🚀 go-pugleaf

In article <1992Dec22.190951.7673@news2.cis.umn.edu>, oleary@staff.tc.umn.edu
() said:
>>>>Consider the sentence which would come first on an alphabetized
>>>>list of 100-word sentences of English.
>>>>
>>>>It is either a true sentence of English or a false one. No one has
>>>>ever interpreted it (I'll wager). With the possible exception of
>>>>one of us, no one ever will.
>>
>>Response from O'Leary:
>>
>>>Not only do you not define truth with respect to sentences of English, your
>>>example is circular.  The sentence is or isn't syntactically correct and may
>>>or may not have semantic content.  By saying that the sentence is on a list
>>>of English sentences, you imply that it is syntactically correct.  The
>>>semantic content of the sentence, however, still depends on it being
>>>interpreted.
>>
>>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."

>>The rest of the objection is very close to jibberish.
>>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.

>>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.

>"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.

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.

>>The complaint that my example is "circular" is ridiculous. No circularity
>>has been pointed to.
>
>It was circular in that truth value seemed to be defined by you saying
>that your sentence was on a list that your sentence was on.  It was so
>obvious that even you pointed it out.

What on earth are you talking about?

What could possibly have led you to believe that I was trying to
define "truth value" by saying that my sentence was on a list that
my sentence was on? I wasn't trying to define "truth value" at all.

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

Jamie