Re: The fallacy of strengthened liar's paradox.

On Dec 28, 6:19 pm, LauLuna <laureanol...@xxxxxxxx> wrote:
On Dec 27, 3:57 pm, Newberry <newberr...@xxxxxxxxx> wrote:





On Dec 27, 5:54 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

Newberry says...

On Dec 26, 9:13=A0am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
Let P be the sentence "This sentence is meaningless." Is it true or
false? It should not be difficult to answer. Tractatus Logico-
Philosophicus says: "In order to tell whether a picture is true or
false we compare it with reality." [2.223] When we attempt to compare
"This sentence is meaningless" with reality we find that it is not
comparable with anything. It is not a picture of a fact; it is
meaningless.

We can analyze the situation further:
Case A: P is true.
If P is true. Then it is the case that it is meaningless. But then it
cannot be true. This is a contradiction. Therefore P is not true.

Case B: P is false.
If P is false then it is not the case that it is meaningless. It is
the opposite of what it claims. This is a contradiction. Therefore =A0P
is not false.

Case C: P is meaningless.
If P is meaningless then nothing is the case. There is no
contradiction.

That analysis is just silly. It doesn't clarify anything at all.
You came to the conclusion that P is meaningless. Was that
a meaningful conclusion, or not?

Absolutely.

Perhaps you want to say that it is never meaningful to say that
something is not meaningful?

P: Q is meaningless
Q: This sentence is meaningless

P is true, Q is meaningless. Since Q is not a picture of a possible
fact it is meaningless. That is what P says. Therefore P is true. Q
cannot say about itself that it is meaningless. Since it does not have
any meaning it cannot speak, so to speak.

Your resolution is not a resolution at all. It doesn't *resolve*
anything. *Why* is Q meaningless? Normally, a simple sentence can
be understood through (1) figuring out what the subject of the
sentence is, and (2) figuring out what is being said about that
subject. In the case of Q, the subject is Q itself. What is being
said about the subject is that it is meaningless. So what is
meaningless about Q? How *can* it be meaningless? Your analysis
doesn't actually explain anything.

Your resolution is actually inconsistent, as well. Rather than
talking about "This sentence", suppose that a guy named "Bob"
compiles a book that lists all the known paradoxes. It's called
"Bob's Book of Paradoxes". For example, it might go like this:

    1. "All Cretans are liars" said the man from Crete.
    2. This sentence is false.
    3. Can God create a rock too heavy for him to lift?
    4. Let R be the set of all sets that are not elements of themselves.
     .
     .
     .
   42. Sentence number 42 of "Bob's Book of Paradoxes" is meaningless.
     .
     .
     .

Now, as shown above, sentence number 42 makes the claim that sentence
number 42 is meaningless. So it's just like "This sentence is meaningless".
So by your analysis, sentence number 42 is meaningless. So we conclude:

   Sentence number 42 of "Bob's Book of Paradoxes" is meaningless.

But that *is* sentence number 42!

Again, this has already been discussed:

QUOTE:

This leads immediately to tokenism as
the thesis that different tokens
of a same non indexical sentence can
have different logical values
when used in different logical contexts.

DUH.  That is basic.  That is trivial.  That has been known
since Frege if not before.  Frege's personal example in
the relevant paper was "Russia and Canada quarreled today."
Obviously that has different truth-values depending on what
day it is.
END OF QUOTEhttp://groups.google.com/group/sci.logic/browse_frm/thread/22e12a7a46...Hide quoted text -

- Show quoted text -

But this is an indexical sentence. Tokenism is the claim that even non
indexical expression-tokens (or occurrences, perhaps) of the same
expression-type may be logically non equivalent.

I think you're on the right way. Please, let me suggest again a
distinction between sentences (as syntactic objects) and propositions
(the semantic objects sentences use to express according to some
linguistic codes). This can show, for instance, that there is no
strict self-reference in Gödel sentence.

The distinction between expression-types and expression-tokens is
necessary as well.

Let me add that, while this kind of solution seems appealing and
intuitive, it is by no means fully developed and clarified. E.g. why
and when is self-reference impossible?

Consider the three following sentences:

A) this sentence has five words

B) this sentence is false

C) all propositions are either true or false

All of them seem to be self-referential in some way but only B) seems
pathological.

Why?- Hide quoted text -

- Show quoted text -

I will expand on this shortly. Did you write any paper about tokenism?
URL?
.

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