From: oleary@staff.tc.umn.edu ()
Subject: Re: Truth again
Organization: University of Minnesota
Date: Tue, 29 Dec 1992 12:28:48 GMT

NOTE:  I'll be cutting a good portion of the quoting from the many previous
       articles in this thread.  Refer back to previous articles if I
       cut too much.

In article <1h7tpjINNp3f@cat.cis.Brown.EDU> PL436000@brownvm.brown.edu,
(Jamie) writes, among other things:

>>>Of COURSE I didn't define truth with respect to sentences of English.
>>>Would you like me to do so? What sorts of criteria must I meet? If
>>>O'Leary insists, I will do my best to define truth for English, but
>>>I'm not promising anything.
>>
>>In order to enter a meaningful discussion of "truth value" we must define
>>a common basis for it for at least the set we are considering (English
>>sentences).
>
>Now O'Leary wants me to define "truth value." Of course, I didn't
>use that expression in my posting, so I don't know why O'Leary
>thinks I want to have a discussion about it. However, I shall
>now define "truth value" in extension:
>
>The truth values are "true" and "false."

Thank you.  You did, BTW, start using truth value later in the post.

>>>By saying that the sentence is on a list of English sentences I
>>>OBVIOUSLY imply that it is syntactically correct. Does O'Leary
>>>deny that the syntactically correct sentences of English are
>>>enumerable? They are obviously enumerable by an alphabetic list.
>>>Does he deny that there are ANY 100-word sentences of English?
>>>Or that the set of 100-word sentences of English is enumerated
>>>by alphabetization? Or that the list has a first entry?
>>
>>Since an infinite number of sentences can be formed with the syntactic
>>rules provided by the English language, yes, I'll deny that the
>>syntactically correct sentences of English are enumerable.  I don't,
>>however deny the existence of your particular sentence.
>
>You might possibly want to check on the meaning of "enumerable"
>before you insist that my construction is impossible.
>The set of positive integers is enumerable, and yet it has infinitely
>many members.
>To be enumerable it suffices for a set to admit of a 1-1 correspondence
>with the integers.
>
>Even for finitists, though, there should be no problem whatsoever
>with an enumeration of the 100-word sentences of English. There
>are only finitely many of them.

I meant enumerable in a meaningful way.  A random number sequence is also
enumerable, but the correlation between the enumeration and the random
number is meaningless.  This is at best a fringe issue, since I've already
acknowledged that your finite list can be sorted alphabetically (and then be
enumerated if you wish).  For the whole of syntactically correct English
sentences, however, the same cannot be said.

>>>The semantic content of a sentence depends on its being interpreted
>>>in one sense. This is precisely the point I have been making.
>>>If we regard English sentences as intepreted, then they have a truth
>>>value. Whether they have truth value is independent of whether anyone
>>>has ever actually interpreted them, or whether anyone ever will
>>>interpret them. THAT was the point Randall was making. He worried
>>>that he could not give an example of a sentence that no one has
>>>ever interpreted or ever will. So I gave an example, not by
>>>constructing it but by describing a definite English sentence.
>>
>>Without interpretation, truth value (however you may wish to define it) is
>>meaningless.  Even with interpretation, truth value is, at best,
>>inconsistent between interpretations.
>
>I won't pretend to understand what this means.

It means that there is no meaningful truth value without interpretation; the
observer affects the observed.  Much like Schroedinger's cat, the sentence
is neither true nor false until we have interpreted it.

>>"The sky is green."
>>
>>What is the truth value of the above sentence?
>
>That sentence is false. Its truth value is "false."
>
>I am assuming that the sentence is a sentence of English.

Ah, but when you say that you assume that the sentence is a sentence of
English, what you are really saying is that you assume your interpretation
of this sentence is the same as that of other English speakers.  You assume
that my concept of sky is your concept of sky and that we interpret green
the same.  I leave it as an exercise for the reader to give a truth value
to: "The policeman is attractive and sexy."

>The whole POINT of this discussion is (or was) that sentences
>can be thought of as interpreted strings. That is exactly what
>I was claiming. By contrast, others seemed to think that sentences
>cannot be understood as interpreted unless someone actually interprets
>them. My example was supposed to fill in an example-sketch offered
>by Randall to show that there are sentences that no one has ever
>interpreted nor ever will, but which are true or false even so.

See my comments above about Schroedinger's cat.

>I doubt that I will respond to this poster again. His objections
>are nonsense.

Then I guess the nonsense stops here.


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