Truth, Ramsification, and the pluralist’s revenge

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 Philosophy DOI: 10.1080/00048400902941315  D o w n  l o a  d e  d B y : [ C a  l  i  f o r n  i a S t a t e U n  i v e r s  i t y L o n g B e a c  h ] A t :  1  7 :  1  6  2 J u n e  2  0  1  0  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  D o w n  l o a  d e  d B y : [ C a  l  i  f o r n  i a S t a t e U n  i v e r s  i t y L o n g B e a c  h ] A t :  1  7 :  1  6  2 J u n e  2  0  1  0  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  D o w n  l o a  d e  d B y : [ C a  l  i  f o r n  i a S t a t e U n  i v e r s  i t y L o n g B e a c  h ] A t :  1  7 :  1  6  2 J u n e  2  0  1  0  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  D o w n  l o a  d e  d B y : [ C a  l  i  f o r n  i a S t a t e U n  i v e r s  i t y L o n g B e a c  h ] A t :  1  7 :  1  6  2 J u n e  2  0  1  0  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  D o w n  l o a  d e  d B y : [ C a  l  i  f o r n  i a S t a t e U n  i v e r s  i t y L o n g B e a c  h ] A t :  1  7 :  1  6  2 J u n e  2  0  1  0
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