Abstract
According to alethic functionalism, truth is a generic alethic property related to lower level alethic properties through the manifestation relation. The manifestation relation is reflexive; thus, a proposition’s truth-manifesting property may be a lower level property or truth itself, depending on the subject matter properties of the proposition. A true proposition whose truth-manifesting property is truth itself, rather than a lower level alethic property, is plainly true. Alethic functionalism relies on plain truth to account for the truth of propositions with challenging subject matter properties, such as logically complex propositions and truth attributions. In this paper, it is argued that plain truth leads to a number of serious problems for alethic functionalism. First: Shapiro (in Analysis 71:38–44, 2011) argues that plain truth threatens alethic functionalism with collapse to strong alethic monism; it is argued here that collapse is not merely threatened, but that, on pain of contradiction, collapse is immediate. Second, alethic functionalism’s commitment to alethic pluralism requires lower level alethic properties to be ways of being truth, where one property’s being a way of being the other property is irreflexive; thus, alethic functionalism is incoherent due to the conflicting commitments to a manifestation relation which is both reflexive and irreflexive. Third, it is argued that a reflexive manifestation relation leads to the contradiction that a lower level alethic property which manifests truth is both identical to and distinct from truth itself. Fourth, careful examination of the notion of a core truism shows that Objectivity and the correspondence intuition are the only core truisms. Finally, it is argued that the first and fourth problems jointly entail a collapse of alethic functionalism to strong correspondence monism.
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Notes
Thus, for example, Lynch writes: “But such properties [as superwarrant] play the truth-role, if at all, only accidentally. That is, they may have the truish features, but only when they are possessed by atomic propositions of a certain domain” (Lynch 2009, p. 78).
Following recent convention, ‘\(\langle \hbox {p}\rangle \)’ abbreviates ‘The proposition that p’. The cases as well as the examples for each case are Lynch’s; see Lynch (2009). Lynch argues that true moral propositions have their truth manifested by a non-representational alethic property and proposes that concordance, a coherence-like property, is the truth-manifesting property for moral propositions; see Lynch (2009, Chap. 8).
Lynch (2009, pp. 90–91; 2013, Sect. 6). The problems posed to alethic functionalism by mixed compound propositions, i.e., logically complex propositions with multiple subject matter properties, and mixed inferences, i.e., inferences involving propositions with different subject matter properties, have received a fair amount of discussion; see Beall (2000), Connolly (2012), Cotnoir (2009), Edwards (2008, 2009), Lynch (2001, 2004, 2006, 2013), Pedersen (2006), Sher (2004, 2005, 2013), Tappolet (1997, 2000), and Wright (2005).
Pedersen and Wright formulate these theses in terms of sentences, rather than propositions. I formulate these theses in terms of propositions in order to accommodate Lynch, who takes propositions to be the primary bearers of truth; otherwise, I retain the formulations in Pedersen and Wright (2013a).
As above (Sect. 1), Lynch presents the scope problem as follows: “for any sufficiently robustly characterized truth property F, there appears to be some kind of propositions K which lack F but which are intuitively true (or capable of being true)” (Lynch 2009, p. 49). It may be pointed out (and I thank an anonymous referee for doing so) that Lynch may reply that the characterization of truth given by alethic functionalism is merely that truth is the property which has the truish features essentially, which is not sufficiently robust to flout the lesson of the scope problem. It is important to keep in mind that the essence of the scope problem is not the robustness of the alethic property or its characterization, but that no (sufficiently robustly characterized) alethic property seems suited to manifest truth for the complete range of true propositions, due to the wide variation in their subject matter properties. According to alethic functionalism, truth is manifested by a plurality of lower level alethic properties; and the lesson of the scope problem is that there is no single property bearing the manifestation relation to truth for all true propositions. Thus, if truth manifests truth for every true proposition, there is a single alethic property bearing the manifestation relation to truth for all true propositions, which flouts the lesson of the scope problem.
Shapiro also writes that “This would be to give up on functionalism” (Shapiro 2011, p. 40). As I understand it, this would not require giving up on functionalism about truth, though it would require giving up on pluralism about truth, as Shapiro points out.
A reflexive relation is a relation, R, on a set, S, such that every element, x, of S bears R to itself (Cf. Gamut 1991, p. 110). It is still possible for elements in the set to bear R to other objects. For example, the relation of being less than or equal to (\(\le \)) is a reflexive relation on the set of real numbers (as well as any set of numbers). The having-the-same-height-as relation is reflexive on the set of objects, H, which are exactly 200 cm tall. Each element of H is such that it bears R to itself and to the other elements of H. (The having-the-same-height-as relation is also symmetric.) Plain truth requires that manifestation be a reflexive relation so that both truth and lower level alethic properties may manifest truth.
