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

A sentence is meaningful if it is a picture of a possible fact. A
meaningful sentence it true if it corresponds to reality, false
otherwise. For example the apple I am looking at is green. But it is
possible that it would be red. Therefore the sentence "The apple is
red" is meaningful but false.

A: "The apple is green" <---> The apple is green
B: "The apple is red" <---> The apple is green
C: "The Good is identical" <---> [blank]

Sentences themselves are facts and we can make other sentences about
them. Thus we have

K: "A is true" <---> {"The apple is green" <---> The apple is green}
L: "B is false" <---> {"The apple is red" <---> The apple is green}
M: "C is meaningless" <---> {"The Good is identical" <---> [blank]}

In order to discover if

D: "This sentence is false"

is true we have to compare it with reality. That is we have to check
if D is false.

A1: "This sentence is false" <---> "This sentence is false" is false

But the fact on the right side is an attribute of a sentence. We need
to observe if "This sentence is false" is false. So again we have to
compare D with reality. This gets us into an infinite loop and the
comparison with reality cannot be done. D is not a picture of a
possible fact. So we have:

M1: "D is meaningless" <---> {"This sentence is false" <---> [blank]}

The situation is different with

E: "This sentence has five words"

We can very easily compare E with reality. The sentence itself is a
fact and all we have to do is to is to count the words in it. E refers
to syntactic features of itself that can be readily verified and
there is no infinite loop. So we have:

K1: " 'This sentence has five words' is true" <---> {"This sentence
has five words" <---> "This sentence has five words" has five words}

Now let us consider

F: "This sentence is meaningless."

How do we compare it with reality. The sentence says that F <-->
[blank]. Is this the case? To find that out we need to compare F <-->
[blank] with reality, so we have to interpret F. The interpretation of
F is F <--> [blank]. We again have infinite regress.

M2: "F is meaningless" <---> {"This sentence is meaningless." <--->
[blank]}

The important observation is that F is not saying anything. In
particular it is not saying that it is meaningless. M2 does say it but
a sentence cannot say about itself that it is meaningless. In order to
see that let's try a variant of M

M': M' is meaningless <---> { M' is meaningless <---> [blank]}

There is no need to say that the two different strings "M' is
meaningless" are NOT two different instances but the same instance
unfolded. We now observe that M' cannot be the case. The "M' is
meaningless" on the left is meaningful but the one on the right is
not. M' is the root of the extended liar fallacy. It assumes both at
the same time that the sentence is meaningful and that it is not.


.

Relevant Pages

  • Re: Liars Paradox
    ... dark" to reality, you have to compare "this sentence is false" to ...  This sentence is not a picture of any possible state of affairs. ... above is meaningless. ...
    (sci.logic)
  • RE: Set and {} comparison confusion
    ... I can compare properties of some object. ... > I see this code as meaningless on python's. ... >> less time to sort. ... Once two lists without ...
    (comp.lang.python)
  • RE: Set and {} comparison confusion
    ... I can compare properties of some object. ... one python is heavier then other ... I see this code as meaningless on python's. ... Once two lists without ...
    (comp.lang.python)
  • Re: The fallacy of strengthened liars paradox.
    ... When we attempt to compare ... "This sentence is meaningless" with reality we find that it is not ... It is not a picture of a fact; ... This is a contradiction. ...
    (sci.logic)
  • Re: Question for Simon Mason
    ... published are meaningless without details of how they were measured. ... Paul - xxx ... why I should engage with him when it suits him. ... He can compare the item in my photos with an alcohol meter search on e- ...
    (uk.rec.cycling)