GREG RAY
TARSKI AND THE METALINGUISTIC LIAR !
ABSTRACT. I offer an interpretation of a familiar, but poorly understood portion
of Tarski’s work on truth – bringing to light a number of unnoticed aspects of
Tarski’s work. A serious misreading of this part of Tarski to be found in Scott
Soames’ Understanding Truth is treated in detail. Soames’ reading vies with the
textual evidence, and would make Tarski’s position inconsistent in an unsubtle
way. I show that Soames does not finally have a coherent interpretation of Tarski.
This is unfortunate, since Soames ultimately arrogates to himself a key position
that he has denied to Tarski and which is rightfully Tarski’s own.
In Understanding Truth, Scott Soames subjects Tarski to a serious
misreading. Soames attributes to Tarski an argument, the Metalinguistic Liar, which plays a pivotal role in Soames’ understanding
of Tarski’s position. However, the argument in question is not at
all Tarski’s argument. Soames has fundamentally misunderstood
Tarski’s response to the Liar. In addition to making Tarski’s position
inconsistent in an unsubtle way, Soames’ interpretation itself can
be shown not to be self-consistent. In this paper, I will present and
argue for what I take to be the correct reading of (the relevant portion
of) Tarski’s work. In the light of this, I will then critically examine
Soames’ interpretation – substantiating the negative assessment just
briefed.
Soames is by no means alone in misreading and misunderstanding Tarski on at least some of the points which will concern
us. The reading of Tarski to be offered here constitutes a needed
corrective for several widespread misunderstandings, in addition to
those special to Soames’ case. Our investigation will be fruitful
also in bringing to light a number of unnoticed aspects of Tarski’s
work.
Portions of this paper were presented to the Society for Exact Philosophy
(Montreal, 2001) and to the American Philosophical Association (San Francisco,
2003).
!
Philosophical Studies 115: 55–80, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
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GREG RAY
Let us enter here for later reference, a formulation of (what
is for all intents and purposes) Tarski’s Liar Argument. For the
sake of argument, let us assume that ‘the sentence with feature f’
uniquely denotes the sentence which is quoted (i.e., referred to by
quote-name) in sentence (a) below. Our argument will be given in a
fragment of English which is in principle exactly specifiable. Also,
for simplicity, we will suppose that ‘L’ refers to a language which
looks and is structured just like our fragment of English and has no
false cognates.
(a)
(b)
(c)
‘The sentence with feature f is not true in L’ is true in L
iff the sentence with feature f is not true in L.
‘The sentence with feature f is not true in L’ is identical
to the sentence with feature f.
So, ‘The sentence with feature f is not true in L’ is true in
L iff ‘The sentence with feature f is not true in L’ is not
true in L.
It is worth stating carefully how this problematical argument is
supposed to constitute an affront to reason. First, suppose you think
that (a) and (b) represent beliefs that you hold. Then, certainly, (c)
represents something that could be validly inferred from things you
believe. But, (c) is logically self-contradictory, and this suggests that
your beliefs are in a sorry state indeed. You would be rationally
compelled to conclude that you had a false belief. It is hard to see
how (b) could be the culprit, so suspicion falls on (a). However, (a)
could not represent a false belief you had either, because we can
prove (a) is not false:
After all, a claim [like (a) which is of the form] !A iff B" can be false only if (i)
A is true and B is false or (ii) A is false and B is true. Where A is !’S’ is true" and
B is S, these combinations cannot occur, for (i) if S is false, then the claim that it
is true cannot be true and (ii) if S is true, then the claim that it is true cannot be
false. (Soames, 1999, p. 51)
1. TARSKI’S INCONSISTENCY ARGUMENT
Tarski presents the Liar Argument, but does not propound it. Rather,
Tarski makes crucial reference to the Liar Argument in the course of
giving a general Indefinability Argument. In the service of this latter
TARSKI AND THE METALINGUISTIC LIAR
57
argument is another which centrally concerns us, namely his Inconsistency Argument, and it is within this sub-argument that reference
to the Liar Argument plays its role. Some Tarskian terminology will
aid our further exposition.
An exactly specified language is an interpreted language for which we have distinguished primitive vocabulary, compositional grammar, set of axioms, and rules of
inference and definition.1
An assertible sentence of an exactly specified language is a theorem of that
language, i.e., a sentence that is in the deductive closure of the axioms of the
language.2
Here, then, is my formulation of Tarski’s Inconsistency Argument. Let M be an exactly specified, English-cognate language
sufficient for formulating the Liar Argument, and for completeness,
let us also suppose that the language, L, which the Liar Argument is
about, is also an exactly specified one.3
(1)
(2)
(3)
(4)
(5)
Suppose sentence (a) is a conceptually assertible sentence
of M.
Suppose sentence (b) is an empirically assertible sentence
of M.
Suppose the ordinary rules of logic apply in M (i.e., the
rules of inference of M underwrite the usual deductive
moves).
It follows that the deductively inconsistent sentence, (c),
is derivable from (a) and (b) by the rules of inference of
M.
Hence, the language, M, is inconsistent.
This argument is not a problematical argument and its suppositions
are not ones that we are supposed to have any antecedent reason
at all to reject. There are exactly specifiable languages for which
these suppositions evidently hold, such as that fragment of English
used in giving the Liar Argument earlier. For this reason, Tarski held
that an exactly specified language as much like English as possible
would be inconsistent – a claim that has been a source of consternation and a subject of misinterpretation largely because people have
been puzzled by what it was supposed to mean for a language to be
inconsistent. My answer to this is simple enough: it means exactly
what the above argument needs it to mean.
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GREG RAY
To say that an exactly specified language is an inconsistent language is to say that
the set of theorems of the language is deductively inconsistent.
In the remainder of Part 1, I will provide textual evidence that this
is the right understanding of Tarski’s Inconsistency Argument. In
the course of this, I will take the liberty of marking a number of
interesting and heretofore unnoticed historical points. Then, in Part
2, I will argue that where we have gotten it right, Soames gets it all
wrong.
1.1. Textual Support
Authority for our formulation of the Inconsistency Argument is
drawn from an examination of a passage from Tarski (1944,
pp. 348–349), but the materials of this argument had an earlier life
in (Tarski, 1935), and it will be instructive to first examine this
earlier argument, Tarski’s Colloquial Inconsistency Argument. In
§1 of his 1935 essay, Tarski is addressing himself to the question
of whether it is possible to give a satisfactory definition of ‘true
sentence’ for ordinary or colloquial languages, such as English.
After considering and rejecting a number of ways of trying to
construct either a semantical or structural definition, Tarski suggests
a general argument to the effect that no way will work.
