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ABSTRACT: Functionalists about truth employ Ramsification to produce an implicit definition of the theoretical term true, but doing so requires determining that the theory introducing that term is itself true. A variety of putative dissolutions to

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TRUTH, RAMSIFICATION, AND THEPLURALIST’S REVENGE
Cory D. Wright
Functionalists about truth employ Ramsiﬁcation to produce an implicitdeﬁnition of the theoretical term
true
, but doing so requires determining thatthe theory introducing that term is itself true. A variety of putative dissolutionsto this problem of epistemic circularity are shown to be unsatisfactory. Onesolution is o
ﬀ
ered on functionalists’ behalf, though it has the upshot that theymust tread on their anti-pluralist commitments.
1. Introduction
Truth-theorists are sometimes asked what a theory of truth is about. Inanswering ‘truth’, we go around in a very small circle. A less loopy answermight instead begin with a little more philosophical spadework. Forinstance, we might try to gainfully reinterpret the question as a questionabout how the terms used to talk about truth—such as
truth
or
true
—are tobe deﬁned.
1
After all, for any given theory of truth
T
, such terms aretheoretical terms; and questions about how to deﬁne theoretical terms havewell-known answers.Inﬂationists often take this route, claiming that
true
attributes a propertywhich consists in being
F
. Functionalism about truth is one such inﬂationarytheory, although its central thesis is the further claim that being
F
is afunctional kind rather than a structural one.
2
More speciﬁcally,
(
fnct
)
true
refers to the single higher-order functional role property
F
of having lower-order properties
r
1
,...,
r
n
that realize it.
To arrive at this thesis, functionalists suppose that
true
can be deﬁnedimplicitly via the quasi-formal technique of Ramsiﬁcation.
1
Given that philosophers of language don’t have a consistent and uniﬁed theoretical vocabulary fordiscussing semantic, semiotic, and alethic relations (
reference
,
deixis
,
signiﬁcation
,
designation
,
predication
,
denotation
,
proﬁling
,
satisfaction
, etc.), I’ll generally use terms for reference as the most neutral genus-levelfamily of terms allowing us to bypass thorny questions about which are the most grammatically appropriateto invoke and when. In certain contexts,
attribution
—although clearly not synonymous with terms forreference—will be preferable.
2
Functionalism about truth, which sometimes goes by the misnomer
alethic functionalism
, has beendeveloped primarily by Lynch [2000, 2004, 2005, 2009]. The theory was anticipated by Laﬂeur [1941], to alimited extent, and again in a more recognizable form by Pettit [1996]. For additional exposition, see Devlin[2003], Wright [2005], and Sher [2005].
Australasian Journal of Philosophy
Vol. 88, No. 2, pp. 265–283; June 2010
Australasian Journal of Philosophy
ISSN 0004-8402 print/ISSN 1471-6828 online
2010 Australasian Association of Philosophyhttp://www.tandf.co.uk/journals DOI: 10.1080/00048400902941315
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My contention is that theories of truth employing Ramsiﬁcation face aproblem of epistemic circularity. The problem arises because any suchimplicit deﬁnition proceeds, at least in part, on the basis of explicitdecisions that certain sentences containing the
deﬁniendum
are themselvestrue. Rather than simply dispensing with Ramsiﬁcation itself [cf. Lynch2009], I propose nine putative dissolutions to the problem. Afterexplaining why each fails, I o
ﬀ
er a positive solution on behalf of functionalists. The solution, however, requires of functionalists that theyslough o
ﬀ
certain monistic assumptions. Since both the problem and thesolution generalize to any theory of truth relying on Ramsiﬁcation todeﬁne the theoretical terms used to talk about truth, pluralism becomes apressing issue. I leave it as an open question whether pluralists have aviable position themselves.
2. Why Implicit Deﬁnition?
Perhaps the most straightforward way to deﬁne theoretical terms is simplyto provide explicit and noncircular deﬁnitions of the form
defn
ð Þ
x
: . . .
x
. . .
