&KDUOHV3DUVRQVRQWKH/LDU3DUDGR[
$XWKRUV'DYLG6FKPLGW]
5HYLHZHGZRUNV
6RXUFH(UNHQQWQLV9RO1R0D\SS
3XEOLVKHGE\Springer
6WDEOH85/http://www.jstor.org/stable/20012273 .
$FFHVVHG
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .
http://www.jstor.org/page/info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
Springer is collaborating with JSTOR to digitize, preserve and extend access to Erkenntnis (1975-).
http://www.jstor.org
DAVID
CHARLES
PARSONS
SCHMIDTZ
ON THE LIAR
Tarski
that any satisfactory
proposed
of the form (T), namely
equivalences
=
Cp1 is true p)
(T)
definition
PARADOX*
of truth must
imply all
[Tarski 1944, p. 344]
as Tarski well knew,
1935, p. 165] any
[Tarski,
of the form (T) cannot be
implies all equivalences
can readily be constructed
as
formally correct, because Liar Paradoxes
of the form (T). For example,
the
suppose we create
equivalences
sentence The
sentence
numbered
(1) is not true'. Then we give it a
Unfortunately,
that
definition
number.
The
(1)
Now,
sentence
numbered
(1) is not true.
let us use the sentence numbered
of the form (T):
(1) to construct
the following
equivalence
sentence
The
numbered
(1) is not
not
tence numbered
true.
is
(1)
(2)
true'
is true =
the sen?
sentence
numbered
(1) is also denoted
by the definite
we
sentence
'the
numbered
that
The sentence
(1)',
may say
description
=
sentence
numbered
numbered
(1) The
(1) is not true'. Further, we
name of (1) with the above definite
in (2), the quotation
may replace,
to
obtain
description
Since
(3)
the
sentence
The
numbered
bered (1) is not true.
In response,
Charles
Parsons
(1)
constructed
is true =
the sentence
a restricted
which I shall call (P).
(P)
Cp1 is true or
version
num?
of (T),
=
-?
rp1 is false)
('p1 is true
p)
If we suppose (P), then it follows in cases where
the consequent
is a
and hence false, the antecedent
contradiction
is also false. Therefore,
are neither
true nor false. Thus, accepting
Liar sentences
(P) would
seem to solve the problem.1
Erkenntnis
?
32: 419-422,
Academic
1990 Kluwer
1990.
Publishers.
Printed
in the Netherlands.
420
DAVID
SCHMIDTZ
an account of what
without
it means
to be neither
Unfortunately,
nor
an
true
ad hoc label
false, this solution does little more than create
even if we had
for paradoxical
of schema (T). Moreover,
equivalences
such an account, claiming that The
sentence numbered
(1) is not true'
as we can see from
is neither true nor false would still be problematic,
the following:
A.
B.
C.
D.
sentence numbered
(1) is not true' is neither true nor
false, (assumption)
sentence numbered
The
(1) is not true' is not true and The
not true' is not false, (from A)
sentence numbered
is
(1)
=
sentence
The sentence
numbered
numbered
(1) The
(1)
is not true' (since the sentence numbered
is
also denoted
(1)
The
by its definite
The sentence
numbered
E.
F.
identicals)
The sentence numbered
sentence
numbered
The
of B)
plification
Have we uncovered
from sentence E that
G.
description)
numbered
(1) is not true and the sentence
not
is
false
of
(from B and substitutivity
(1)
The
sentence
of D)
(1) is not true, (simplification
not
not
is
true,
true' is
(1)
(sim?
a contradiction?
numbered
Suppose
(1) is not
I went
on
to infer
true' is true.
sentence
G explicitly
contradicts
F. Moreover,
if schema
is true, sentence G follows from sentence E. But we
(P)'s consequent
cannot
is true in
infer G because we cannot assume the consequent
is true in this case
this case. We can deny that schema (P)'s consequent
schema
without
(P). We need only deny that the ante?
abandoning
cedent
is true. In other words, we may deny that sentence E is true
to G, escaping
the outright
reductio of
and thereby avoid the move
schema (P). We may instead claim that sentence E is neither true nor
Sentence
false.2
than
The claim is ad hoc, of course, but the problems
go deeper
we may not have derived
statements
that contradict
that. Although
that we were
able to
it remains somewhat
each other,
paradoxical
a
nor
true
from
true
false
neither
infer
premise.
something
validly
as one that preserves
we think of a valid argument
truth
Normally,
CHARLES
ON THE LIAR
PARSONS
PARADOX
421
redefine validity, or should we abandon many of the
we
took to be valid?
heretofore
rules of inference
Nor does it help to retreat even further by saying schema (P) never
true. Suppose we say
that the premise
A) was
(sentence
implied
Should we
value.
