Truth (bearers) pluralism

Think of the tools in a tool-box: there is a hammer, pliers, a saw, a screwdriver, a rule, a glue-pot, nails and screws. - The function of words are as diverse as the functions of these objects.

Wittgenstein, L. (1953, §11, p. 9e).

Abstract

As for many other properties, to understand the nature of truth attention should be paid to the kind of entities that are apt to bear it. In particular, I argue that different kinds of truth bearers tend to support different properties of truth. After that, I show that there are reasons to admit a plurality of truth bearers. As a consequence of these two results, a plurality of truth properties may be naturally admitted. The general upshot of the paper is a new way to motivate alethic pluralism, which stems from considerations on the nature of representations rather than from considerations on what is represented. This new version of truth pluralism—truth (bearers) pluralism—is shown to be theoretically fertile and promising against some standard criticisms.

1 Introduction

If truth is a property, one can wonder what kind of entities are apt to bear it. Different candidates have been considered and assumed over the years, including propositions in different guises, sentences, utterances, beliefs, and assertions, among others. Sometimes the choice of one kind of truth bearer is done at the expense of the others. Other times a more tolerant attitude is adopted by giving a privileged role to one kind—the primary bearer—and somehow reducing truth ascriptions to other bearers to ascriptions to the fundamental one.¹ While the choice of a truth bearer sometimes goes unstressed and the role it plays in a theory of truth might look secondary, its importance should not be neglected.² One reason is that truth bearers can be relevant to determine a conception of truth. Even if a certain truth conception is not entirely dictated by the choice of truth bearers, it is certainly constrained by it. A second reason is that theories developed for different truth bearers need not be in competition, since they just describe properties of different sorts of entities. For example, what truth is for propositions could well be different from what truth is for utterances. In principle, the two views could be both correct without conflict. As David writes: “The standard segregation of theories into competing camps (found in textbooks, dictionaries, and handbooks) often proceeds under the assumption -really a pretense- that they are intended for the same sorts of truth-bearer taken as primary.”³

In this paper I elaborate on these ideas and propose a version of pluralism about the property of truth that stems from the admission of different kinds of primary truth bearers. On the one hand, I show that the resulting view of truth (bearers) pluralism is an interesting new option to articulate alethic pluralism. An option that has been unfortunately neglected, or at least not explicitly formulated so far. On the other hand, I argue that it can be supported by various considerations, making it not just an interesting theoretical possibility, but also a potential contender. Truth (bearers) pluralism makes it also easier to counteract certain criticisms raised against alethic pluralism in recent years.⁴

The paper goes as follows. In the next section 2, and its several subsections, I review some of the main truth bearers enlightening what truth property they tend to support or rule out. Next, in Sect. 3, I discuss two ways of arriving at pluralism about truth, namely from what our discourses are about, and from the semantic nature of those very discourses. In Sect. 4, articulating the latter idea, I argue that there are reasons to admit a plurality of truth bearers. In particular, I show how a scope problem, usually motivating truth pluralism, also afflicts truth bearers and can motivate a similar pluralism. Once a plurality of truth bearers is in play, given the results of Sect. 3, also a plurality of truth properties is naturally admitted. In Sect. 5, some of the consequences of truth (bearers) pluralism are discussed. I then conclude the paper.

2 Truth bearers and truth properties

If we are interested in understanding what a certain property is, an important initial step is that of figuring out what its bearers are and what they are like. This seems a reasonable way to proceed for many, mutually related reasons. First of all, different kinds of entities are apt to have different kinds of properties. A family does not have the same kind of properties of a river or a number. Second, since the nature of the bearer can impose constraints on what its properties can be, taking the bearer into account helps determine what such properties must be like. For example, since a river occupies space, at least some of its properties will probably be related to its spatial configuration and geographical position. Third, the bearer might have such a specific nature that the relevant property might be almost entirely dictated by the bearer itself. Clearly, this does not mean that we should expect an investigation on a property to entirely resolve into an investigation of its bearers. Many other considerations can easily exceed such an inquiry. However, deliberately ignoring the part of the story concerning the bearers seems an unwise move. Similarly, it can well be admitted that in certain cases focusing on the bearers might be irrelevant. If a property is universally instantiable, like self-identity, there would be little pressure, if any at all, to address what its bearers are. Whatever they are, self-identity applies. For many properties (and relations), however, this is not the case. They go only with a specific kind of bearer and ascribing them to other sorts of entities would result in falsities or in lack of truth value, due to category mistakes or metaphorical talks. For example, colors apply to perceivable objects and decomposition in prime numbers apply to natural numbers. Such ascriptions cannot be exchanged, since numbers do not have colors and perceivable objects are not decomposable in prime numbers.

Let us now focus on the property of truth. What sort of entities are apt to be true? Answering this question means establishing what the (primary) bearers of truth are. Different candidates have been put forward and different views about them have been discussed. The main ones, on which we may restrict our attention here, are propositions and sentences.⁵ Let me briefly review these candidates displaying their main virtues and drawbacks. Since the following is quite common philosophical knowledge, I will limit myself to a quick reminder of some key points, assuming that the reader is familiar with the matter. In addition and more interestingly, however, I will also argue that each kind of truth bearer leads to, or at least naturally supports, a certain conception of truth. Before proceeding, a preliminary caveat on this last point is in order. To determine truth properties, alethic pluralists usually resort to platitudes about truth.⁶ If a property validates such platitudes in a certain area of discourse, the property is considered a truth property in that area. Although this approach implicitly relies on a unique kind of truth bearers, I assume that the truth platitudes are quite independent of the choice of truth bearers and could be generalized to a good extent. Accordingly, for different truth bearers, (generalized) platitudes could help determine what truth property they are suited for. In any case, truth platitudes will play virtually no role in what follows, and can be considered as a mere implicit background to be invoked if needed.

