On Apr 3, 5:58 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:

But then what about
the sentence

This sentence cannot be assigned a truth value, since it
involves infinite regress.

Meh. It requires orders of magnitude more machinery to
formalize than the previous ones, and what would be the
lesson learned in doing so? That trying to model natural
language formally is a bad idea?

On Apr 3, 8:38 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:

It doesn't have anything to do with natural language,
specifically. It has to do with the meaning of the
predicate "true".

I have no idea what you're driving at.

My default conception of "true" is that it is one of
two values in the boolean domain,

My default conception of "true" is that it is one of
two values in the boolean domain, and my default
conception of evaluating expressions is within a
computational model.

On Apr 3, 8:12 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

As usual, "This statement is not true" yields a paradox even with
Marshall's third possibility.

I suppose I see what you mean, but I have to point out that
under a wide range of evaluation models, "not true" and
"false" are exactly the same thing, so your above sentence
would be the same as the liar's paradox.

I may just be overly pragmatic in my thinking, but I really
don't see the value to the logician of riddles.

Natural language has ambiguous, nondeterministic,
context-sensitive semantics by design and intent.

Marshall says...

I take the view that the paradoxical aspect isn't the real issue
with the Liar's Paradox; rather it's the infinite regress, which
is every bit as present in the Truth Teller as in Liar. Neither
statement can be assigned a truth-value because both
statements require that they be assigned a truth value
before they can be assigned a truth value.

Then we have three types of sentences, true, false, and
sentences involving infinite regress. But then what about
the sentence

This sentence cannot be assigned a truth value, since it
involves infinite regress.

But then what about
the sentence

This sentence cannot be assigned a truth value, since it
involves infinite regress.

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

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.

On Apr 3, 9:29 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
Marshall says...

On Apr 3, 8:38 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
It doesn't have anything to do with natural language,
specifically. It has to do with the meaning of the
predicate "true".

I have no idea what you're driving at.

That the Liar Paradox has nothing to do with natural language,
specifically.

Okay, perhaps I wasn't explicit enough with my original reply.
My reaction to your statement, "The Liar Paradox has nothing to
do with natural language" is yes, the same issue shows up in
other contexts besides natural language ones, which can be
seen by translating Liar's from its natural language form into a
formal language. However I don't understand *why* you're saying
this particular sentence at this point.

Meh. It requires orders of magnitude more machinery to
formalize than the previous ones, and what would be the
lesson learned in doing so? That trying to model natural
language formally is a bad idea?

Well, a *sentence* is neither equal to the boolean
value true nor is it equal to the boolean value false.
So how does it make any sense to call a statement
true or false?

Um, I'm guessing you're asking leading questions as
part of some sort of pedagogical technique.

On Apr 3, 9:43 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
Marshall says...

I may just be overly pragmatic in my thinking, but I really
don't see the value to the logician of riddles.
Natural language has ambiguous, nondeterministic,
context-sensitive semantics by design and intent.

The Liar Paradox doesn't have anything specifically to do with
natural language.

Do you see your reply as having some relevance to what
I wrote?

On Apr 3, 11:16 am, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:

Do you see your reply as having some relevance to what
I wrote?

Yes. You said: "Natural language has ambiguous, nondeterministic,
context-sensitive semantics by design and intent". I responded
by saying that that has nothing to do with the Liar Paradox
(the subject of this thread). Maybe you didn't intend for your
statement to have any relevance to this thread?

Have you found success in the past with the technique of
repeating the same phrase over and over again in response
to requests for clarification?

On Apr 3, 11:06 am, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
Marshall says...

Um, I'm guessing you're asking leading questions as
part of some sort of pedagogical technique.

Look, you made a post about the Liar Paradox. I don't
think that your post made very much sense. But if you're
not interested in defending it, I'll let it drop.

If you think something I wrote didn't make much sense,
I'd invite you to point out what you object to specifically.

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

No. Just like you compared "All apples are cubes that glow in the
dark" to reality, you have to compare "this sentence is false" to
reality. But it CANNOT be compared to reality, hence it is
meaningless. Since it cannot be compared to reality it is not a
picture of any possible state of affairs. It is as simple as that!

Newberry <newberr...@gmail.com> writes:
No. Just like you compared "All apples are cubes that glow in the
dark" to reality, you have to compare "this sentence is false" to
reality. But it CANNOT be compared to reality, hence it is
meaningless. Since it cannot be compared to reality it is not a
picture of any possible state of affairs. It is as simple as that!

How is it that I can't compare "This sentence is false" to reality,
but I *can* compare "This sentence has five words" to reality?

Newberry <newberr...@gmail.com> writes:
No. Just like you compared "All apples are cubes that glow in the
dark" to reality, you have to compare "this sentence is false" to
reality. But it CANNOT be compared to reality, hence it is
meaningless. Since it cannot be compared to reality it is not a
picture of any possible state of affairs. It is as simple as that!

How is it that I can't compare "This sentence is false" to reality,
but I *can* compare "This sentence has five words" to reality?