The breakdown of all previous attempts leads us to suppose that there is no satisfactory way of solving our problem. Important arguments of a general nature can
in fact be invoked in support of this supposition as I shall now briefly indicate. . . .
These antinomies [of the liar and of heterological words] seem to provide a
proof that every language which is universal in the above sense [as is colloquial
language], and for which the normal laws of logic hold, must be inconsistent. This
applies especially to the formulation of the antinomy of the liar which I have given
. . . If we analyse this antinomy in the above formulation we reach the conviction
that no consistent language can exist for which the usual laws of logic hold and
which at the same time satisfies the following conditions: (I) for any sentence
which occurs in the language a definite name of this sentence also belongs to
the language; (II) every expression formed from [’x is true if and only if p’] by
replacing the symbol ‘p’ by any sentence of the language and the symbol ‘x’ by
a name of this sentence is to be regarded as a true sentence of this language; (III)
in the language in question an empirically established premiss having the same
meaning as [premise (b) of the Liar Argument] can be formulated and accepted
as a true sentence. (pp. 164–165)
TARSKI AND THE METALINGUISTIC LIAR
59
Tarski is infamous for his claim that ordinary languages such as
English are inconsistent, and this passage is the basis for this
reputation. The claim has caused a good bit of discussion and
consternation. Indeed, it has even been disputed whether Tarski
really holds the infamous view.4
Surprisingly, it has gone unobserved in all these discussions that
Tarski’s view changed – he later reconsidered and rejected his initial
argument as well as its conclusion. At least by 1944, Tarski clearly
felt that he could not make good on the argument as it stood. In
(Tarski, 1944), he makes a closely-related but more cautious case.
If we now analyze the assumptions which lead to the antinomy of the liar, we
notice the following:
(i)
We have implicitly assumed that the language in which the antinomy is
constructed contains, in addition to its expressions, also the names of these
expressions, as well as semantic terms such as the term “true” referring
to sentences of this language; we have also assumed that all sentences
which determine the adequate usage of this term can be asserted in the
language. A language with these properties will be called “semantically
closed.”
(ii) We have assumed that in this language the ordinary laws of logic hold.
(iii) We have assumed that we can formulate and assert in our language an
empirical premise such as the statement (2) which has occurred in our
argument [i.e., premise (b) of the Liar Argument].
It turns out that the assumption (iii) is not essential, for it is possible to reconstruct the antinomy of the liar without its help. But the assumptions (i) and (ii)
prove essential. Since every language which satisfies both of these assumptions is
inconsistent, we must reject at least one of them. (pp. 348–349)
This seems superficially like the same argument again, but the
crucial thing to realize is that this argument does not pertain to
colloquial languages at all, but is addressed only to what Tarski
calls “exactly specified” languages, and is accordingly given using
some of the technical language associated with that notion (namely,
assertability).5 Tarski then makes a point of saying that this revised
claim does not apply to colloquial language. The only lesson he now
would draw for colloquial language is, by comparison, remarkably
chaste.
The problem arises as to the position of everyday language with regard to this
point. At first blush it would seem that this language satisfies both assumptions
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GREG RAY
(i) and (ii), and that therefore it must be inconsistent. But actually the case is not
so simple. Our everyday language is certainly not one with an exactly specified
structure. We do not know precisely which expressions are sentences, and we
know even to a smaller degree which sentences are to be taken as assertible. Thus
the problem of consistency has no exact meaning with respect to this language. We
may at best only risk the guess that a language whose structure has been exactly
specified and which resembles our everyday language as closely as possible would
be inconsistent. (p. 349)
There is clearly a repudiation of his earlier argument in this. Tarski’s
considered view was not that natural languages are inconsistent.
Moreover, Tarski indicates in this passage that he cannot, after all,
give satisfactory sense to the notion of a colloquial language being
inconsistent. That is the sense of the second to last sentence quoted
above and it is the reason that he feels that he cannot claim to
have the general argument pertaining to colloquial language that he
claimed to have in his 1935 essay.6
Tarski’s revised argument still employs the notion of a language
being inconsistent. It is just that Tarski does not think he can make
fully clear talk of colloquial languages being consistent or inconsistent. He also tells us why this is in the passage above and this
will be our key to understanding how Tarski wishes to understand
the (in)consistency of a language. A language like English is not an
exactly specified language, and for various reasons it is in particular
not at all clear what would count as the assertible sentences (or
theorems) of English, and it is for this reason it is not fully meaningful to talk about such a language being consistent or inconsistent.
I think we should understand this line of reasoning as indicating that
Tarski was thinking of the inconsistency of a language in terms of
the technical notion of an assertible sentence. This is why Tarski
wanted to introduce the notion of an exactly specified language and
give the argument in its light, because he thought the terms of the
argument could be made clear using the technical terms associated
with this notion.
This hypothesis is borne out by the revised version of the inconsistency claim that Tarski gives. The 1944 claim boils down to
this:
Any exactly specified language which is such that (i) the T-sentence premise of a
Liar Argument can be asserted, (ii) the empirical premise of the Liar Argument
can be asserted, and (iii) the normal laws of logic hold, is inconsistent.
TARSKI AND THE METALINGUISTIC LIAR
61
The technical language of assertibility is new to the argument. And it
should now be easy to see what is the argument which stands behind
this claim and it is, consequently, also easy to read off from this what
inconsistency in a language must come to. Evidently, any exactly
specified language which meets the three conditions mentioned
would be one in which a logical contradiction could be derived
from the assertible sentences of the language using the inference
rules of that language. Since the assertible sentences (theorems) of
a language are closed under the inference rules of the language this
is just to say that a logical contradiction would be a theorem of the
language. This, in my interpretation of Tarski, is all it comes to to
say that an exactly specified language is inconsistent7 – a wholly
unmysterious notion that does precisely the work that Tarski needs
of it in his Inconsistency Argument (and the larger argument which
it serves).
We are now in a position to draw an extremely important lesson
from the text. Tarski does not hold that all the T-sentences are
true, and in particular, he does not hold that the T-sentence for the
liar sentence is true. Since this is really the only sensible stance
for Tarski this should not be entirely surprising. Nonetheless, it is
contrary to a certain ill-considered view of Tarski’s position which
is certainly to be met in the literature, and is, I suspect, widespread.
Indeed, it is likely because philosophers have thought that Tarski
thought all T-sentences true that they have seen in the notion of
an inconsistent language something mysterious. On their understanding, Tarski accepts as true sentences which he knows to be
inconsistent, but proclaims the language of these sentences itself
inconsistent as if this somehow could make an end of the matter,
somehow relieve one of the responsibility of rejecting an assumption of the paradoxical argument. That would make the notion of
an inconsistent language objectionably mysterious. These philosophers would also seem to be making the mistake of supposing
Tarski propounds the Liar Argument, whereas, we have seen, his
Inconsistency Argument only refers to (and hypothetically supposes
the assertability of) the premises of the Liar Argument.
