Re: Updated unexpected hanging paradox bibliography

george says...

>Daryl McCullough wrote:
>> My Tim Chow statement is different in that it does not rely
>> on *truth* or falsity. As Tarski shows, there is no consistent
>> way to deal with "is true" in a self-referential language, but
>> there is no comparable argument about "is believed by Tim
>> Chow".
>
>There IS, WHEN you ARE Tim Chow.

That's right. From the point of view of Tim Chow, there is
no consistent way to reason about the beliefs of Tim Chow.
However, there is no problem, from the *outside* with saying
that it has a truth value.

>"Tim Chow does not consistently believe this sentence."
>is NOT a legitimate SENTENCE, ultimately, and self-
>reference DOES have a lot to do with that.

Why isn't it a legitimate sentence?

>Self-reference is necessary to the possibility of
>the existence of a sentence that (like this one)
>can have different-beliefs-about-it held by consistent
>believers who are otherwise (other than their identities
>and their beliefs about THIS sentence) identical.

I don't think so. Suppose you have two people that
are identical. Call them Tim and Tom. We construct
two sentences, G1 and G2 such that

G1 <-> Tim doesn't believe G1
G2 <-> Tom doesn't believe G2

Now, if Tim and Tom are *really* identical (and we know this),
then the mechanisms for their beliefs are identical, and so we
can argue

G1 <-> G2

Any argument that Tim can't believe G1 can be turned into
an argument that Tom can't believe G2, and vice-versa.

But Tim and Tom can argue this, as well. So if Tim can
never believe G1, then neither can Tom.

--
Daryl McCullough
Ithaca, NY

.

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