[FOM] The liar paradox

[Arnon Avron]

Since Nik Weaver explicitly mentions my name
in his paper "The Liar Paradox is a Real problem",
and is quoting there a message of mine to FOM, I feel 
obliged to make a short response. 

First of all, I should be honest and clarify
that I do not deserve the honor given to me
by Weaver in his paper. There is nothing original
in my views concerning the `liar paradox'.
These are essentially Yehoshua Bar-Hillel's
views as described in his paper "Do Natural Languages
Contain Paradoxes?". (I read this paper in Hebrew 
more than 45 years ago, but an English version has been 
published too: First in Studium Geneale 19,
391-397, 1966; then in his book "Aspects of Language",
1970.) In the long time that has passed since I  read
that paper of Bar-Hillel I came across nothing
that refutes its content, and I can't imagine that
something ever will: What is written there
is obviously true (at least to me; obviously not to Weaver).

Second: I declare that beyond this single reaction,
I do not intend to enter to this notorious trap of 
an endless debate on the "Liar Paradox".
It is a fruitless debate that will never come to an 
end (very much like the debate about the 
"proofs" of the existence of God).  Thus Weaver says 
in his recent paper that  "Whatever simple idea you have 
for an easy resolution of the liar paradox - we've 
tried it, and it does not work". I, in contrast,
maintain: "Whatever complicated way you have
to make the liar paradox a serious problem -
we've seen something similar, and it does not work".
My experience tells me that in situations like this 
there is no point to continue arguing.

Third: Weaver's main argument  in his new paper
is that viewing the "Liar sentence" as meaningless 
forces us to abandon the logical principle of 
Term substitution. However, this principle is indeed
*obviously* false in the way he presents it in 
his paper. Thus it might surely happen that 
each of three persons, A, B, and C, says the *same*
sentence: "my only brother is 20 years old", and
what A says is true, what B says is false, and what
C says is meaningless. Does anybody seriously
see this situation as a violation of term substitution?  

Forth:   I have several deeper critical comments
about Weaver's discussion of the `liar paradox'
at the first 6 sections of his paper. But I am
not going to dwell on these sections any further, because 
their content is simply irrelevant to Bar-Hillel's
views.  These views are hinted just once in
Weaver's paper: at the beginning of Section 7
he writes: "One might hope to find a way out by
ascribing truth not to sentences but rather
to the abstract `propositions' those sentences
(allegedly) express". This short comment
tries to make the impression that only the liar
paradox causes people to distinguish between
propositions on one hand, and sentences that might 
at certain situations express them on the other. 
But as my example above shows
(together with Bar-Hillel's examples in his paper), this
distinction is necessary for compelling reasons that
have nothing to do with the `liar paradox'.

  Anyway, I do apologize that I have been so brief in
my previous posting on the subject, taking for granted
that the readers would understand that by saying 
that a sentence is meaningless, I meant that
it expresses no proposition. Actually, even this would 
in principle have been too brief. Clearly,
it is not a sentence that may  express a proposition,
but its utterances (or instances). In fact, different 
instances of the same grammatically correct sentence 
may express different propositions, or no
proposition at all.

  Of course, one might ask a lot of interesting questions
here, like: What kind of thing is a proposition? How do 
we know what proposition (if at all) a certain instance of 
a sentence expresses?  However, the interest and difficulty of 
such questions have very little do do with the liar paradox - 
much less, e.g., than the connection between the set-theoretical 
paradoxes and similar questions concerning sets and linguistic terms
that might denote them. (For me, and I believed that at least in 
the past also for Weaver, these similar questions about sets
and terms would have been crucial for FOM even had no paradoxes 
ever been found in naive set theory. On the other hand,
I do not find the above questions about propositions 
as very important for FOM.)

  I would like to end with a friendly advice to Weaver. 
After reading the whole of his new paper it is clear to 
me that what interests him is not really the liar
paradox, but theories of truth. In the second half
of his paper he brings independent arguments  why this is an
important topic. By structuring his paper like this
(and with the title he has given it) he repeats what I believe
to be the great mistake he has done in structuring his book.
Potential readers of his book get the impression that
what he is saying is that the liar paradox is a horrible
problem, and the only way to combat it is by developing
a satisfactory theory of truth. Since what he says about
this paradox at the beginning of his book cannot convince most 
people that the liar paradox is indeed a real problem on its own, 
he loses by that a lot of potential readers. However, what Weaver
really thinks (I believe) is that developing a satisfactory 
theory of truth with such and such properties is important for 
reasons which are independent of the liar, but the liar sentence 
provides a big obstacle for achieving this goal.  I suggest
that future editions of Weaver's book should better present things
in the latter way.


Arnon Avron