Some of the confusion, of course, is owing to the fact that Tarski
does not address the question of the truth of the premises of the Liar
Argument directly.8 Again, it is really the only option for Tarski,
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GREG RAY
so the attribution should not be difficult or controversial. Still, if
further proof of Tarski’s stand is wanted, we can readily infer from
what he does say in the following way. As we have seen, Tarski
originally claims that a consideration having to do with the Liar
Argument shows that colloquial language is inconsistent. He later
repudiates this claim, offering us instead the claim that exactly
specified languages in which certain sentences are assertible are
inconsistent. Now, if you think that Tarski thinks the T-sentence
for the liar sentence, i.e. the first premise of the Liar Argument, is
true, or if you think, as Scott Soames (1999, p. 64) does, that Tarski
thinks assertibility implies truth, then you should find Tarski’s latterday repudiation extremely puzzling. After all, “a contradiction is a
contradiction wherever it may be found, in informal or in formal
surroundings” (Tucker, 1965, p. 60). Now, (i) the Liar Argument
can be formulated in colloquial language, (ii) Tarski is supposed
to hold that the T-sentence premise is true, (iii) nobody thinks the
minor premise is not true, and (iv) Tarski finds it barely conceivable
that one could repudiate the classical laws of logic.9 Taken together,
this should give Tarski all the license in the world to conclude that
a contradiction can be validly inferred from true premises. Whether
we want to pronounce colloquial language “inconsistent” on this
basis or call it something else, it is unhappy by any measure. So,
why did Tarski come to think he was not in possession of just the sort
of result he earlier argued for? Worse, if assertability implies truth,
it looks like Tarski’s commitment even to the revised inconsistency
claim brings us right back to the above argument, and hence his
repudiation simply could not come off – and for a rather unsubtle
reason.
The only way to untangle this mess is to recognize that Tarski
very sensibly does not hold that the T-sentence for the liar sentence
is true. In his revised inconsistency claim, it is only supposed
hypothetically that the T-sentence for the liar sentence is assertible.
This serves Tarski’s purpose and enables him to withhold commitment to an argument like the above because (and only if) he does
not suppose that assertibility entails truth.
Furthermore, there is evidence which suggests that Tarski never
held that the T-sentence for the liar sentence was true. In this regard,
it is worth noting how close the language of Tarski’s Revised Incon-
TARSKI AND THE METALINGUISTIC LIAR
63
sistency Claim is to the original inconsistency claim which said, in
essence, that
Any colloquial language which is such that (i) the T-sentence premise of a
Liar Argument is to be regarded as true, (ii) the empirical premise of that Liar
Argument can be accepted as true, and (iii) the normal laws of logic hold, is
inconsistent.
Here, because the target is colloquial language, Tarski does not
advert to the technical notion of an assertible sentence, but another
phrase stands in its place which looks like it might well have
been (more or less vaguely) intended to stand for some correlative
notion.10
1.2. The Real Significance of the Inconsistency Argument
One might worry that the reading of Tarski on offer is in tension
with itself in the following way. Doesn’t the non-truth of certain
T-sentences make it just a mistake to include them among the assertible sentences of a language? Granted, ‘assertible’ is being used as a
technical term in Tarski, but the notion of an inconsistent language
is tied to it, and so ipso facto is the conclusion of the Inconsistency Argument. Doesn’t letting the T-sentence for the Liar count as
assertible in spite of it’s not being true threaten the significance of
the conclusion of that argument? After all, it is in general neither
surprising nor problematic that a contradiction might be derived
from a set of sentences the members of which are not all true.
These are serious questions for the Tarskian view as we are now
understanding it.
To begin, we should remind ourselves of the various aims Tarski
announces in connection with the Inconsistency Argument. In the
1935 essay Tarski’s aim is to show that no satisfactory definition
can be given for a colloquial truth predicate. He states this aim very
clearly and after sketching the argument for the inconsistency of
colloquial language, he sums up as follows.
If these observations are correct, then the very possibility of a consistent use of
the expression ‘true sentence’ which is in harmony with the laws of logic and the
spirit of everyday language seems to be very questionable, and consequently the
same doubt attaches to the possibility of constructing a correct definition of this
expression. (p. 165)
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GREG RAY
So, the conclusion as far as definitions is concerned is that you could
not construct for colloquial language a satisfactory definition of
‘true sentence’ that was “in harmony with the laws of logic and the
spirit of everyday language”. This is because (i) the universality of
colloquial language will ensure the T-sentence for the liar sentence
can be formulated, and (ii) in order that the definition be satisfactory
it would have to underwrite that T-sentence, but (iii) by deploying
the laws of logic we can derive from this a contradiction.11 But a
definition which entails a contradiction is an improper definition
– and thus would not be “formally correct”, and would certainly
count as unsatisfactory by Tarski’s lights.12 Call this overarching
argument, Tarski’s Indefinability Argument.13
The main thing to notice about this is that Tarski’s aim and the
line of argument supporting it do not crucially involve the claim
that colloquial language is inconsistent. One could construct the
argument to go via this general claim, but it is not at all necessary
to establish Tarski’s point. Thus, in spite of the attention that has
been paid to Tarski’s claim that colloquial language is inconsistent,
it is something of an aside (and one that Tarski ultimately retracts)
– something to which he never assigns special independent significance. Importantly for us, whatever is the definition of ‘inconsistent
language’ it will meet Tarski’s argumentative needs just in case it
implies that the truth definition supposed in the Indefinability Argument must be an improper one. The meaning I have suggested for
‘inconsistent language’ in §1 seems to fit the bill well enough.14
Moreover, as I said, Tarski could get his conclusion by an easy
recasting of his Indefinability Argument in a way that does not go
via the notion of an inconsistent language.
1.3. Where We Are
To sum up, we have given a careful formulation of Tarski’s Inconsistency Argument, and a simple and unmysterious definition of
‘inconsistent language’ that comports well with Tarski’s use of this
term. Several items of note came out of our investigation – some of
which will play a role in the sequel. First, Tarski did not think all Tsentences are true. In particular, he did not think the T-sentence for
the liar sentence is true. Accordingly, he must not have thought that
the assertible sentences (theorems) of an exactly specified language
TARSKI AND THE METALINGUISTIC LIAR
65
must all be true. The texts comport well with these conclusions, and
we cannot make sense of key passages without accepting them.15
Part of our argument was based on an unsubtle, but also heretofore
unacknowledged change in Tarski’s position between 1935 and
1944.