¼
df
;
where ‘...
x
...’ is some
deﬁniendum
involving the unique term being deﬁned,‘
¼
df
’ is the relation of deﬁnitional equation, and ‘––––’ is the
deﬁniens
interms of which
x
is explicitly deﬁned but doesn’t occur.Theoretical terms often resist explicit and noncircular deﬁnitions,however. Indeed, scientiﬁc theories are renowned for occasioning termsthat have technical or specialized senses, or express unfamiliar or exoticconceptualizations, or stand for unobservable posits or abstracta of questionable repute: e.g.,
caloric
,
dark matter
, or
superstring
inphysical theory,
ﬁtness
or
race
in biology, and
sense-datum
,
id
, or
intelligence
in the psychological sciences. Call these recalcitrant terms the
t
-terms of a scientiﬁc theory
T
. A
t
-term-introducing theory
T
needn’t beexclusively scientiﬁc, however. Many of our more interesting philosophicalconcepts are those whose expression—e.g.,
causation
,
representation
,
person
, and
well-being
—has also proven resistant to explicit noncirculardeﬁnition.The reasons for resistance vary widely. Often, they are purpose-relative.Those
t
-terms introduced stipulatively, for example, can simply fail toachieve their intended aim; those introduced descriptively may under-estimate the wide variety of actual usages; those introduced ampliatively canfail to constitute a su
ﬃ
cient theoretical improvement; and so forth. In othercases, the reasons for resistance are term-speciﬁc. For example, slingshotarguments await those correspondence theorists attempting to deﬁne
truth
in terms of a structural relation of correspondence between truth-bearersand facts. For a term like
coherence
, the di
ﬃ
culty is due to a certain lack of mathematical precision among comparative approaches to the analysis of
COHERENCE
[Millgram 2000: 82–3].
266
Cory D. Wright
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In still other cases, attempts at explicit non-circular deﬁnition are furtherencumbered because the
t
-term targeted for deﬁnition has quotidiancounterparts that enjoy common and versatile usage in ordinary discourse.Such cases seemingly induce a feeling of trying to deﬁne something that isparadoxically strange but familiar, profound yet mundane [Lynch 2005: 29;Næss 1938: 159–60]. One observes this in even the earliest and mostelementary of the Platonic dialogues—Socrates’s attempt to formulateampliative deﬁnitions of
friendship
in the
Lysis
, for example. And as thenumber of distinct counterparts increases, the encumbrance is furthercompounded. The di
ﬃ
culty in explicitly deﬁning the
t
-term
sentence
inlinguistic theory, for example, is due not so much to its merely havingadditional senses, but to its having hundreds of them [Ries 1931].In the case of
truth
, Davidson [1996] urged that the appropriateresponse is to quit: attempts to give any kind of general deﬁnition areunwittingly involved in folly simply because the term
truth
—as he tookTarski to have shown—is indeﬁnable. For some, Davidson’s brand of primitivism seems unduly pessimistic. An alternative strategy for managingdi
ﬃ
culties incurred from attempts at explicit and noncircular deﬁnitions of
t
-terms is simply to o
ﬀ
er implicit deﬁnitions instead. Rather than equatinga
deﬁniendum
with some
deﬁniens
, implicit deﬁnitions take the form of certain true sentences
s
j
,
s
k
,...that are constitutive of
T
and in which the
deﬁniendum
occurs. For example,
t
-terms like
point
,
line
, and
radius
, whichoccur in the axioms of Euclidian geometry, are commonly said to beimplicitly deﬁned by those axioms. The assumption underlying thisstrategy is that, in reckoning that
T
is true, one assigns, implicitly, its
t
-terms the meanings they would need to have in order for
T
to be true.Accordingly, it’s su
ﬃ
cient for determining what a
t
-term means that thetheorist determine some, perhaps even many, of the true sentences inwhich it features as a subsentential component.The strategy of implicit deﬁnition forms the basis for the quasi-formaltechnique of Ramsiﬁcation, which has long been o
ﬀ
ered as a way to deﬁne
t
-terms by exchanging them—purportedly without loss of meaning—for a‘street-level’ vocabulary. Since the meanings of those
t
-terms weren’t wellunderstood in the ﬁrst place, then quantifying over the variables that replacethem stands to produce a deﬁnitive sentence serving as a descriptivelyadequate substituend for the srcinal theory.