It may be wondered whether alethic functionalism could instead include a manifestation relation for which truth manifests itself but which is such that not all other properties self-manifest. That is, it might be wondered whether alethic functionalism might adopt a non-reflexive manifestation relation. Note that since a reflexive relation is a relation, R, on a set, S, such that every element of S bears R to itself, and an irreflexive relation is a relation such that no element of S bears R to itself, reflexive and irreflexive relations are not jointly exhaustive. For example, the relation of liking is a non-reflexive relation on the set of people. The manifestation relation is a formalization of the is-a-way-of-being relation, and is the basis for maintaining that lower level properties which manifest truth are genuine alethic properties. As formulated by Lynch, the manifestation relation justifies the claim that properties manifesting truth are alethic properties, since the manifesting properties have the conceptually essential features of the immanent property. Although it may be technically feasible for alethic functionalism to include a non-reflexive manifestation relation, such a relation would very likely not justify the claim that properties manifesting truth are alethic properties. I thank an anonymous referee for calling this option to my attention.
Lynch (2013, p. 31). This is a clarification of the definition in Lynch (2009), where the manifestation relation is introduced as follows: “Let us say that where property F is immanent in or manifested by property M, it is a priori that F’s essential features are a subset of M’s features” (Lynch 2009, p. 74; Lynch’s italics). Also, it should be pointed out that ‘just when’ may be read as ‘only if’, rather than ‘if and only if’, in which case the quoted sentence gives a necessary condition for manifestation, rather than a definition. In fact, since a lower level alethic property is supposed to manifest truth only for propositions having an appropriate subject matter property, there is a good reason to read the quoted sentence as giving only a necessary condition of manifestation. The definition of the manifestation relation including these two necessary and jointly sufficient conditions is discussed and argued to be problematic below, in Sect. 4.
Strictly speaking, the definition of ‘manifestation’ is ambiguous; that is, it may also be read such that if F has no conceptually essential features, it follows trivially that every property manifests F. Given that the manifestation relation is the relation through which truth is one and many, it seems to suit alethic functionalism better that manifestation requires that the immanent property have conceptually essential features. Because truth has conceptually essential features, and also because manifestation is reflexive on either reading, this ambiguity does not affect this discussion.
One alternative is to redefine the manifestation relation as follows: M manifests an immanent property F just when (i) it is a priori that F’s conceptually essential features are a subset of M’s features; and (ii) the subject matter properties (including logical complexity) of the proposition which has M are the appropriate subject matter properties for M. However, this redefinition of the manifestation relation is problematic for several reasons, discussed below, in Sect. 4.
The resulting theory is similar in some respects to Lynch’s earlier functionalist theories of truth, e.g., Lynch 2001, but there are some significant differences. For instance, Lynch’s earlier view is a version of identity functionalism, while the resulting theory is a version of specifier functionalism; cf. David (2011, p. 746; 2013, pp. 43, 61).
Another option is to redefine the manifestation relation as follows: M manifests an immanent property F just when (i) it is a priori that F’s conceptually essential features are a subset of M’s features; and (ii) the subject matter properties (including logical complexity) of the proposition which has M are the appropriate subject matter properties for M. This redefinition of the manifestation relation is problematic for several reasons, discussed below, in Sect. 4.