There are several respects in which these conclusions flout understandings of Tarski to be found in the literature. First, Tarski’s 1935
argument for the inconsistency of colloquial language is usually
read as assuming that the T-sentence for the Liar sentence is true.
Tarski’s amended 1944 argument clearly avoids this implication,
and careful examination of the 1935 argument reveals that the initial
argument probably did not make this commitment either. Second,
and more generally, it is often enough just tacitly assumed that
Tarski’s whole T-sentence strategy of truth definition is founded
on the assumption that all T-sentences are true.16 In fact, various
people have thought that Tarski’s view would require or is prefaced
on the idea that T-sentences are apriori true or analytically true or
logically true. Since Tarski allows (as he must) that some wellformed T-sentences are not even so much as true, these writers have
certainly missed an important point. Thirdly, and finally, Tarski’s
talk of inconsistent languages has almost always been misread or
treated as something hopelessly mysterious. Careful attention to the
argument in which the notion occurs yields a simple and natural
interpretation that does the job the argument requires – in fact, it is
so simple an interpretation, it may well explain why Tarski didn’t
think an explicit definition of the phrase was required. And, I might
add, if we were all careful and sympathetic readers, he would have
been right in this.
2. SOAMES’ METALINGUISTIC LIAR
Scott Soames (1999) offers a rather surprising interpretation of the
part of Tarski which we have been discussing. According to Soames,
Tarski holds that natural languages like English are languages in
which there are true contradictions. This is quite surprising both
because Tarski was evidently quite logically conservative, but also
because it attributes to Tarski a position that is straightforwardly
incoherent, as we will see.
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GREG RAY
The key to understanding how Soames comes to this interpretation is understanding his reading of the Inconsistency Argument
passage (pp. 164–165, quoted earlier). Soames’ idea is that Tarski
was there suggesting a “metalinguistic reformulation of [the Liar
Argument] based on the claim that the premises of [the Liar Argument] are true sentences of English. Since these premises were used
in [the Liar Argument] to derive a contradiction, one would expect
the assumptions in [the metalinguistic argument] to be used to derive
the metalinguistic conclusion that a contradictory sentence is true in
English” (p. 53). To make this reconstruction yield the result Tarski
claims, Soames proposes that (for Tarski) a language is inconsistent
just in case some sentence and its negation are both true in that
language.17 The resulting “metalinguistic Liar” argument as Soames
reconstructs it, then, goes as follows (cf. p. 55).
A1.
A2.
A3.
A4.
C1.
C2.
C3.
C4.
A5.
C5.
The sentence with feature f is a sentence of English.
All instances of schema T are true in English.
‘The sentence with feature f = “The sentence with feature
f is not true” ’ is true in English.
The usual laws of logic hold in English – that is, all
standard logically valid patterns of inference are truth
preserving in English.
‘ “The sentence with feature f is not true” is true iff the
sentence with feature f is not true’ is true in English.
(From A1, A2, and the definition of what it is to be an
instance of schema T.)
‘The sentence with feature f is true iff the sentence with
feature f is not true’ is true in English. (From C1, A3,
and A4’s guarantee of the truth-preserving character of
the law, substitutivity of identity.)
‘The sentence with feature f is true and the sentence with
feature f is not true’ is true in English. (From C2 and A4:
tautological consequence.)
‘The sentence with feature f is true’ is true in English and
‘The sentence with feature f is not true’ is true in English.
(From C3 and A4: simplification of conjunction.)
‘The sentence with feature f is not true’ is a negation in
English of ‘The sentence with feature f is true’.
So, English is inconsistent. (From C4, and A5.)
TARSKI AND THE METALINGUISTIC LIAR
67
There are immediate problems with this as a reconstruction of
Tarski. First and foremost, it is not hard to see that the position being
attributed to Tarski is unsubtly incoherent. To see this, let us note
with Soames the following.
This metalinguistic version of the Liar parallels the earlier nonmetalinguistic
version and, on the face of it, would seem to call for a similar response. In
the case of [the Liar Argument], we derived a contradiction. Since no one can
rationally accept a contradiction, we must reject at least one premise or rule of
inference used in the derivation. In the case of [the metalinguistic Liar], we did
not derive a contradiction, but we did derive the conclusion that a contradiction is
true . . . However, this result seems no more acceptable than the result of [the Liar
Argument]. Thus it seems that here too we must reject either a premise or a rule of
inference. . . . However, this was not Tarski’s attitude toward [the metalinguistic
Liar]. Whereas he clearly did not accept the premises, rules of inference, and
conclusions of [the Liar Argument], he apparently was willing to do so in the
case of [the metalinguistic Liar]. (pp. 54–55)
This difference in attitude between the two arguments would indeed
be puzzling. Coming to the conclusion that a contradiction is true
does sound as bad as inferring a contradiction. Yet, things are rather
worse than that. Soames appears not to realize that his reconstructed
argument is easily extended to an explicit contradiction (using A4
and C4 in the obvious way).18 So, now we have two arguments that
lead to contradictions (one explicitly, one by trivial extension), and
on Soames’ interpretation Tarski sensibly rejects the one, but (foolishly) accepts the other. Tarski’s stance looks quite inexplicable and
his position straightforwardly incoherent.
These are good reasons to look for something amiss in Soames’
interpretation of Tarski. I hope and trust that the arguments of Part
1 will already have shown how far from the mark Soames’ interpretation is, but to drive the point home, I will now argue that Soames’
reading of Tarski is itself incoherent, and this should give us the
strongest possible reason for rejecting it. The problem is not far to
seek. First, Soames is very clear that Tarski “did not accept the
premises, rules of inference, and conclusions of [the Liar Argument]”. Indeed, in the face of the Liar argument, Tarski says, “If
we take our work seriously, we cannot be reconciled with this fact.
We must discover its cause, that is to say, we must analyze premises
upon which the antinomy is based; we must then reject at least one
of these premises” (1944, p. 348). Now, we should wonder, however,
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GREG RAY
what premise or inference step of the Liar Argument does Soames
think that Tarski rejects? Does he reject some classical logical principle? Hardly, and this is hinted by the fact that, as Tarski has it,
we must reject one of the premises. Moreover, Soames has Tarski
committed to classical inference in (A4). Then is it a premise that
is rejected? Again the answer is ‘No’. The Liar Argument has only
two premises.
(a)
(b)
‘The sentence with feature f is not true in L’ is true in L
iff the sentence with feature f is not true in L.
‘The sentence with feature f is not true in L’ is identical
to the sentence with feature f.
But Soames’ “metalinguistic Liar” interpretation of the passage
in Tarski is based on the idea that Tarski is giving an argument
which takes as premises the truth of both of these sentences. This
is represented by premises (A2) and (A3) in Soames’ construction.
