Re: The fallacy of strengthened liar's paradox --- NAFL-acceptable self-reference

On Jan 2, 10:05 pm, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:
On Jan 1, 10:55 pm, Marshall <marshall.spi...@xxxxxxxxx> wrote:


On Jan 1, 8:26 am, "R. Srinivasan" <sradh...@xxxxxxxxxx> wrote:

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.

Suppose Mr. X had a sentence in mind, but because of some
drug-induced state instead said "False this is sentence." What
does that tell us about the meaning of some other sentence?
Nothing. Even if the other sentence we wish to consider is
a reordering of the words of the first sentence.

Sure. But that is because "False this is sentence" is not even
gramatically correct. I wouldn't call it a sentence. But let us take
"'False' is the truth-value of this sentence". That would seem to
override my objection at first sight. But it really doesn't. The same
objection applies, because how can someone know the truth-value of a
sentence before even defining it? If Mr. X were to drop after uttering
"'False' is the truth value of this...."  then again assuming "this"
points to the sentence under construction, Mr. X cannot possibly have
had any sentence in mind to which he is trying to attribute the truth-
value of "False".

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.

Syntax does not require time. It just requires order.

That is correct. A sentence must be presented with the words in the
correct order. But the issue I am considering is how a human mind
actually understands that sentence. Just as a human being can utter
only one word at a time, I claim that a human being can also read (or
conceptualize, understand etc.) only one word at a time. For example,
consider "This sentence is meaningless". Although all the words are
visible at any given time, the human mind actually reads "This" first,
then "sentence" and so on. While reading a word, we actually "utter"
it in our minds, and while uttering it, we have no other word in mind.
It is our memory that enables us to make sense of all the words put
together, after having read them one at a time, in the given order. To
see this clearly, just consider that somebody else is reading out that
sentence out to you. You clearly hear only one word at a time, and it
is your memory that enables you to put them all together and make
sense of  the sentence.

As for "order", it is the human conception of space and our ability to
distinguish left from right, top from bottom, etc. that makes "order"
possible. In other words, even "order" could actually be a mind-
dependent concept, in the sense that some other alien creature could
have senses that take in the words of the presented sentence in a
different order, or maybe not even in any fixed order.

Keeoing this in mind, let us re-formulate the sentence in question in
an *exactly* equivalent manner as follows:

"This sentence, which has not yet been defined, is meaningless"

Now we can clearly agree that the above sentence attempts to attribute
the property of "meaninglessness" to a non-existent sentence.

I do not agree that the above sentence does not exist.

To the left of and including "defined" in the above sentence, we
clearly have no completed sentence. To the right we have "is
meaningless" which makes an assertion *about* a sentence, which we
have just correctly asserted as incomplete and therefore non-existent.
As I said in my previous post, to assert that a sentence indeed exists
you would have to accept Platonic existence of the sentence indpendent
of our attempted definitions. So in the above sentence, "is
meaningless" actually is about that Platonically existent sentence
which "exists" despite our incomplete definition. In other words, if
"This sentence" actually points to that Platonically existent object,
then our inability to demonstrate a construction for that object
before declaring it as "meaningless" is not a fatal objection. This
may be OK in classical logic, but not in NAFL, which requires us to
explicitly construct the objects being referred to.

Conclusion: When somebody utters "This sentence is blah blah blah..."
then s(he) should have a *constructed* sentence in mind the moment
"sentence" is uttered.

A different syntax could put the word "sentence" at the end,
and then your objection goes away. Your objection depends
on English word order.

No not really. I have given an example at the beginning of this reply.


There is a way to override the objection that I presented and make
self-reference (of sorts) acceptable in NAFL. The three main criteria
that should be satisfied are:

1. A logic is needed to account for the time-dependence involved in
sentence creation and the human process of reading (understanding)
that sentence. NAFL fits the bill.

2. When a sentence is being created, it can refer to itself as an
incomplete sentence. It cannot refer to itself as a completed sentence
even if "sentence" occurs at the end of the sentence in question. The
reason is that some constructive property of the sentence in question,
which needs to be verified, will then occur at the beginning of the
sentence and no construction will be available for that property when
it is mentioned. See the examples given below.

3. A sentence cannot refer to its own semantics (i.e., its truth or
falsity of meaningfulness or meaninglessness, etc.). This is so
because the semantics of a sentence is up for consideration (i.e. can
be decided upon) only *after* the construction of that sentence is
complete, i;e. the human mind must have a construction available for
the completed sentence before considering its truth, falsity etc.
Truth, falsity or meaningless, etc. are not formalizable within NAFL
theories and therefore cannot appear within formal sentences in the
language of NAFL theories. However, a sentence can validly make
constructively verifiable prediction(s) about its own *syntax*. See
the example below.

Keeping 1-3 in mind, consider the following sentence:

This incomplete sentence, which is under construction, will be
completed and when completed, will contain seventeen words. (P)

There is still a question mark as to which sentence a human being
would have in mind when uttering "this incomplete sentence" above, but
let us take for granted that "this incomplete sentence" points to the
same sentence under construction. Note that the sentence P only refers
to its own syntax, i.e., it predicts its own completion and also
predicts that it will contain seventeen words when complete. So let us
now assess the semantics of P from the NAFL point of view.

Let us consider a human mind which is reading the sentence P.

-- While the human mind is reading P, and gets to "This incomplete
sentence" there is a construction available for the incomplete
sentence, namely "This incomplete sentence". So there is no problem
from the NAFL point of view.

-- After the reading is complete, the human mind verifes
(constructively) the two facts mentioned about the incomplete
sentence, namely that it has indeed been completed and that its
completion does contain seventeen words. So the human mind concludes
that P is true with respect to a suitable theory in which the terms
contained in P are defined and the truth of P is via a consructive
proof in that theory. Note in particular that when "seventeen words'
is read by the human mind, a construction is indeed available for the
seventeen words in quesion.

Observe that P only refers to itself as an "incomplete sentence". Next
consider the following sentence in which a completed sentence is
referred to:

Seven words are present in this sentence (Q)

Again let us take for granted that "this sentence" refers to Q. Now
the word "sentence" in Q refers to the completed sentence Q and indeed
a construction is available for Q when "sentence" is uttered. But when
the human being utters "Seven words", it does not have seven words in
mind and I feel that Q is still not an acceptable sentence within NAFL
theories.

Note that P is not vulnerable to this objection. When "seventeen
words" are uttered by the human mind, it does have a construction for
the seventeen words.

Regards, RS
.

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