3. Deﬁning Alethic Terms Implicitly
3.1 Ramsiﬁcation
The standard version of Ramsiﬁcation is the one popularized by Lewis[1970],
3
which begins by amassing whatever principles
P
j
,
P
k
,... areconstitutive of the postulate of
T
or otherwise relevant to its introduction
3
Modiﬁcations and alternatives to Lewis’s version abound; see, e.g., Craig [1953], Martin [1966], Bohnert[1967], Bedard [1993], Hawthorne [1994], and Horwich [1997]. None of them circumvents the problem of epistemic circularity discussed herein.
Truth, Ramsiﬁcation and the Pluralist’s Revenge
267
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of the target
t
-term.
4
Having ﬁxed upon this set of principles, the secondstep is to order and then conjoin them to form a single sentence which ismaterially equivalent to (
T
:
P
1
,...,
P
n
). Lewis had us rewrite the result as
T
ð Þ
R
t
1
;
. . .
;
t
n
;
o
1
;
. . .
;
o
n
ð Þ
;
so as to isolate the
t
-terms targeted for implicit deﬁnition. (For the purposeof homogenizing the variables that will appear in forthcoming derivations,Lewis also proposed that we convert all functors and predicative
t
-termsin the postulate of
T
to their corresponding nominalizations, i.e.,
t
-name
1
,...,
t
-name
n
.)Any such implicit deﬁnition necessitates a large register of additionalterms, against which the meaning and use of
t
-terms can be situated. Afterall, the string
t
-name
1
,...,
t
-name
n
would be quite useless otherwise— nearly incomprehensible, practically incommunicable, and certainly un-grammatical. The remainder of
R
therefore consists in what Lewis called
old-or-srcinal-or-other terms
. Unfortunately, Lewis said little else abouthow to characterize these
o
-terms, though the very idea of an
o
-term isperhaps su
ﬃ
ciently intuitive. If need be, we can precisify it as follows. Let anexpression
x
be an
o
-term in a given language
L
i
ﬀ
x
is a symbolic structure
S
i
with unit status in the grammar of
L
prior to the formulation of
T
, where[
S
i
] exhaustively consists in a phonological unit [
p
] that (literally) calls tomind a semantic unit [
s
] for speakers of
L
(i.e. [[
s
]–[
p
]]). An
o
-sentence is thenany sentence of
L
free of
t
-terms.The next step is to replace every
t
-name instance with a correspondingsubscripted variable (
x
1
,...,
x
n
) ranging over individuals in the domain of
R
. In the case at hand, all terms pertaining to truth, truths, truth-talk, judgments-of-truth, etc. are stripped out, as well as terms that arepotentially interdeﬁnable with them—
assert
,
real
,
fact
, etc. Doing so resultsin an open sentence,
T
0
ð Þ
R x
1
;
. . .
;
x
n
;
o
1
;
. . .