Now, whatever it is to “reject a premise”, presumably one cannot
sensibly be thought to affirm the truth of the premises one rejects.
So, Soames has Tarski affirming the liar premises, too. We can only
conclude from this that Soames does not, after all, have a coherent
interpretation of Tarski that he is working with. He both holds that
Tarski rejects some premise of the Liar Argument (or a rule of inference), and holds that Tarski accepts both those premises (and the
rules of inference). I cannot imagine a worse outcome for a bit of
interpretation.
2.1. An Unfortunate Segue
Soames is confused about (doesn’t know) what Tarski rejects of
the Liar Argument. I argued earlier that Tarski rejects the only
sensible thing to reject, namely, the truth of the T-sentence for the
liar sentence. However, Tarski never tells us this outright. Tarski tells
us that in the face of such an argument you have to look back and
reject some premise you relied on, but he never really identifies any
premise of that argument as the culprit. What he does say at one key
point is sufficiently misleading, however, that it may well explain
how Soames came to this pass. Let us briefly review the two key
passages. In Tarski (1935), after giving the Liar Argument, Tarski
tells us19
TARSKI AND THE METALINGUISTIC LIAR
69
The source of this contradiction is easily revealed: in order to construct the assertion (β) [our Liar premise (a)] we have substituted for the symbol ‘p’ in the
scheme (2) an expression which itself contains the term ‘true sentence’ (whence
the assertion so obtained – in contrast to (3) or (4) – can no longer serve as a
partial definition of truth). Nevertheless no rational ground can be given why such
substitutions should be forbidden in principle.
I shall restrict myself here to the formulation of the above antinomy and will
postpone drawing the necessary consequences of this fact till later. (p. 158)
This leaves the matter unsettled. When Tarski later “draws the
necessary consequences”, he is not concerned to say something
about the Liar Argument itself. Rather, after considering several
unsuccessful ways of trying to solve the problem of giving a definition of ‘true sentence’ applicable to colloquial language, he wished
to offer a general argument to the effect that no satisfactory way
of solving the problem is possible. He adverts back to the Liar, but
only by offering (in the passage quoted earlier) the Inconsistency
Argument (as part of making his colloquial indefinability argument).
This does not tell us directly what we are to think about the Liar
Argument offered earlier.
It is in Tarski (1944), after presenting the Liar Argument, that
Tarski tells us that this antinomy presents us with an intolerable situation in the face of which we cannot rest content, but must discover
its cause, reject a premise. Tarski follows this remark with some (for
us) tangential remarks and that ends section 7 of the essay. In section
8, he begins with this familiar passage.
If we now analyze the assumptions which lead to the antinomy of the liar, we
notice the following:
(i)
We have implicitly assumed that the language in which the antinomy is
constructed contains, in addition to its expressions, also the names of these
expressions, as well as semantic terms such as the term “true” referring to
sentences of this language; we have also assumed that all sentences which
determine the adequate usage of this term can be asserted in the language.
A language with these properties will be called “semantically closed.”
(ii) We have assumed that in this language the ordinary laws of logic hold.
(iii) We have assumed that we can formulate and assert in our language an
empirical premise such as the statement (2) which has occurred in our
argument.
It turns out that the assumption (iii) is not essential, for it is possible to reconstruct the antinomy of the liar without its help. But the assumptions (i) and (ii)
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GREG RAY
prove essential. Since every language which satisfies both of these assumptions is
inconsistent, we must reject at least one of them. (pp. 348–349)
This is an terribly misleading segue. It seemed as though Tarski was
setting up to tell us what premise of the Liar Argument was to be
rejected, but this is not what he does. The assumptions he lists here
are not the premises of the Liar Argument at all, and the “rejection”
to be offered here is not a rejection of the expected sort. What Tarski
does is “choose” to only consider languages that are semantically
open, i.e. that do not meet condition (i). But no one could sensibly
think that Tarski is “rejecting” (i) in the sense of saying there are no
semantically closed languages.20 What is going on? It is clear that,
just as in 1935, Tarski is just thinking of these conditions as ones
which jointly prohibit a satisfactory definition being given. In short,
he has moved on to the task of determining a restricted context in
which the problem which he has set himself may yet be soluble.
For these purposes he is only seeking to avoid the Liar, not assess
it, diagnose it or explain it. No doubt it is this unfortunate segue
from section 7 to section 8 that led Soames to think that he knew
what Tarski rejected of the Liar Argument (while at the same time
committing him to the premises of that argument).
Now, maybe Tarski has just slipped here and does not see that
he has shifted in the face of one problem raised (the intolerable
situation presented by the paradoxical argument) to the pursuit of
another problem (the definitional project). However, it is well to
note that Tarski’s definitional project does not require that he pause
over philosophical diagnosis of the Liar paradox per se, and so we
need see no kind of mistake in the fact that he does not.21 Perhaps
also Tarski thought it was a fool’s game to try to go on to say more
about the Liar Argument, having once recognized the danger which
it portends.22 Fool’s game or no, it is a game that the philosopher
cannot help but play. While Tarski may have been reticent about
it, we feel that something is owing on this score, and we have
already done the work to show that Tarski rejects what he must:
the T-sentence for the Liar.
2.2. A Near Miss
I have argued that Soames is also mistaken to interpret Tarski’s
talk of inconsistent languages as he does. First, recall that when
TARSKI AND THE METALINGUISTIC LIAR
71
Tarski first gives the Inconsistency Argument, his aim is to establish
that no satisfactory definition of ‘true sentence’ can be given for
colloquial language. So, for his argumentative purposes, he only
needs his argument to vouchsafe this result, and this, as we may
see, does not require that he maintain that colloquial language is
inconsistent in any antecedently recognized sense. By 1944, Tarski
realizes that he should be directing this argument toward an exactly
specified, universal language, and then only indirectly drawing a
conclusion about colloquial language. So reconceived, his desired
result (no satisfactory definition) would follow, if the inconsistency
of a language was a matter of there being a contradiction among the
assertible sentences of the language. And this, I have proposed, is
the correct understanding of Tarski’s talk of inconsistent languages.
In a footnote, Soames (1999) considers something like this interpretation, but he is unable to see the promise of it for two reasons.
First, he unwisely treats Tarski’s ‘assertibility’ common-sensically,
rather than as a technical term. This is evident in the reasoning he
marshals.
