc.,
printed endlessly onto the paper remains of ever more dead trees.
Let's work together to spread and even sharpen the logical necessity
of the long-awaited demise of the Liar's Paradox. It's dead!
Very Respectfully,
Ray Donald Pratt
.
- References:
- The Reasoned Death of the Liar's Paradox
- From: raydpratt
- The Reasoned Death of the Liar's Paradox
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