It remains the case that schema
is true, and sentence A is neither
case where
true premises
yield
false.
that schema (P) itself
Suppose we retreat further yet to the position
true nor false. Then even if it has important
is neither
implications,
unclear. We noted our
why we should take them seriously becomes
lack of an account of what 'neither true nor false' does other than pick
out paradoxical
of schema (T). Now it appears we should
equivalences
conclude that schema (P) is neither true nor false. And all this seems to
mean is that schema (P) has its own somewhat paradoxical
implications.
true nor false.
A is neither
(P) implies sentence A. If schema (P)
true nor false, then we still have a
that are neither true nor
conclusions
sentence
NOTES
*
referee
from
and to an anonymous
to Vann McGee,
Scott Sturgeon,
I am grateful
on an earlier
comments
draft of this paper. Remaining
for very helpful
are entirely mine.
mistakes
1
sentence
numbered
The
the so-called
Consider
(1) says of itself
'revenge
problem'.
it is not true. But that is
true nor false, then in particular
that it is not true. If it is neither
Erkenntnis
it is true after all,
sentence
(1) has been
trying to tell us all along. Therefore
once again. The revenge
for paradox
however,
presupposes
problem,
leaving us bound
numbered
a well-defined
term 'true' such that the sentence
(1) is true "after all". That
what
term
cannot
sentence
in the object
true. The
defined
be
numbered
(1) is not
in another.
sense and not true
2
The other approach
would
There
be
language,
sentence
because
numbered
is no contradiction.
to defuse
the
tension
the
in the object
language
true in one
(1) is therefore
p. 35]
[See Parsons,
sentences
E and F with
between
that helped
Parsons
and metalanguage
language
object
the revenge
however,
my argument,
1.] Unlike
[See note
and says, "Look! The Liar
itself, as it were,
argument
steps back to observe
problem's
true after all!" Because
the revenge
sentence
does
this, tjhe
says something
problem
to defend
he
is not on Parsons
the object-metalanguage
distinction
burden
of proof
the same
distinction
solve
revenge
the
between
problem.
is on one
takes no such step, the burden of proof
argument
an
is heavy
And
the
distinction.
burden
metalanguage
object
responds
to natural
to be relevant
One
for anyone who,
like Parsons, wants his answer
languages.
in natural
has to argue that such language
level jumps are there to be made
languages.
makes
who
Now
"That's
in reply.
Since
my
to it with
I assert
reply,
suppose
something
(say, in a court of law) and you immediately
not true!" If the language
natural
I
level story correctly
describes
languages,
DAVID
422
no
have
reason
language
to think
that would
you
SCHMIDTZ
are contradicting
me. What
a mysterious
view
of natural
be.
REFERENCES
Charles:
[1] Parsons,
Essays
on Truth
'The Liar Paradox',
1984,
and the Liar Paradox,
Oxford
in Robert
L. Martin
Press,
University
(ed.),
Oxford,
pp.
Recent
9-45.
Reprinted from Journal of Philosophical Logic 3, (1974) 381-412.
of Truth
in Formalized
1975, 'The Concept
[2] Tarski, Alfred:
Languages',
in Tarksi's
Semantics,
Metamathematics,
by J. H. Woodger
Logic,
(1956) pp. 152-278.
versity Press, Oxford,
[3] Tarski,
Alfred:
Phenomenological
submitted
Manuscript
Final version
received
Department
University
New
Haven,
U.S.A.
CT
06520
'The
Semantic
4 341-376.
Nov.
19,
1987
May
17,
1988
of Philosophy
Box 3650
Yale
1944,
Review
Conception
of
Truth',
Translation
Oxford
Philosophy
Uni?
and