In this view, it is somehow built into the nature of English that certain sentences
are assertable without proof, others are assertable only when derived by recognized rules of inference from sentences of the first sort, and still others are
assertable only when empirical and perhaps observable conditions obtain . . . The
language could then be considered inconsistent on the grounds that it sanctions
the assertion of inconsistent sentences. . . . This interpretation of Tarski [has a
chance of working] only if it is maintained that the rules of a language can dictate
the assertability of a sentence that is not true. But how can that be? It is hard to
imagine that it should be a condition of my speaking English that I be willing to
assert things that are not true. (p. 64)
This line of reasoning would go nowhere, if Tarski had stuck with
the term “theorem of the language” which is a technical term which
is for him synonymous with “assertable sentence”.23 Second, when
it comes to the hedging language in those key passages of Tarski
(1935) that we noted, Soames overlooks them head-on.
[Tarski’s] formulations of the conditions under which languages are supposed
to be inconsistent indicates that he thought [that the assertability of a sentence
required its truth]. As we have noted, in Tarski [1935] the premises leading to
inconsistency assert that instances of the schema T, including (P1), are true and
that an empirical premise, such as (P2), is also true. (p. 64)
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GREG RAY
So, Soames doesn’t make anything of the small locution in the 1935
paper (“to be regarded as true”), fair enough. But what about the
testimony of the later 1944 paper where Tarski uses “assertibility” in
parallel argumentative positions. Soames rejects this evidence quite
incredibly.
Essentially the same argument is given in Tarski (1944), [except for appeal
to assertability in the key positions]. Tarski’s apparent willingness to regard
these two formulations as equivalent versions of the same argument indicates
that he did not distinguish between truth in a language and assertability in a
language in a way that would [allow assertable sentences that were not also true].
(p. 64)
This is a grudging reading of Tarski and an incautious one. Soames
would use the earlier paper to trump the evidence of the later paper
on the grounds that it is the same argument both times. That is
grudging, because it denies to Tarski his considered view. It is incautious, because Tarski’s two arguments are not even about the same
things – the earlier is an argument about colloquial language, and
the later is about exactly specified languages only. Tarski (1944)
is an expression of Tarski’s considered view over which Soames
runs roughshod here. In addition, we showed earlier that Tarski most
certainly could not have held assertability implies truth.
In summary, Soames attributes to Tarski a view which is in an
obvious way inconsistent. Worse, Soames is himself inconsistent in
his interpretation of Tarski. In short, he is not operating with any
coherent understanding of (this part of) Tarski’s view at all.
2.3. A Note on Tarski’s T-Strategy
Before closing, I will take this opportunity to make a remark on a
matter close to this discussion which I think is of no small significance in understanding Tarski’s work on truth. We saw that Soames
makes the mistake of thinking that Tarski thinks that all T-sentences
are true, and I suspect that this is a widespread assumption – one
which is closely connected with people’s understanding of Tarski’s
T-strategy of truth definition. The “revelation” that not all the Tsentences can be true (and that Tarski did not think of them as such)
might, then, seem to put pressure on the strategy of truth definition
which was Tarski’s starting point. T-sentences were recommended
TARSKI AND THE METALINGUISTIC LIAR
73
to us as a way of trying to build a definition of a truth predicate.
Tarski even speaks of T-sentences as individually providing “partialdefinitions” of the truth predicate they employ.24 So, we should now
wonder, isn’t this just a mistake? This question deserves an answer,
though our treatment of this issue here must be brief.
I think that, in order to understand what is going on here,
one needs something like a distinction between a truth predicate’s
job assignment and its job performance – a distinction which
many discussions of Tarski and T-sentences lack.25 By dint of our
linguistic intentions and practices, ‘is a true sentence of’ expresses
(in one sense of that word) our concept of sentential truth. It is
this that determines the job assignment of the predicate – how
it is supposed to work – by dictating something like application
rules. These rules are such as to universally prescribe T-sentences
without exception. It is this conceptual underpinning that justifies
Convention T.26
How does this help us understand the T-strategy? T-sentences
recommend themselves to us on conceptual grounds. Our naive
belief is that T-sentences are conceptually underwritten in such a
way as to guarantee their truth, and this makes it easy to accept
the thought that T-sentences can be used to give a correct definition
of a truth predicate. This turns out not to be quite the right reason
to accept the T-strategy. Rather, the T-strategy – as embodied in
Convention T – is a reflection of the job assignment that any truth
predicate has which is to express our concept of truth. So, it is not
because T-sentences are true, but because they are supposed to be
true that we should cleave to them in setting out a definition – that is,
if our aim is “to catch hold of the actual meaning of an old notion”,
not “a familiar word used to denote a novel notion” (Tarski, 1935,
p. 341).
We have seen, however, that truth for all T-sentences cannot
be maintained. Thus, it is part of the lesson of the Liar that (in
sufficiently expressive languages) nothing could possibly perform
the assigned job of a truth predicate. Thus, truth predicates are
precisely cases where the job performance of a predicate sheers
away from its job assignment. What we need to understand is that
the failure of truth for some T-sentences is a (necessary) failure of
job performance, and so does not at all tend to undermine the T-
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GREG RAY
strategy, as embodied in Convention T, since, in the final analysis,
that strategy is rooted in and justified by ideas we have about the job
assignment of truth predicates.
3. CONCLUSION
The interpretation I have offered of Tarski provides a needed
corrective for a number of misunderstandings to be found in the
literature. Crucial to this corrective is a proper understanding of
the use Tarski makes of the Liar Argument, and the role that his
Inconsistency Argument has to play in his Indefinability Argument.
Among the fruits of our examination of Tarski is a clear and simple
meaning to be attached to Tarski’s talk of inconsistent languages –
an easy resolution to the befuddlement over this in the literature. We
uncovered a heretofore unrecognized shift in Tarski’s position on
the indefinability of truth predicates in natural language. We saw
just how important it is to understand and keep clearly in mind
that Tarski’s view is not committed to the truth of all T-sentences,
and we uncovered particular evidence that Tarski thinks that the
T-sentence for the liar sentence is not true. One upshot of this is
that Tarski’s original Indefinability Argument is typically misread,
and more broadly, Tarski’s T-strategy of truth definition is typically
misunderstood.
Our subsequent analysis of Soames’ discussion of Tarski showed
that he was mistaken or confused on a number of fronts. Soames has
a mistaken idea about what Tarski’s talk of inconsistent languages
comes to. This is part of what leads him into mistaking Tarski’s
Inconsistency Argument for a “metalinguistic liar argument” – an
interpretation which does not make good sense of the obvious way
in which the Inconsistency Argument merely subserves Tarski’s
Indefinability Argument. We saw that Soames interpretation of
Tarski makes Tarski inconsistent in an unsubtle way. We found, in
fact, that Soames does not have a coherent interpretation of Tarski
going at all on this point. As a part of making this case, we were
able to show that Soames is confused about – does not know – what
Tarski rejects of the Liar Argument. Tarski rejects the T-sentence for
the Liar. That Soames misses this is particularly disturbing, because
TARSKI AND THE METALINGUISTIC LIAR
75
it is part of the view that he himself wants to champion. Soames’
way out is to say that the T-sentence for the Liar sentence is neither
true nor not true. But, as far as I can see, this is just an unfortunate
way that Soames has of trying to say that the T-sentence is neither
true nor false. Thus, at the end of the day, Soames arrogates to
himself this much of Tarski’s own view, having first denied the view
to Tarski himself.