In other work on the problem of mixed compound propositions, Edwards proposes as an independent solution that logically complex propositions are subsumed by the domain of discourse which has logic as its subject matter property, and that the logical domain has its own lower level truth-determining property: “When we talk about the relationship between a compound and its components, it is plausible to think that we are operating within the domain of logical discourse: it is the appropriate logical rules which dictate the correct relationships. Thinking along alethic pluralist lines, the truth property here will be whatever property it is that is identified with truth in the logical domain. It is this property that a conjunction has when both of its conjuncts are true, and that a disjunction has when one or more of its disjuncts are true” (Edwards 2009, p. 686). As above, the domain-specific properties, F, are related to truth through biconditionals of the form: In domain of discourse x, \(\langle \hbox {p}\rangle \) is true (has the property truth) iff \(\langle \hbox {p}\rangle \) has property F. Here, simple determination pluralism faces a dilemma as to whether there is an explanation as to why a truth-determining property determines truth for propositions in a given domain. If there is no explanation at all as to why a truth-determining property determines truth for propositions in a given domain, then the assignment of a truth-determining property is arbitrary, and the theory is unsatisfactory. In this respect, truth seems to be disanalogous to winning, if what constitutes winning may be stipulated arbitrarily. On the other hand, suppose that there is an explanation as to why a certain truth-determining property determines truth for propositions in a given domain, and that domains of discourse are distinguished according to subject matter properties, as Edwards holds. This option is not unfriendly to simple determination pluralism. For example, Edwards writes, “if a domain is deemed to deal in genuinely representational content, it is likely that a property like correspondence will be the truth-determining property for that domain” (Edwards 2013, p. 117). However, this strategy raises the very same problems which plain truth raises for Lynch. Since the component propositions of a logically complex proposition may have any subject matter property and may themselves be logically complex, stipulating that there is a lower level property which determines truth for propositions in the logical domain identifies a lower level property which determines truth for propositions of every subject matter property and logical form, and therefore poses the same threat of collapse to strong alethic monism which alethic functionalism faces by adopting plain truth. That is, since that property determines truth for the logical domain, and the logical domain contains logically complex propositions whose component propositions belong to every domain of discourse, the truth-determining property for the logical domain is an excellent candidate for determining truth in all domains of discourse, which threatens a collapse to strong alethic monism.
In a later paper on simple determination pluralism, Edwards writes, “Truth is given as the property that is exhaustively described by the truth platitudes” (Edwards 2013, p. 118).
Following the passage quoted just above, Edwards writes, “While, according to simple determination pluralism, these properties are essential in the story about why a proposition is true, they are not identical to the truth property itself, nor do they manifest the truth property” (Edwards 2011, p. 45). Here Edwards seems to recognize this point; yet he also presents simple determination pluralism as a version of alethic pluralism. This is an equivocation on ‘alethic’. For Lynch, the manifestation relation is designed to justify the claim that truth is both one and many, i.e., that the lower level properties are alethic properties, since the truth-manifesting properties have the conceptually essential features of the immanent property, truth. However, it is not sufficient to support this claim that there be some relation holding between truth and the lower level properties. If the relation holding between truth and the lower level properties is merely a resemblance or similarity relation, then the lower level properties are not alethic properties in this same sense of ‘alethic’. On simple determination pluralism, a lower level property determines truth for propositions in a suitable domain of discourse, but the lower level properties are not themselves alethic properties. It may be suggested that the lower level properties are alethic properties, since they satisfy restricted versions of the unrestricted platitudes satisfied by truth for their domains of discourse (Cf. Pedersen and Wright 2013b, p. 92). However, this yields only resemblance or similarity relations.
I thank an anonymous referee for pressing me to discuss this option.
Two additional strategies are available, but very unpromising. One is to allow that there are as many lower level alethic properties as there are combinations of subject matter properties. See Lynch (2013, Sect. 6), Cotnoir (2013), and Shapiro (2011) for discussion. Another is to assign truth-manifesting properties based upon some property of a proposition other than subject matter properties.
As above, Lynch claims that a lower level alethic property manifests truth only for propositions having appropriate subject matter properties, though this condition is not included in the definition of the manifestation relation. A redefined manifestation relation is discussed below, in Sect. 4, according to which M manifests an immanent property F just when (i) it is a priori that F’s conceptually essential features are a subset of M’s features; and (ii) the subject matter properties (including logical complexity) of the proposition which has M are the appropriate subject matter properties for M.
Generally, a property space may have any integral number of dimensions, n, and a determinate may occupy k dimensions, 1 \(\le \) k \(\le \) n.
In fact, the irreflexivity of the determinable-determinate relation is one of the goals of Funkhouser’s analysis, and is a stated criterion of its success; cf. Funkhouser (2006, p. 549). There is a broader sense of ‘way’ in which an object or property or any thing is a way of being itself. The sense of ‘way’ employed here is narrower, such that the is-a-way-of-being relation is irreflexive.
For some related discussion, see Wright (2013, pp. 141–145).
As a quick aside, it should be pointed out that if Lynch’s argument is that truth is the appropriate truth-manifesting property for a truth attribution because a truth attribution is a predication of truth, his reasoning contains a non sequitur.
