Re: Socrates and the Liar

On Dec 19, 1:58�pm, Gene Ledbetter <ledbetterg...@xxxxxxxxx> wrote:
The truth of a statement depends on the truth of the facts it asserts,
e.g.,

x: Cats have wings.

The truth of a statement that asserts the truth of another statement
depends on the truth of the facts the other statement asserts, e.g.,

y: x is false.

Contrary to its claim, the Liar Paradox is not a statement of truth.
It is not a statement of fact. It asserts the truth of a statement
that is not a statement of fact (itself), i.e.,

z: z is false.

Consider statements x and y:

x: Cats have wings.
y: x is false.
y: It is false that cats have wings.
y: Cats do not have wings. (i.e., y = ~x.)

Now consider statements r and s, where there is no statement r:

r: []

s: r is false.

Statement r, which does not exist, is not a statement of fact. So
statement s, which asserts the truth of statement r is nonsense.

Finally, consider statement z:

z: z is false.

Statement z, which is contrived to refer to itself, asserts the truth
of a statement, that asserts the truth of a statement, that asserts
the truth of a statement, that ..., etc., ad infinitum. (Statement z is
infinitely recursive.) Since statement z will never assert the truth
of a statement of fact, statement z is nonsense in the same way that
statement s is nonsense.

Gene Ledbetter

Before I make an analysis, I would first conjecture that there are no
relationships between what a sentence refers to, its meaning, and its
string, other than that they are tools of reading. Further, the tools
of reading do not inform an act of reading even if they facilitate it.
The significance of this may (or may not) become apparant below:

Keeping that in mind, your formulation of statement r as a no-
statement is ambiguous. It can either be that r does not fulfill the
necessary conditions of reading, or that r is 'mere nonsense', or that
the model (instantiating condition) of statement r is incommensurable
with our familiar reading model, or, that r is an irretrievably lost
or hidden statement, like a missing fragment of the bible.
I think the latter case would fulfill your criteria of a statement. It
would, therefore, be quite appropriate to say that, 's says that r is
false' (or true), IF you hold that facts can be referred to.

But you conflate facts with statements. A statements is a generic term
for the tools of reading and is not an object with semantic, or any
other properties.

Concerning 'z: z is false'.
I think that confusing the many tools of reading, one for another, is
evident here. A sentence, such as 'z' is assumed to be both string
(marks on paper), referential, and non-referential. Most sentences are
non-referential; their meaning 'emerges' without a referential
middleman.

But now I can bring in my stipulation at the start of my response to
you (top): you have treated as a single object all three tools of
reading as if they were contributing to an act of reading. To say that
'z is a sentence' is to conflate the tools of reading into one
object.

In other words, a logical treatment that conflates an act of reading
with its tools in formulations such as 'sentence x', confuses
semantics with syntax and physical presence (ink on paper). For a
LOGICAL z is both referential and meaning-emergent because of their
identity with a single string. This is a mistake. The law that says
that 'two things are the same if they are identical' is only valid if
the two things arise in the same instantiating framework. But they do
not arise in the same instantiating framework. The tools of reading do
not describe the act of reading.

So my basic criticism is that you conflate string, syntax and
semantics with formulations such as 'sentence x', and that this
conflation does not authorise an act of reading, nor inform it, nor is
it an act of reading. 'This sentence ...' presents the tools of
reading in a condensed form, but no act emerges from it unless we
suppose that the tools of reading inform the act of reading, which
they do not. Some sentences are referential, some not, but 'this
sentence ... ' confuses us into thinking that we have made an act of
reading through the disjunctions of the tools of reading.
.

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