Re: OUTGOEDELING A HUMAN?

abo says...

Yes, right, sorry. For the moment I have to be satisfied with, "This
sentence is not true in L," where L is the language of the sentence,
which I presume you will say I can't say.

You can say it, but a sentence doesn't have any power to demand
to be interpreted in any particular way. There will be multiple
interpretations of any sentence.

You can say that L is the interpretation intended by the person who
wrote the sentence (if any). Then

This sentence is not true, according to the interpretation that
Daryl had in mind when he wrote it.

Since I didn't have any particular interpretation in mind when
I wrote that (I was just trying to be paradoxical), then that
sentence is true, according to the interpretation I give it
*now*.

But you don't know what "unrestricted true" means. In particular,
you don't know what it means for the Liar sentence to be true.

Sure I do.

I don't think you do.

It's true if it asserts a fact which corresponds with the way the
world is - just like any other sentence.

And what does "corresponds with the way the world is" mean? Suppose
the state of the universe is completely determined by the positions
and velocities of every particle (as Newton believed). So what does
it mean for a sentence such as "This sentence is not true" to correspond
with the way the world is?

That is, I understand the sentence "This sentence is not
true,"

Well, how do you understand that sentence?

As I just said.

You didn't actually say anything. You came up with
a synonym for "is true", namely "corresponds with the way the
world is", but that synonym has no more meaning, in general
than "is true" does.

I think we must. Grammatical sentences have meaning.

It's usual to distinguish between syntax and semantics.
Being grammatical is a matter of syntactic form. Being
meaningful is a matter of *semantics*. One doesn't imply
the other.

Anyway, your description of the sentence as "meaningless"
is not a resolution, because it is simply a classification device,

Right. That's the way any logical difficulty is resolved.
You start by clarifying the sorts of objects under discussion,
and their relationships.

and as you yourself pointed out, "meaningless" is subsumed under
"not true." It doesn't provide any explanation. So your move
to talking about "true in L" doesn't help;

It helps in the sense that it is a *consistent* approach to
reasoning about sentences that mention truth. Most other
approaches are inconsistent.

you might as well have called the Liar sentence
"paradoxical" (any sentence to which we might want to assign both
"true" and "not true" is "paradoxical") and left it at that.

No, we can't just leave it at that. I already explained, calling
it "paradoxical" doesn't work. It's inconsistent and contradictory.
Let the Paradoxical Liar be:

The Paradoxical Liar is either false, or paradoxical.

Calling the Paradoxical Liar paradoxical is *itself* paradoxical:
So we can't consistently *talk* about the Paradoxical Liar.

What we *can* do, which is the sensible approach, is to avoid
discussing the truth, falsity, or paradoxicalness of the Liar.
Don't make any claims about the Liar sentence at all. That works.
But calling it "paradoxical" isn't a consistent approach.

--
Daryl McCullough
Ithaca, NY

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