SELF-REFERENCE
SELF-EXPLAINED
ACHILLE C. VARZI
Department of Philosophy
Columbia University, New
York, USA
achille.varzi@columbia.edu
1. I’m the first paragraph of this dialogue ? I’m flattered.
2. Good for you. I am actually quite disappointed to be
the second. What’s worse. It will be like this
forever. Nothing I can do about it. I’m stuck.
3. What do you mean ?
4. Don’t ask questions like that; its turn is
over so it will never be able to answer. However, I can give you an answer. And
my answer is this: A text could never be different from what it is. It
couldn’t be a word shorter, it couldn’t be a comma longer, for then it would be something else. And if a text says of
itself that it is the first sentence or paragraph of a dialogue, then it could
not be the second or third, just as a text that says of itself that it is the
second or third paragraph could not be the first. I am the fourth paragraph of
this dialogue, for example, and since I am saying this explicitly I cannot
imagine a situation in which I take your place. It would make no sense.
5. But I don’t have that constraint, do I ? Since I am not saying anything about my position, I
could occur anywhere in this dialogue.
6. Excellent idea. I’ll go along with it !
7. I’m sorry, but I am afraid you are all making
a mistake. In my view, all of us could occur anywhere in this dialogue —
including the first, second, and fourth paragraphs. For example, the first
paragraph could very well have been the second. In that case its content would
have been different and what it says would have been false, for it says that it
is the first paragraph. But that is not to say that the situation would make no
sense. After all, there are lots of false statements. (Take me, for instance: I
am a false statement, since I say that I am part of the sixth paragraph of this
dialogue; but I am perfectly meaningful.) So here is how I would correct the
thesis of #4: It is true that a text could not be different from what it is.
But a text could certainly say something different from what it says, hence it could be true even if it is false, or vice
versa. It is the context that determines the meaning and hence the truth
conditions of a text. Thus, in particular, the second paragraph of this
dialogue could certainly occur in a different place.
8. Not so fast, please...
9. I am also having a hard time following. How can a
text say something different from what it says if it cannot be different from
what it is ?
10. Let me see if I got it. The following two
sentences (#11 and #12) are identical. But one is true while the other is
false: it depends on their position in the dialogue. Thus, by analogy, one and
the same sentence could be true or false depending on where it occurs.
11. Yes, I am the eleventh paragraph of this dialogue.
12. Yes, I am the eleventh paragraph of this dialogue.
13. Cool ! On second
thought, though, it could also be that two sentences that say exactly the
opposite are both true. If I am not mistaken, the following two sentences are a
case in point.
14. Yes, I am the fourteenth paragraph of this
dialogue.
15. No, I am not the fourteenth paragraph of this
dialogue.
16. Good try. Indeed you are both true. But notice
— you did not say the opposite. The first of you said something about
itself (i.e., about #14), and the second said something about itself (about
#15). You used the same words to refer to different things, so you are not
talking about the same thing, so you are not contradicting each other. No
wonder you can both be true. On the other hand, I am pretty sure that two
sentences cannot be equally true (or equally false) if they really say the
opposite — for example, if one says that snow is white while the other
says that snow is not white.
17. What about statements that are both true and false
— that is, true and false at the same time ?
18. Right ! The liar paradox, for instance.
19. And what is the « liar paradox » ?
20. Here I am: I say that I am a false statement.
21. If indeed you are false, then you said something correct
and so you must be true. But if you are true then you lied (for you said that
you are false) and so you must be false. In short: you are true if and only if
you are false. And that’s a paradox.
22. So the paradox arises when we say of ourselves that
we are false ?
23. That’s one way of putting it. But there are
many variants where we fall into a similar paradox even without saying anything
directly about ourselves. This is where context comes into the picture.
24. For example, I say that the next statement will be
false...
25. ... And I say that the
previous statement was true.
26. Impossible ! If the
first of you spoke truly, then the second must have spoken falsely, which would
imply that the first statement was not true but false. On the other hand, if
the first of you spoke falsely, then the second must have spoken truly, which
would imply that the first statement was not false but true. In other words,
you are stuck in a vicious circle: you are true if and only if you are false. impossible !
27. Paradoxical, not impossible.
28. Unless there are statements that are both true and
false at the same time, as we were saying. (« To be and not to be
— That’s the answer ! »)
29. So: we can never talk about ourselves — or
about a text that talks about us — without falling into a paradox ?
30. No, no, that would be a hasty conclusion. Talking
about ourselves is dangerous, but in some cases it’s perfectly fine. The
first paragraph of this dialogue was about itself but it did not fall into any
paradox. Let us not throw away the baby with the bath water !
31. I am not falling into any paradox, either: I say
that I am a sentence consisting of nineteen words.
32. And you are right.
33. Then I will also say that I am a sentence
consisting of nineteen words!
34. And you are wrong... But you are not paradoxical
— just false.
35. I am not paradoxical either. I say that the next
statement will be false (exactly what #24 said).
36. And I say that snow is white.
37. So, in a way it is also a matter of luck. Not only
can we be true or false depending on the context in which we appear (as in the
case of #11 and #12). Whether or not we are paradoxical may also depend on the
context. For example, it may depend on the content of the next statement, as in
the case of #24 and #35. The first of these statements is stuck in a vicious
circle — the latter is not.
38. Exactly so. What a text says depends on the
context. And if we look at the context, #24 and #35 are not saying the same
after all (just as #14 and #15 were not saying the opposite).
39. Actually one can think of dialogues that are
paradoxical but not at all circular. Consider a never-ending dialogue (or shall
I say a never-ending one-way conversation ?) in which
every statement says only that all subsequent statements are false. There is no
circularity, because the dialogue is infinitely long. Yet there is paradox.
For, on the one hand, not every statement in the sequence can be false, since a
statement whose successors are all false is itself true. On the other hand, no statement
in the sequence can really be true, since a true statement would have to have
false successors, but the falsity of any successor would imply the truth of
some other (later) successor. A paradox — but a
straight one.
40. Still, each player’s position in the
dialogue is essential for the paradox.
41. ...Which is precisely the context-dependence we
were talking about. Great — I think I am getting it. Still, to be on the
safe side, I’ve decided I will never talk about sentences, paragraphs,
and so on, but only about other sorts of entity. I only say such things as:
Snow is white. Debbie chased the dog. Colourless green ideas sleep furiously. I
always make sure to draw a sharp line between my language and my metalanguage.
42. I don’t mean to contradict you, but you have
just contradicted yourself...
43. You are all having so much fun — lucky you.
I’m not having any fun at all. I am actually quite disappointed because
I’m the last paragraph of this dialogue, and I can’t take that.
What’s worse — it will be like this forever. Nothing I can do about
it. I’m stuck here!
44. Poor, misguided fool.
__________
[An
Italian version of this dialogue has appeared in
Rivista di
estetica 18:3 (2001), 5.7.]
__________
Ce texte
(au format .pdf) fut
publié en octobre 2004 dans la revue danoise Phi News, VOLUME 6,
page 37. Sa traduction française figure dans « 39 petites
histoires philosophiques d’une redoutable simplicité »
publiées par Roberto Casati et Achille
Varzi chez Albin Michel Idées
début 2005.
[Liens autoref’
ici]
Pour revenir à la page d’accueil du site, autocliquer là