Re: The fallacy of strengthened liar's paradox.
- From: Charlie-Boo <shymathguy@xxxxxxxxx>
- Date: Thu, 14 Feb 2008 07:30:09 -0800 (PST)
On Jan 7, 5:35 am, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:
On Jan 6, 9:49 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:
On Jan 1, 11:26 am, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:
On Dec 26 2007, 4:21 am, Newberry <newberr...@xxxxxxxxx> wrote:
On Dec 25, 2:47 pm, John Jones <jonescard...@xxxxxxx> wrote:
On Dec 24, 11:11�pm, Newberry <newberr...@xxxxxxxxx> 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 �P
is not false.
Case C: P is meaningless.
If P is meaningless then nothing is the case. There is no
contradiction. In a three valued logic (T, F, M) we conclude that P is
meaningless.
It is not correct to say that if the sentence is meaningless than what
it SAYS is true. This argument assumes that it becomes TRUE half way
through the argument and then it IS THE CASE that it is meaningless.
Thus the sentence confirms our initial assumption that it was
meaningless. But if it stays meaningless all the time it confirms
nothing.
Clearly, if the sentence does not have any meaning then it does not
have the meaning that it is meaningless.
This gives us the basic insight that all self-referential, paradoxical
sentences, including possibly Goedel's sentence, are probably
meaningless.
Let P be the sentence "This sentence is meaningless." Is it true or
false?
I can't start this car. You have not said what sort of object P a
sentence is, nor even specified what sentence you refer to by 'it'..
"This" in the sentence "This sentence is meaningless" obviously refers
to the sentence in quotation marks.
That is not obvious at all. I agree with John Jones. To see what the
problem is, consider the following thought experiment:
Lat us say Mr. X blurts out "This sentence is....." and exactly at
that point he drops dead. Can you now let us know what is the sentence
that Mr. X had in mind? The answer is we cannot be sure at all. All we
can say is that if Mr. X had no sentence in mind at the time of his
death, he was attempting to attribute some property to a non-existent
sentence. If the sentence itself is non-existent, then any attributed
property to it (e.g. "meaninglessness") is also non-existent.
The problem here is that we human beings can parse sentences only when
their words are read sequentially, which means that the informal
notion of "time" is important in understanding what sentences mean.
No, I believe the Chinese read right to left. (I should know, since
most of my g/f''s are Chinese - or at least Asian.)
What I said was that the human mind can only understand the meaning of
a sentence by reading it one word at a time. Some languages (e.g.
Chinese) may be set up for reading from right to left, others from
left to right, etc. But all of us can read and understand only one
word a time. For example, take "This sentence is false". Clearly we
have to pronounce the words of this sentence (even while reading it
mentally, rather than aloud) to understand what they mean. And clearly
we can only pronounce one word at a time. So we have to pronounce
"This" first, then "sentence", then "is" and then "false", and it is
clearly a temporal process.
From the NAFL point of view, the following sentence is legitimate:
"Precisely nine words will be present in this sentence."
What is the smallest self-contained description of a proof in NAFL, of
a theorem that is commonly given in texts, that you are aware of?
C-B
Because when we utter "nine words" while reading the above sentence,
we are not immeditately committed to the existence of those nine words
because of the use of the future tense ("will be"). Note that when we
read "this sentence" we do have a construction available for the full
sentence and the nine words.
Now consider
"Precisely eight words are present in this sentence"
This is not acceptable in NAFL for the following reason. When the
human mind reads "are present", it is already committed to the
existence of the eight words in question. The words "are present": are
therefore *about* those eight words. But at that stage after reading
"are present" the human mind reading that sentence has no construction
available for those eight words. This is objectionable in NAFL for
reasons that will be clear if one understands NAFL.
Consider that a human being just after reading "are present" tries to
figure out what eight words are implied. This proposition is
undecidable, for clearly no construction is available at that stage
for the eight words. But such undecidability would contradict NAFL
principles. I will elaborate later.
Now consider:
"At least four words are present in this sentence."
This is NAFL-acceptable self-reference, because after uttering "four
words" (when parsing the above sentence) a human mind does have a
construction for the four words, namely "At", "least", "four" and
"words" And after reading "sentence" the construction for the full
sentence available. This is also crucial. Thus
"This sentence contains five words"
is not NAFL-acceptable because after uttering "this sentence", no
construction is available to the human mind for any sentence.. But
note that we do have a construction for the five words after reading
"five words".
Regds, RS- Hide quoted text -
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