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 this problem of epistemic circularity are shown to be unsatisfactory. One solution is offered on functionalists' behalf, though it has the upshot that they must tread on their anti-pluralist commitments.

Notes

¹Given that philosophers of language don't have a consistent and unified theoretical vocabulary for discussing 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-level family of terms allowing us to bypass thorny questions about which are the most grammatically appropriate to invoke and when. In certain contexts, attribution—although clearly not synonymous with terms for reference—will be preferable.

²Functionalism about truth, which sometimes goes by the misnomer alethic functionalism, has been developed primarily by Lynch [2000, 2004, 2005, 2009]. The theory was anticipated by Lafleur [1941], to a limited extent, and again in a more recognizable form by Pettit [1996]. For additional exposition, see Devlin [2003], Wright [2005], and Sher [2005].

³Modifications 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.

⁴Lewis allowed for the postulate of 𝒯 to be of arbitrary length—anything from a single sentence to a decidably infinite set of sentences. As we shall see, its content must be anything but arbitrary, which immediately 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 by later scrutinization. Although this response ignores what's interesting about the question, Wright was correct in presupposing that the technique generally works on a ‘more-the-merrier’ basis (in so far as obtaining more information facilitates the identification of candidate denotata). And yet, too much merriment can result in an 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, which demarcates minimal competence with the concept expressed by the τ-term, from the full amassed collection, which characterizes the conceptual content of 𝒯 in its entirety [Lynch 2009: 13–16 ff]. There is a serious problem, however, with settling on the appropriate criteria for inclusion and exclusion [Wright 2005]. Since this so-called criteria problem is likely to remain unsettled for a while, let us momentarily bracket it and assume—with functionalists and other enthusiasts—that there is some extant procedure for fixing upon some subset of the essential or privileged principles, or at least some criteria for extracting and distilling them.

⁵Of course, the derivation from 𝒯 to yields a less informative and more abstract sentence (roughly, in the same sense that the sentence there is at least one truth logically entails the less informative and more abstract sentence there is at least one entity). Yet, as Ramsey famously noted, the magnitude of 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,

are not necessarily as expressively powerful as ; for τ-names may irrigidly denote where various realization formulae fall within the scope of different quantifiers. In the case of pluralism about truth, irrigid denotation might be something comfortably accommodated or tolerable.

⁶For further discussion of the scope problem, see Sher [1998], [2004] and Lynch [2004]. For discussion of the problems faced by pluralists about truth, including equivocation, generalization, and mixed inference, see, e.g., Lynch [2000], [2004], Wright [2005], Sher [2005], and Pedersen [2006].

⁷Some of these ‘problems’ arise from a faulty characterization of the nature of semantic and conceptual ambiguity, and so are easily dissolved.

⁸The motivation to employ the functionalist apparatus of roles and realizers in the first place would be far less persuasive if the set of realizers turned out to be a set of cardinality one.

⁹ Pace Lewis [1970: 432–3], the specific type of theoretical defect is falsity. Lewis's claim is fairly straightforward in cases where 𝒯 is unrealized. The τ-names miasma and phlogiston, for example, are introduced by the theories of miasmatic transmission and phlogistification under the assumption that the existential quantifier binding each x_i  ∈ R implies existence; but we count those theories as being false since they imply the existence of non-extant entities. Likewise, if 𝒯 is some version of monism or pluralism about truth and no ordered n-tuple of entities satisfies their respective realization formulae, then the sentence there's either one or many ways of being true is false. Cases of 𝒯 being multiply realized are far less straightforward. We can certainly concur that multiple realization is less desirable than unique realization, since being unable to non-arbitrarily (re-)identify the i ^th entity of the ordered n-tuple of the realization by the i ^th term of 𝒯′ is surely a defect. But it's unclear why that defect is one of falsity. As Bedard [1993: 506] notes, extreme complexity and weakness—like multiple realization—is unattractive; yet, we don't count 𝒯 as false simply because it's not simple or strong enough. In any case, given that functionalism is a version of monism about truth (there is but one F-role per ; see [Wright 2005: 13–15]), let us momentarily bracket these complications.

¹⁰Thanks to a referee for prompting closer scrutiny of this distinction.

¹¹Thanks to a referee for raising this clever objection.

¹²Functionalists need not—and don't appear to—Ramsify over meaning postulates of the form x means y or explicit definitions (recall, for instance, that they arrive at as a result of Ramsification, not prior to it). But they certainly could, and certainly should if moved to make intra-theoretical refinements over time. Suppose that functionalists engage in successive iterations of Ramsification over 𝒯 (i.e., Ramsification over 𝒯 on the first iteration, over 𝒯's successor 𝒯′′ on the second, over 𝒯′′'s successor 𝒯′′′′ on the third, etc.). Then we should expect that any claims about truth derived from 𝒯 on the 1^st iteration, such as , would be acceptable for invoking in successive iterations of Ramsification over any successors of 𝒯, and that failure to explicitly affirm the claims arrived at when articulating 𝒯′′, 𝒯′′′′, etc. would justify doubt about the truth of the initial theory 𝒯.

¹³Thanks to Michael Horton for pressing this objection.

¹⁴ Pace Field [1973], the inability to determine that all conjuncts of R are true merely leaves the τ-terminology referentially indeterminate, in which case the definiendum may partially denote more than one thing. Presumably, pluralism about truth is consistent with such results.

¹⁵The questions are made even thornier to the extent that error theories, which suggest T-schema instances are false, are plausible. (Ironically, some advocates of error theories have employed functionalism about truth e.g., Devlin [2003], to support their view.)

¹⁶Also unclear would be how to uphold the very distinction between what Carnap and Lewis called the analytic versus synthetic postulate of 𝒯 (i.e., τ- and o-sentences, respectively) if o-terms and τ-terms are sometimes co-referential, synonymous, or otherwise interdefinable.

¹⁷Lynch, Horwich, and others often take the principles of a theory of truth (𝒯: P ₁, … , P_n ) to be platitudes, where platitude picks out those claims that, inter alia, reflect the ordinary uses of terms in a given linguistic community. Yet, τ-terms have no such ordinary uses for platitudes to reflect, ex hypothesi. Therefore, τ-terms do not occur in platitudes. Platitude-talk therefore seems to instigate a dilemma. If platitudes are the constituents of 𝒯 and true is a τ-term, then true cannot occur in 𝒯 and so cannot be implicitly defined by Ramsification over it. But then, the only terms whose ordinary uses could be reflected by platitudes are o-terms; and so if true is instead an o-term, then it can occur in 𝒯. But then Ramsification would again become superfluous, since Ramsification is unnecessary for defining o-terms.

¹⁸I would like to thank Thomas Sattig, Michael Horton, and two anonymous referees for their constructive comments.