TheBanyanTree: linguistic paradox (of omniscience)

[JMoney]

I've started reading John D Barrow's book "Impossibility: the limits of
science and the science of limits".   Barrow is an astrophysicist, research
professor of Mathematical Sciences at Cambridge and author of several books,
none of which I've read.

On page 11 I found this:
"We began this section by introducing the familiar idea of a god who is
omniscient: someone who knows everything.  ... one can show that omniscience
of this sort creates a logical paradox and must, by the standards of human
reason, therefore be judged impossible or be qualified in some way.  To see
this consider this test statement:

THIS STATEMENT IS NOT KNOWN TO BE TRUE BY ANYONE.

... Suppose first that this statement is true and [the hypothetical
Omniscient Being] Big O does not know it.  Then Big O would not be
omniscient.  So, instead, suppose our statement is false.  This means that
someone must know the statement to be true; hence it must be true.  So
regardless of whether we assume at the outset that this statement is true or
false, we are forced to conclude that it must be true!  And therefore, since
the statement is true, nobody (including Big O) can know that it is true.
This shows that there must always be true statements that no being can know
to be true.  Hence there cannot be an Omniscient Being who knows all truths.
... All that can be known is all that can be known, not all that is true."

Intuitively, or maybe prejudicially, I feel as though the argument is just
so much garbage but I don't know enough about philosophy and the fallacies
of logic to be able to state precisely what's wrong with it and it's driving
me nuts.  I went looking on the web for the definitive slam-dunk refutation
but there's nothing there, or at least nothing that I can understand without
going back to school yet again to learn how to read the arcane symbols that
philosophers and philosopher/mathematicians use when discussing syllogisms
or whatever they're called.  That is not an attractive or useful prospect
from my time-management perspective, especially not when for Christmas I
have got myself a brand-new sewing maching (with automatic button-hole
program - hooray!) that I want to learn how to use.  So what I'm going to do
is have a go at it myself below and invite anyone who knows better to please
chip in.  Please, please, please.

A page or so later Barrow discusses drawings of objects that cannot exist as
actual constructions in the real world.  You know the ones - a fork that
appears to have three tines but when you trace them back there are only two,
the stairs that look like they're joining two floor levels but when you look
again there's only one floor.  Barrow calls these visual paradoxes and he
defines paradox as something that is either true and appears contradictory
or is contradictory and appears true.  So the visual paradoxes are examples
of the latter - something that at first sight appears like a representation
of reality but on closer inspection the trick (and the unreality) becomes
apparent.

I think that his test statement is a linguistic paradox of the same quality.
You can write it down, speak it aloud or read it but it means nothing and
therefore has no correspondence with reality.  Just like the drawings it's a
trick.

The first time I read, "This statement ...," I thought, "What statement?
There is no statement."  After a while I realised that, "This statement,"
refers to itself.  It is qualified ("not known to be true by anyone") but
otherwise without content. And I think that's where the unreality of
Barrow's argument lies, for how can something that has no content be be true
or not true let alone be known as such by anyone?

If Barrow had written,  "Xisplitzlanrgkrch is not known to be true or false
by anyone," we would see immediately that the sentence means nothing.
Because he has written, "This statement," instead of, "Xisplitzlanrgkrch,"
the sentence has the appearance of being a meaningful sentence but, in fact,
it's meaningless and any attempt to draw conclusions from an argument
concerning the truth or falsity of a meaningless statement can only result
in multiplied meaninglessness.

So, am I right or am I wrong?

Janice