From: baruch@nynexst.com (Robert Baruch)
Subject: Re: Premises of "objectivism?"
Reply-To: baruch@nynexst.com
Organization: NYNEX Science & Technology, Inc
Date: Fri, 22 Jan 93 17:37:48 GMT

In article 93Jan21194341@bast.sics.se, torkel@sics.se (Torkel Franzen) writes:
> In article <1993Jan21.144005.26462@nynexst.com> baruch@nynexst.com 
> (Robert Baruch) writes:
> 
>    >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.
> 
>   Actually "declaring A to be without meaning" does not enter into it.
> But the essential point is indeed that A is defined as a sentence,
> that is, syntactically, independent of questions of meaning. Suppose
> we define four sentences A, B, C, D by
> 
>      A = "The sentence A is false"
>      B = "The sentence D is false"
>      C = "The sentence D is true and false"
>      D = "1+1=2
> 
> The definitions of A,B,C,D are equally unproblematic. Now if we go on
> to consider which of the sentences A,B,C,D are *true* as sentences in
> ordinary English, interpreting the letters "A", "B", "C", "D" in those
> sentences as referring to the sentences just defined, we find that D
> is true, C is false, B is false, and A paradoxical, i.e. apparently
> true if and only if it is false.

I agree.  We can define away all we like, and, of course, the definitions
themselves are true (since we just defined them).  But when we attempt
to affix a truth-value to one side of the definition, working off
the definition, we must treat the sentences as logical propositions, and
we quickly find that A cannot be a logical proposition.  It is a paradox,
in the sense that it is essentially self-contradictory, based on valid
deduction from acceptable premises (so my dictionary tells me).

> 
>   Now a possible way out is to suggest that the sentence A is not in
> fact a meaningful English sentence, unlike B,C,D. Here is where your
> comments are inadequate. For what you say boils down to only this,
> that A is meaningless because it is paradoxical. This is not very illuminating,
> for it does not give us any insight at all into what uses of the predicate
> "x is a true sentence" are meaningful, and how such meaningful uses
> can be understood. In short, philosophers have wanted to do better.
> 
>   To give you some feeling for this, when people speak about looking for
> "solutions" to the paradox of the Liar, they want some theory or insight
> that applies equally to such variants of the Liar sentence as
> 
> 
>    T = "T is a true sentence"
> 
>    M = "M is either a false sentence or a meaningless string of characters"
> 

I now feel that when you say A = "A is false", the quotes indicate a literal --
a string with no inherent meaning. If we were to explicitly specify that
the quoted string is a logical expression which is to be evaluated, we would
get something like, 

   " A is true if and only if the statement 'A is false' is true ", or
   " A is false if and only if the statement 'A is false' is false "

(the two are the same because of the if-and-only-if)

(or, equivalently, " A if and only if [the statement 'A is false'] ")

So if you state explicitly that when you say,

  A = "A is false",

you mean 

  " A iff [A is false] "

then we see the self-contradictory nature of the "proposition".


I agree that "A is false" has meaning, and that to define A as the sentence
"A is false" is perfectly valid. 

However, you must tell me what you mean by a "meaningful use of a sentence".

--Rob