From: ramsay@math.ubc.ca (Keith Ramsay)
Newsgroups: alt.philosophy.objectivism
Subject: Re: Premises of "objectivism?"
Date: 21 Jan 1993 19:27:30 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: galois.math.ubc.ca

Regarding: A = "A is false"

In article <1993Jan21.144005.26462@nynexst.com> baruch@nynexst.com writes:
>But, let us continue.  You say that A is a sentence.  And you define A.
>If you expect me to accept the definition, you must first tell me if you
>want me to treat A as a collection of symbols without meaning, or as a
>collection of symbols with meaning.

It is plainly a string of symbols. I think the participants here all
agree that it does not yield a proposition (although I have read it
argued elsewhere that it is a false proposition). The main issue is
the reason why. Is it adequately "explained" in a meaningful sense by
the law of identity, or is there a more difficult aspect to the
question, requiring further efforts to elucidate?

>If you tell me that A is a collection of symbols without meaning (which
>happen to spell "A is false"), then I will agree to your definition, and
>state that it is a meaningful definition now that you declare A to be 
>without meaning.

We can all see that A is a string of symbols; the question is *how* to
interpret it to determine what meaning it might have (or whether it
has one at all):

>But if you say that A is a collection of symbols with meaning, then I must
>analyze the meaning as follows: 
>
>You say
>that A is sentence which is false.  This implies that A has a fixed truth
>value.  But then A is a logical proposition, because a logical proposition is
>a statement which has a fixed truth-value, and your fixed truth-value is
>"false".

No, Torkel Franzen did not claim that A is false. He just exhibited
"that A is false" as an example.

>But when I treat A as a logical proposition, I find self-contradiction, and
>so I conclude that A is not a logical proposition.  Yet you claim it
>is, because 
>you claim that A is false.

I don't think that Torkel Franzen asserted that it was a proposition,
either; correct me if I missed it.

>I won't get into a repeat of my argument of the last post; you
>already know it. 
>
>But you rejected it out of hand.  You must tell me if you want me to analyze
>the meaning of A, or if you want me to close my eyes to any possible meaning
>of A, and just treat it as a collection of symbols.

The argument shows that if we treat A as a proposition in the usual
fashion, we get a contradiction. This convinced us, of course, that it
does not yield a proposition. But can we give a sound criterion for
what makes a sentence represent a proposition?

The argument you have given indicates one possible criterion:

    If the assumptions that a sentence P connotes a true proposition
    and the P connotes a false proposition both lead to
    contradictions, then P is not a proposition.

But this hardly solves the problem in general. There are many
propositions which appear to be meaningless for essentially the same
reason as A is meaningless, but to which this explanation of yours
does not apply. Consider:

 (0)  The sentence labeled (0) in Ramsay's article of Jan. 21 is
      *true*.

This is also "meaningless", but not because we can't consistently
assign a truth-value to it. We can consistently assign either truth
value to it, which suggests perhaps why it is "meaningless".

Consider a (revision of) the earlier version of the sentence:

 (1)  If the sentence labeled (1) in Ramsay's article of Jan. 21
      represents a true proposition, then there is a Santa Claus.

This is bad because, although we *could* assign it a truth value
consistently, we can only do so by believing in Santa Claus. So we
really need a stronger criterion, one that doesn't depend upon our
being able to judge such matters as the existence of Santa Claus --
which is not really relevant, is it? Suppose we consider instead

 (2)  If the sentence labeled (2) in Ramsay's article of Jan. 21
      represents a true proposition, then there *isn't* a Santa Claus.

One is almost tempted to consider (2) true-- after all, it has a
"then" clause which is true. We can consistently assign "true" to it,
and we cannot consistently assign "false" to it. On the other hand, it
doesn't seem as though the proposition-hood of sentences should be
something which depends upon external factors in quite such a direct
way; in general, it does not seem as though the meaningfulness of

 (2') If the sentence labeled (2') in Ramsay's article of Jan. 21
      represents a true proposition, then X.

should depend upon whether the proposition we fill in for X is true.
We should be able to tell already whether (2') is "really asserting
something" without knowing the truth about X, shouldn't we? Or should
we? How does one determine this?

It is also possible to beef up the paradox somewhat as follows:

 (3) The sentence consisting of the string S, followed by a quotation
     mark, followed by a second copy of S, followed by a second
     quotation mark and a period, either does not represent a
     proposition, or represents a false proposition, where S="The
     sentence consisting of the string S, followed by a quotation
     mark, followed by a second copy of S, followed by a second
     quotation mark and a period, either does not represent a
     proposition, or represents a false proposition, where S=".

In this instance just for fun I've arranged that the sentence gives
instructions on how to construct itself (rather than depend upon the
context of my posting's labelings of sentences). Now, (3) is indeed
the sentence which consists of S then `"', S, and `".'. I'm inclined
to say that (3) does not represent a proposition. Based on the usual
logic that from P we can infer P or Q, I also would like to assert
that (3) either does not represent a proposition or represents a false
one. But it appears as though (3) is making just exactly this claim.

One last one:

 (4) If the sentence consisting of the string S, followed by a
     quotation mark, followed by a second copy of S, followed by a
     second quotation mark and a period, represents a meaningful, true
     proposition, then Santa Claus exists, where S= "If the sentence 
     consisting of the string S, followed by a quotation mark,
     followed by a second copy of S, followed by a second quotation
     mark and a period, represents a meaningful, true proposition,
     then Santa Claus exists, where S= ".

or

 (4') If (4') is meaningful and true, then Santa Claus exists.

Here, we are inclined to argue in a manner parallel to what you have
argued before, namely, that since Santa Claus doesn't exist, and since
as a result there is no consistent way to assign a truth value to
(4'), then (4') must be meaningless (and hence certainly not both
meaningful and true).

But (Santa does not exist)-->((4) not both meaningful and true) is the
contrapositive of (4)!

Keith Ramsay            "Being a computer means not having 
ramsay@math.ubc.ca       to say you're sorry."
Newsgroups: alt.philosophy.objectivism