Tarski invites misunderstanding of his reaction to the liar by an
unfortunate segue in (1944). This is compounded by a common
misunderstanding of Tarski’s use of the Liar. Philosophers expect,
contrary to evidence, that Tarski takes himself to be offering some
kind of solution to the Liar Paradox, but Tarski’s use of the Liar
Argument does not require this nor does the evidence suggest that
Tarski thought otherwise.
NOTES
1
Of course, we do not ordinarily think of languages as coming equipped with,
e.g., a privileged set of axioms. So, Tarski’s exactly specified languages are more
highly individuated than are languages in the ordinary sense. They are also more
precisely circumscribed – there is always a determinate fact of the matter about
what is the vocabulary of an exactly specified language, for example.
2 In an empirical, exactly specified language, we can discriminate between
empirically and conceptually assertible sentences, insofar as the axioms of the
language are distinguished into those that are sanctioned on conceptual grounds
and those that are sanctioned by having met some specified standard of empirical
confirmation. An empirically assertible sentence could then be identified with the
theorems of the language which are not in the deductive closure of the conceptual
axioms. Tarski believes that a variant of the liar without the empirical premise is
possible and so does not elaborate the idea of assertibility for empirical languages.
There is the barest hint at (Tarski, 1944, p. 347).
3 For simplicity, I give this argument for an English-cognate language, but the
argument obviously generalizes.
4 See Martin, 1949; Stroll, 1954; Herzberger, 1965; Levison, 1965; Tucker, 1965,
p. 60; Sinisi, 1967; Soames, 1999; Hugly and Sayward, 1980.
5 It is notable, that, while the 1944 essay otherwise follows closely the pattern
of the 1935 essay, Tarski has rearranged his materials so as to first introduce the
notion of an exactly specified language and restrict attention to such languages.
His revised inconsistency claim is then given in this context.
6 An anonymous referee for this Journal suggests that the 1944 argument should
be read as a clarification rather than a revision of Tarski’s 1935 argument.
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GREG RAY
According to this suggestion, Tarski’s original argument was not directly about
colloquial languages in the first place. In support of this, the referee points out the
guardedness of Tarski’s concluding statement (that a consistent use of ‘true’ “in
the spirit of everyday language seems to be very questionable”) and opening statement (the antinomies “seem” to provide a proof that no language like colloquial
language could be consistent). Now, Tarski’s 1935 paper was groundbreaking
work, and for this reason the gray area between clarification and revision is
probably wide. Still, there are a number of considerations which speak against
the proposed reading of Tarski, and so in the end I do not hold with the referee’s
opinion. Firstly, the proposal makes the 1935 argument at best very misleading.
On this reading Tarski holds the argument he presents only seems to prove
colloquial language is inconsistent. Locutions such as ‘it seems that’ are common
enough in academic writing, but they do not generally have the sense of ‘it seems
(but only seems) that’, and when they do it is never in reference to an argument
the author is promulgating! I think Tarski’s guarded bookending of his argument
are simply part of a characteristic caution which we see evidenced throughout
his philosophically-minded work. Secondly, the referee’s proposal would make
the central part of Tarski’s argument about exactly-specified languages, rather
than colloquial languages. However, the notion of an exactly-specified language,
which receives elaborate introduction, is introduced only later in the essay, and
this seems also to speak against the proposal. Finally, let me remark that, this issue
is evidently of historical but not of critical interest. If Tarski’s 1935 argument is
understood to be more like his 1944 argument, then it is so much the worse for
Soames’ treatment of Tarski.
7 Martin (1958, p. 125) gets this point basically right.
8 I think it will be typically thought that Tarski’s own results must recommend
and explain why Tarski would be silent on this point. As one referee put it, “any
claim that the T-sentence for the liar is not true (or that it is true, for that matter)
would presuppose that we can properly use ‘true’ as a truth predicate for the
language in question; and this presupposition is just what Tarski’s argument is
supposed to have undercut.” However, this is a mistake. It is engendered by a
common and incautious understanding of what Tarski’s results show. Not every
use of ‘true’ embroils one in paradox. If it did, the term would never have been so
useful as it is. In particular, there is nothing paradox-inducing about saying that
the T-sentence for the liar sentence is not true. If Tarski held back from saying
something about the T-sentence for the liar for fear of paradox, it seems to me
that fear was baseless. And there is another and happier explanation of this lacuna
which I offer in §2.1. Be that as it may, it is amply clear that Tarski did not refrain
because of any general scruple about talking about truth except in connection with
restricted languages. This is borne out by the 1935 text itself, which is full of talk
about truth – truth in colloquiual language, truth in languages in general, etc. It is
a mistake to think that Tarski must have held or should have held that one ought
not speak of true sentences of English. The proper understanding of what his
positive results show is that much of our talk of truth in colloquial languages can
be preserved (for these are truth claims in well-behaved sublanguages of English).
TARSKI AND THE METALINGUISTIC LIAR
77
Contrary to popular belief, Tarski’s results show that many, many of our uses of
‘true’ are beyond reproach.
9 Tarski expresses such skepticism about repudiating the laws of logic in the
parentherical remark in this passage: “It would be superfluous to stress here
the consequences of rejecting the assumption (ii), that is, of changing our logic
(supposing this were possible) even in its more elementary and fundamental parts”
(Tarski, 1944, p. 348).
10 I have couched this remark in a way that turns on two small turns of a phrase
that appear in the English translation, so it is well to note that corresponding
hedging phrases occur in the German as well as in the original Polish (1933).
11 Of course, an empirical premise is involved also, strictly speaking, but Tarski
thinks a version of the heterological paradox can be used to give a cognate argument here that would require no help from such an auxliary premise (1935, p. 165,
footnote). I have suppressed the role of the empirical premise accordingly. For
a discussion and assessment of the cognate argument Tarski suggests, see Ray,
(forthcoming).
12 This is the whole extent of Tarski’s use of the inconsistency claim in Tarski
(1935). He alludes back to the passage only twice (pp. 167, 248).