;
o
n
ð Þ
;
which Lewis called
the realization formula of
T
. Basically,
T
0
isa speciﬁcation of what must obtain for the postulate of
T
to be
4
Lewis allowed for the postulate of
T
to be of arbitrary length—anything from a single sentence to adecidably inﬁnite set of sentences. As we shall see, its content must be anything but arbitrary, whichimmediately raises a thorny question about which principles to amass [Wright 2005]. Wright [2001: 759]claimed that anything ‘chiming with’ ordinary
a priori
platitudes should be initially counted, followed bylater scrutinization. Although this response ignores what’s interesting about the question, Wright was correctin presupposing that the technique generally works on a ‘more-the-merrier’ basis (in so far as obtaining moreinformation facilitates the identiﬁcation of candidate denotata). And yet, too much merriment can result inan output that is ‘inconvenient’, as Lewis put it, and possibly even counterproductive. Subsequently,enthusiasts of Ramsiﬁcation commonly distinguish some privileged or essential subset of principles, whichdemarcates minimal competence with the concept expressed by the
t
-term, from the full amassed collection,which characterizes the conceptual content of
T
in its entirety [Lynch 2009: 13–16
ﬀ
]. There is a seriousproblem, however, with settling on the appropriate criteria for inclusion and exclusion [Wright 2005]. Sincethis so-called
criteria problem
is likely to remain unsettled for a while, let us momentarily bracket it andassume—with functionalists and other enthusiasts—that there is some extant procedure for ﬁxing upon somesubset of the essential or privileged principles, or at least some criteria for extracting and distilling them.268
Cory D. Wright
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realized—i.e., a ‘job description’ as it’s sometimes put. And the postulate of
T
is realized just in case
T
0
is satisﬁed by any ordered
n
-tuple of entities— i.e., some realizer
r
i
that plays the role or does the job identiﬁed andindividuated by
T
0
. It is uniquely realized just in case exactly one ordered
n
-tuple satisﬁes
T
0
, multiply realized if more than one does, and unrealized if none does. Whether a theory is unrealized, uniquely realized, or multiplyrealized depends on what there is.Articulating the sentence stating that
T
is so realized—namely, its
Ramseysentence
T
0
R
—is achieved by preﬁxing, for each subscripted variable
x
i
2
R
,an existential quantiﬁer binding it.
ð
T
0
R
Þ
9
x
1
;
. . .
;
9
x
n
½
R
ð
x
1
;
. . .
;
x
n
;
o
1
;
. . .
;
o
n
Þ
:
The Ramsey sentence simply speciﬁes that there exists some such realizer
r
i
.And the point of doing so, of course, is to position the theorist to be able tomake the same ontic commitments that would otherwise be incurred byasserting or endorsing
T
.
5
3.2 Application to Theories of Truth
From
T
0
R
, the conditions under which some
r
i
is possessed can then be givenby embedding the Ramsey sentence in the requisite biconditional,
ð
T
L
Þ
r
i
ð
a
Þ
9
x
1
;
. . .
;
9
x
n
½
R
ð
x
1
;
. . .
;
x
n
;
o
1
;
. . .
;
o
n
Þ
&
a
has
x
1
;
. . .
;
x
n
:
T
L
states that an individual
a
has some
r
i
denoted by the (nominalized)
t
-term when and only when the variable
x
i
replacing it both is
R
-related tocertain other terms in the postulate of
T
and is had by
a
. For functionalistsabout truth, the individual is some truth-bearer
s
and the correspondingbiconditional states that
s
has some alethic property
r
i
that realizes the
F
-role just in case the extant value of the variable
x
i
replacing
truth
is both
t
-named by the terms of the theory en masse and is had by
s
:
ð
T
0
L
Þ
s
has some alethic property
r
i
realizing
F
9
x
1
;
. . .
;
9
x
n
½
R
ð
x
1
;
. . .
x
n
;
o
1
. . .
o
n
Þ
&
s
has
x
1
;
. . .
;
x
n
5
Of course, the derivation from
T
to
T
0
R
yields a less informative and more abstract sentence (roughly, in thesame sense that the sentence
there is at least one truth
logically entails the less informative and more abstractsentence
there is at least one entity
). Yet, as Ramsey famously noted, the magnitude of
T
0
R
is no less powerful,given that it makes all the same predictions and inferential connections between observation sentences.Furthermore, as Bohnert [1967] less famously noted, the ﬂight from informativeness is kept at a minimum.For instance, logically equivalent sentences, such as the conjunction of shorter conjunctions,
ð
T
00
R
Þ
9
x
1
½
R
ð
x
1
;
o
1
;
. . .
;
o
n
Þ
;
&
. . .
;
&
9
x
n
½
R
ð
x
n
;
o
1
;
. . .
;
o
n
Þ
;
are not necessarily as expressively powerful as
T
0
R
; for
t
-names may irrigidly denote where various realizationformulae fall within the scope of di
ﬀ
erent quantiﬁers. In the case of pluralism about truth, irrigid denotationmight be something comfortably accommodated or tolerable.
Truth, Ramsiﬁcation and the Pluralist’s Revenge
269
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