TheBanyanTree: linguistic paradox (of omniscience) resolved

[JMoney]

Peter wrote:

> I heard John Barrow three years ago ... He is, in fact, remarkably
unassuming for a world leader
> in cosmology, black holes, and stuff like that. ... and he is
> VERY well thought-of.)

I don't doubt it in the slightest.  Nevertheless everyone's entitled to make
the odd mistake from time to time and this is one of his.

I feel like skiting for a bit about how clever I am to have picked up a
world-leader-in-cosmology's logical boo-boo and to have made a not entirely
incoherent fist of figuring out why it is in fact a boo-boo after only a few
hours of thinking about it, but that would be ungracious and, besides, the
only reason I'm sure it's a boo-boo is because of something else I read in
the book - on pages 195-6 actually.  And no, I haven't read so far so fast.
Housewifely duties continue to claim a lot of the time I would like to use
for reading and learning how to use my new sewing machine.  I got to those
pages merely because, while having my afternoon coffee, I was flipping
through the book, looking for some sort of an explanation of Godel's
theorem, of which I've heard and that's all, when I came across another
interesting little section on paradoxes.

In a discussion on language and meta-language (i.e., language versus
language used to talk about a language) Barrow provides a sentence that can
be used to prove that the Earth is flat, "Either this whole sentence is
false or the Earth is flat," and then proceeds with his proof as follows:

"This sentence is either true or false.  If it is false then, by its own
statement, the Earth must be flat.  It is is true, then either the first
statement 'this whole sentence is false' or the second statement 'the Earth
is flat' must be true.  Since were are now assuming the whole sentence to be
true, the first possibility is excluded, and hence the second must be true.
Therefore, the Earth is flat!  Better still, you can replace 'the Earth is
flat' with any other statement you care to choose and by the same reasoning
prove that it is true."

Now of course the earth is not flat, despite what some people might think,
so there is a flaw somewhere and the flaw is in the sentence.  As Barrow
says, "It mixes statements [the earth is flat] and (meta)statements about
statements [this whole sentence]."  As Barrow also says, "This careful
distinction [between language and meta-language] removes all sorts of
ancient linguistic paradoxes like 'this sentence is false'."

That is precisely what the sentence, "This statement is not known to be true
by anyone" does.  It mixes language and meta-language.  Therefore the proper
conclusion is not that there cannot be an Omniscient Being who knows all
truths but that the sentence is flawed and therefore meaningless.

Obviously Barrow knows that one should distinguish between language and
meta-language in a statement before trying to determine whether the
statement is true or false.  I am left to wonder why he didn't do so when
attempting to prove that there cannot be an omniscient being such as we
usually call God.  Probably for one or more of the usual reasons.

Janice