13 Not to be confused with what is sometimes called “Tarski’s Indefinability
Theorem,” which is a corollary to Gödel’s First Incompleteness Theorem. Also,
I should note here that there are really two Indefinability Arguments – the one to
be extracted from the 1935 essay and the one to be extracted from the 1944 essay.
One concerns colloquial language and the other exactly specified languages. We
downplay this here.
14 This falls out if we suppose that it is a necessary condition on a formally
correct definition that it is not deductively inconsistent with the axioms of the
language. This is not the most narrow such condition on ‘formal correctness’ that
I can think of, since it condemns all definitions in exactly specified languages
in which the axioms of the language are themselves inconsistent. One could
imagine a somewhat more sensitive condition of formal correctness that would
instead have as a necessary condition that a formally correct definition is not
deductively inconsistent with any deductively consistent subset of the theorems of
the language (which were also free of the defined predicate). If we have this more
refined condition on formal correctness in mind, it is a bit more mysterious why
Tarski chose to argue in the way he did – via the inconsistency of the language.
Perhaps that only indicates that Tarski had something like the less refined condition in mind.
15 The evidence from the early paper on the status of axioms is not unequivocal.
In that essay, Tarski says the following by way of general guidance about the
sentences designated as axioms and the rules of inference for the language. “The
sentences which are distinguished as axioms seem to us to be materially true, and
in choosing rules of inference we are always guided by the principle that when
such rules are applied to true sentences the sentences obtained by their use should
also be true” (p. 167). This would seem to have the consequence that anything that
was a correlate in a colloquial language of an assertible sentence, should seem to
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GREG RAY
us to be (on reflection) materially true. It does not seem that we can say this about
the T-sentence for the liar sentence, at least once we see where taking it to be
true leads. It is notable that Tarski does not repeat this sort of thing in 1944. He
chrarcterizes the notion of an axiom of a language in a more formalistic way as
“those sentences which we decide to assert without proof” (p. 346). Moreover, he
conceives of the truth of the axioms of the language not as something guaranteed,
but rather as something that one might be in the position of needing to prove.
“Hence to show that all provable sentences are true, it suffices to prove that all
the sentences accepted as axioms are true, and that the rules of inference when
applied to true sentences yield new true sentences . . .” (p. 354n).
16 Some additional remarks on this head are to be found in §2.3 below.
17 Soames attributes the key elements of this interpretation to an informal suggestion made to him by Nathan Salmon. I assume that it is with permission that
Salmon is here implicated without protest. The idea is, in any case, not a new one.
See (Herzberger, 1965, 1967) which, however, fall short of attributing this sense of
‘inconsistent language’ to Tarski explicitly. See also (Hugly and Sayward, 1980).
All three of these papers make something of a production out of arguing that
there could not be a language in which there were true contradictions. You can
well imagine how the reductio goes. Just possibly Tucker (1965) also had this
same interpretation of what an inconsistent language is supposed to be.
18 From C4 we have: ‘the f is not true’ is true in English. Applying A4, we get:
‘the f is true’ is not true in English. But from C4 we also have: ‘the f is true’ is true
in English. Contradiction. It is important to see that we have not just come to the
conclusion that some language has a funny feature. We have derived an explicit
contradiction – that some item (a sentence) both has and does not have a certain
feature (being true in English).
19 It is worth noting that this passage also tends to undermine a common
misunderstanding of Tarski’s view. The passage suggests pretty clearly that
Tarski does not think that the T-sentence for the Liar sentence is ill-formed
nor consequently that the Liar sentence itself is ill-formed. This also serves to
undermine an even more common mistake concerning Tarski – the mistake of
thinking that Tarski is a “hierarchy theorist” in the sense that Russell was, i.e.,
a theorist who thinks that ordinary languages are implicitly stratified into levels,
with merely partial semantic terms at each level.
20 Famously, Tarski held that ordinary languages are “universal” and hence
semantically closed. In more cautious mood, he maintained that an exactly
specified language as like colloquial language as possible would be semantically
closed.
21 There is some evidence that Tarski thought the diagnostic problem solved,
and clearly saw his problem – the definitional one – as distinct and independent
of the diagnostic one. In the opening paragraphs of Tarski (1935) he tells us that
semantic notions have been looked on with suspicion because of the paradoxes,
even though a more or less satisfactory solution to those paradoxes has been
found. This suggests, as I say, that Tarski thinks the paradoxes have already been
satisfactory solved. If this is correct, then it would seem clear that (a) Tarski was
TARSKI AND THE METALINGUISTIC LIAR
79
not seeing it as part of his job to solve the Liar Paradox, and (b) he also saw the
problem to which he would address himself as distinct from and independent of
such a solution – since the definitional problem was still outstanding.
22 Charity would speak against this, since it seems it would have been a mistake
on Tarski’s part. Cf. note 8.
23 This Soames argument relies on treating “assertability” common-sensically,
but it is at odds with the next Soames argument to be canvassed, which
(mistakenly) urges that Tarski meant ‘assertability’ to imply truth.
24 Though, it is to be noted, he explicitly exempts the T-sentence for the liar
sentence from this status (Tarski, 1935, p. 158).
25 Soames can serve as an example of this, too. Once you bring forth the distinction I speak of, it becomes obvious that there are two senses in which you could
talk of a predicate expressing our concept of truth, namely in the sense of being
a predicate which has been assigned the job, been given the meaning, or, on the
other hand, in the sense of having the conceptually-prescribed extension. These
do not come to just the same thing in the case of a troubled concept like sentential
truth.
26 The sense in which T-sentences are conceptually underwritten can be made
precise. Once clarified, a number of interesting things come to light concerning
Convention T and Tarski’s underlying views about the concept of sentential truth.
For starters, see (Ray, 2002).
REFERENCES
Herzberger, H. (1967): ‘Truth-Conditional Consistency of Natural Languages’,
Journal of Philosophy 64, 29–35.
Herzberger, H.G. (1965): ‘Logical Consistency of Language’, Harvard Educational Review 35, 469–480.
Hugly, P. and Sayward, C. (1980): ‘Is English Consistent?’, Erkenntnis 15, 343–
348.
Levison, A.B. (1965): ‘Logic, Language, and Consistency in Tarski’s Theory of
Truth’, Phil Phenomenol Res 25, 384–392.
Martin, R.M. (1949), ‘Some Remarks on Truth and Designation’, Analysis 10,
63–67.
Martin, R. (1958): Truth and Denotation, Chicago: University of Chicago.
Ray, G. (2002): ‘Tarski, the Liar and Tarskian Truth Definitions’, in D. Jacquette
(ed.), A Companion to Philosophical Logic (pp. 164–176), Malden, MA:
Blackwell.
Ray, G. (in press): ‘Tarski’s Grelling and the T-Strategy’.
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