Tortoise: What do you mean? Sentences can't talk.
Achilles: No, but they REFER to things-and this one refers directly-
unambiguously-unmistakably-to the very sentence which it is! You
just have to think back and remember what quining is all about.
Tortoise: I don't see it saying anything about itself. Where does it say "me",
or "this sentence", or the like?
Achilles: Oh, you are being deliberately thick-skulled. The beauty of it lies
in just that: it talks about itself without having to come right out and
say so!
Tortoise: Well, as I'm such a simple fellow, could you just spell it all out for
me?
Achilles: Oh, he is such a Doubting Tortoise ... All right, let me see ...
Suppose I make up a sentence~I'll call it "Sentence P"-with a blank
in it.
Tortoise: Such as?
Achilles: Such as ...
" __ , WHEN QUI NED, YIELDS A TORTOISE'S LOVE SONG".
Now the subject matter of Sentence P depends on how you fill in the
blank. But once you've chosen how to fill in the blank, then the subject
matter is determined: it is the phrase which you get by QUINING the
blank. Call that "Sentence Q", since it is produced by an act of quining.
Tortoise: That makes sense. If the blank phrase were "is written on old jars
of mustard to keep them fresh", then Sentence Q would have to be
"IS WRITTEN ON OLD JARS OF MUSTARD TO KEEP THEM FRESH"
IS WRITTEN ON OLD JARS OF MUSTARD TO KEEP THEM FRESH.
Achilles: True, and Sentence P makes the claim (though whether it is valid
or not, I do not know) that Sentence Q is a Tortoise's love song. In any
case, Sentence P here is not talking about itself, but rather about
Sentence Q. Can we agree on that much?
Tortoise: By all means, let us agree-and what a beautiful song it is, too.
Achilles: But now I want to make a different choice for the blank, namely:
"WHEN QUINED, YIELDS A TORTOISE'S LOVE SONG".Tortoise: Oh, heavens, you're getting a little involved here. I hope this all
isn't going to be too highbrow for my modest mind.
Achilles: Oh, don't worry-you'll surely catch on. With this choice, Sen-
tence Q becomes ...
"WHEN QUI NED, YIELDS A TORTOISE'S LOVE-SONG"
WHEN QUI NED, YIELDS A TORTOISE'S LOVE-SONG.
Tortoise: Oh, you wily old warrior you, I catch on. Now Sentence Q is just
the same as Sentence P.
Achilles: And since Sentence Q is always the topic of Sentence P, there is a
loop, so now, P points back to itself. But you see, the self-reference is a436 Air on C's String