Re: OUTGOEDELING A HUMAN?

abo says...
stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:

Anyway, I think this is the key difference between us. For you the
Liar does not disambiguate "true". By your own accounts it is
meaningless, and so it is not true.

No, that's not my account at all. It is not correct to call an
ambiguous statement "not true". If there are two red objects
in a room (say, an apple and a stuffed redbird), and someone
says "The red thing is an apple", I can't say that the
statement is true, and I can't say that the statement is not true
unless I know what he means by "the red thing". His words
are meaningless *to me* because I don't know what they mean.
However, after disambiguation, it becomes true or false.

Sorry, I didn't read this before replying in the other thread. Again,
you're putting in epistemological terms, and now I think you are doing
this intentionally. It doesn't matter whether you can "say" a
statement is true, or not true. You can't say Goldbach's Conjecture
is true or not true, but by most accounts anyway (perhaps you have a
different one?), GC *is* true or not true.

That's because arithmetic has a standard interpretation. So
truth or falsity is understood relative to that interpretation.
In contrast, not every sentence has a standard interpretation.
You can't say that something is true or not unless you specify
the interpretation.

Secondly, "red thing" means something. Sure it's possible to insist,
"Snow is white" isn't true or false because maybe 'white' means
"red". But I would guess most people think that's just a silly
objection.

Yes, in English, "snow" and "white" have standard interpretations.
But not everything does. In particular, "true" does not have any
standard interpretation.

Finally, you're not so much talking ambiguity, as talking about a
variable which is not filled in.

You can always cast ambiguity in that way.

According to you, I think, we shouldn't talk about "true"
but "true according to interpretation x".

I'm saying that we should *understand* the word "true" to mean
"true according to interpretation x" where x is either implicit,
or it is left ambiguous.

Let me grant this (temporarily) to you for the sake of
argument. Then if I say, "S is true according to interpretation x",
and I willfully do not fill in "x", then the assertion is not true -
just as "x > 2" is *not* true.

An interpretation (at least in some ways of defining it) assigns
values to all free variables. So x > 2 is true in some interpretations
and false in others.

But anyway, we can certainly stipulate that "true"
should only be used in the form "true under interpretation x".

Anyway, an ambiguous statement is not true if it is left willfully
ambiguous.

I don't agree. Whether something is ambiguous or not is a matter
of interpretation, as well. So we can stipulate that if S is ambiguous
according to interpretation X, then S is not true, according to
interpretation X.

.... Then let L be the sentence

L is not a true ordinary sentence.

... So, our conclusions are:

1. L is not a true ordinary sentence.
2. L is a true level 1 sentence.

... Usually, there is no need to specify the sense of "true" being
meant because it can be figured out from context, or because it
doesn't matter. The Liar sentence is different in that it forces
us to disambiguate.

Now this is more a traditional hierarchal version of "true", where
levels (rather than interpretations) are a variable which needs to
fill in "true".

The levels are different interpretations, but arranged in a way
that is cumulative: Each level adds new meaningful statements.

The more general notion of truth is truth relative to an interpretation,
and the hierarchical notion is a special case.

We have "true in level i", and so on. I'm afraid I
think I can assert, "This statement is not true in any level." Is
there a level in which that statement is true?

I've already been through this before. Yes, there is an interpretation
(not a level) in which "This statement is not true in any level" is true.
One aspect of an interpretation is to specify the domain over which
quantifiers range.

So to interpret a sentence of the form "X is not true in any
level" you have to specify a set L of levels of interpretation.
If X is not true in any interpretation in set L, then

X is not true in any level

is true under the interpretation which interprets "any level" to
range over L. Of course, that interpretation itself cannot be in
the set L.

--
Daryl McCullough
Ithaca, NY

.

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