Note that Lynch’s weak grounding principle (Lynch 2009, p. 90; 2013, p. 34) applies only to compound propositions, and so does not explain the truth of true truth attributions, which are atomic propositions. Note also that it is not feasible to adopt what Lynch calls “the inheritance view” according to which “Truth attributions are true in the same way as the proposition to which truth is ascribed” (Lynch 2013, p. 35). Lynch gives two reasons there why not. In my estimation, the more important reason is that “the inheritance view is hopeless in the [sic] generalizations like
(3) Everything Stewart says is true.” (Lynch 2013, p. 35)
since Stewart may express propositions having many different subject matter properties.
I also presume that a material biconditional cannot be explanatory, since a material biconditional is symmetric, while explanation is asymmetric. Even if there are exceptions to this presumption, Objectivity seems not to be one of them.
Since the truisms are supposed to be folk beliefs, which need only be tacit beliefs or rational commitments, Lynch’s formulation of the correspondence intuition, quoted above, may better capture a folk belief; but for the sake of providing an explanation as to why true truth attributions are true, CI better serves the purposes of alethic functionalism. Also, note that CI is a schema; it should be instantiated only for sentences expressing a proposition which is true with respect to the context of utterance. If it is important that the truisms be propositions, CI should be replaced with CI*,
$$\begin{aligned} \text {CI}^{*} \qquad \forall \hbox {S}\; [\text {If}\;\langle \hbox {S}\rangle \text {is true}, \langle \hbox {S}\rangle \;\text {is true because S}.] \end{aligned}$$where ‘S’ is a substitutional variable.
Lynch argues that true moral propositions have their truth manifested by a non-representational alethic property and proposes that concordance, a coherence-like property, is the truth-manifesting property for moral propositions; see Lynch (2009, Chap. 8).
Lynch writes, “Such a property will have the features described by the core truisms. Features of this sort could obviously be called core features. But in the present case we might as well call them the ‘truish features”’ (Lynch 2013, p. 25).
This may also raise the question as to why there is a special group of truisms: why aren’t all of the truisms involved in the definition of truth and the manifestation relation? Very briefly, there is the risk that truisms may vary among people or over time, in which case there is no single concept or property of truth. Appeal to a set of truisms which do not vary, i.e., the core truisms, avoids this problem. See Wright (2005, especially Sect. 4.3) and Lynch (2005) for an exchange on this and a few other pertinent issues.
Lynch writes that “It is worth emphasizing that one can grant that there are core truisms about truth and still hold that there can be some debate amongst philosophers about which principles those are. The fact that the folk have a—largely implicit—conception of some property does not imply that there will be universal agreement amongst theoreticians as to how best to characterize or capture that conception. Thus in order to accept the general picture, whether a principle counts as a core truism needn’t be settled (nor, given the amount of folk beliefs we have about truth, can we reasonably expect it to be always settled)” (Lynch 2009, p. 16; Lynch’s italics).
See Lynch (2005, Sect. 3) for some related discussion.
Note that this understanding of the core truisms captures Lynch’s remark that to deny many or all of the core truisms would justify others in taking the denier to be changing the subject. In fact, if the core truisms describe conceptually essential features of truth, denying any one of them would justify others in taking the denier to be changing the subject.
It is worth noting that, depending on one’s view of propositions, it is possible for there to be true propositions without there being beliefs or inquiry, in which case Norm of Belief and End of Inquiry are not conceptually essential because they are not essential.
I thank an anonymous referee for pressing me to discuss this point.
The locus classicus is Quine (1970, especially pp. 10–13).
A proposition, p, is concordant if and only if the belief of p is warranted without defeat at some stage of inquiry, the belief of p would remain so at every stage of inquiry, and where the belief of p is warranted just when that belief is a member of a system of beliefs which exemplifies mutual relations of deductive and inductive support, simplicity, predictive power, completeness, and consistency, and where that system is grounded. Concordance without the requirement that the system be grounded is supercoherence; cf. Lynch (2009, Chap. 8).
See also Newhard (2013, Sect. 2).
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Acknowledgments
I would like to thank Douglas Edwards for a helpful exchange, and Michael Lynch for several helpful and congenial conversations about the issues discussed in this paper. I would also like to thank the anonymous referees for this journal for many helpful suggestions which significantly improved the paper, especially one whose efforts were exceptionally conscientious.
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Newhard, J. Plain truth and the incoherence of alethic functionalism. Synthese 194, 1591–1611 (2017). https://doi.org/10.1007/s11229-015-1006-8
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DOI: https://doi.org/10.1007/s11229-015-1006-8