2.1 Sentences and truth

According to a crude purely syntactic view, sentences can be characterized as sequences of words combined according to particular grammatical rules. Sentences are then understood as merely syntactic objects devoid of any meaning, avoiding any appeal to propositions. This is the usual approach towards sentences found in formal languages studied by logicians, or in generative grammar.⁷ Since words and grammar are relative to a language, sentences also depend on a language. Sentences have, as truth bearers, several virtues. In particular, they are familiar entities involved in our ordinary use of natural language and they have a clear and precisely defined structure. Such a determined syntactic structure is what makes sentences the default choice, for example, in formal theories of truth.⁸ Sentences, however, are usually understood as syntactic types, which make them abstract objects, and thus philosophically potentially problematic. Moreover, outside of a purely formal setting, sentences usually require a specific context of utterance in order to yield all necessary elements to determine a truth value. These two considerations can lead to favor utterances, namely specific tokens of sentence types in certain contexts. For simplicity, however, I focus on sentence types here.

As truth bearers, sentences characterized in purely syntactical terms can be criticized for simply missing the boat. After all, a sentence seems to be true in virtue of what it means, not as a mere sequence of symbols.⁹ If a sentence is claimed to be true, it is hard to resist the idea that it is what is expressed by the sentence that is true, whereas the sentence itself is the mere vehicle for a truth-apt content. The objection can be reinforced by noting that the same truths can be expressed in different languages, and thus by different sentences. These considerations may eventually lead to favor propositions, rather than sentences, as primary truth bearers.¹⁰

Before reviewing propositions, let us consider what conceptions of truth easily go with sentences. Prima facie, it might look as if no particular view about truth were dictated by sentences, so that almost any conception of truth could be associated with it. However, if the mere syntactic aspect is stressed, some truth theories suggest themselves. It would be convenient, in particular, if a property of truth could be extracted by the purely syntactic properties of sentences. This seems a hard challenge, since truth (and falsity) might be intuitively related to the representational features of truth bearers. Lacking meaning, pure syntactic sentences seem unable to bear truth, if not indirectly. This prejudice, however, is probably due to a representationalist and even a realist bias. If we get rid of such biases, it is easy to see that the mere syntactic profile of sentences can provide a natural support for an anti-realist conception of truth. Indeed, an anti-realist,¹¹ willing to avoid any troublesome engagement with a mind-independent reality, would be eager to find a conception of truth emerging from the purely syntactic features of truth bearers. If sentences are truth bearers, the problem of the entities sentential truths are about would evaporate. If truth could be grounded in purely syntactic features of sentences, extra-linguistic truth makers would be easier to avoid. From such an anti-realist perspective, a coherentist conception of truth seems an attractive option. For example, if truth is coherence, and coherence is understood as lack of contradiction, then syntax could be enough to characterize truth.¹² Analogously, if coherence is accounted for in terms of logical derivability, a logical calculus and a proof-theoretic approach could do the job. Note that in this sense both contradictions and derivations should be characterized in a purely syntactic way. A contradiction, for example, would be a sentence of a certain form (e.g. a conjunction of a sentence with its negation, where conjunction and negation are understood in syntactic terms), and a logical derivation would be the result of certain manipulations of symbols.¹³ The difficulty of operating such manipulations without appealing to the meaning of the symbols involved could be tackled by adopting an inferential semantics denying priority to representational considerations, or pointing to a formalistic account (at least in mathematics), in which meaning is unnecessary.¹⁴

It is worth stressing that I am not claiming that if sentences are truth bearers, then truth must consist in coherence. Similarly, I am not saying that a coherentist or an anti-realist should opt for sentences.¹⁵ Rather, the point is that sentences as truth bearers and truth as coherence are options that seem to fit particularly well together, yielding an apparently convenient package. If sentences are truth bearers, a coherentist view may have an easier life, regardless of other issues that may keep afflicting it. The situation will be similar for other truth bearers.

Although sentences are particularly well suited to support a coherentist view, other conceptions of truth could be adopted. For example, a deflationary one, in particular in the form of Quine’s disquotationalism, may be another viable option.¹⁶ However, some alternative views might be in tension with the merely syntactic dimension associated with sentences. Consider a Tarskian compositional theory of truth, for example. Apparently, a Tarskian theory is another option that could take advantage of the precise syntactic structure of sentences. When atomic sentences are considered, however, semantic notions (such as reference of individual constants and interpretation of predicates) are required. Once semantic considerations are in play, we seem to depart from a purely syntactic understanding of truth bearers.¹⁷ A similar problem emerges for realist theories like correspondence theories. In these views the relation between language and reality plays a crucial role to articulate the match between the truth bearers and the portion of reality that constitutes truth. Such meaning relations may water down the purely syntactic nature of sentences, pointing to interpreted sentences or even propositions.

2.2 Propositions and truth

Given the difficulties posed by merely syntactic objects, let us consider meaningful ones such as propositions. Propositions are usually understood as the content expressed by (typically declarative) sentences (possibly after the specification of contextual information), and corresponding to that-clauses. Propositions are also often considered the objects of beliefs and other mental attitudes.¹⁸ Since the same proposition can be expressed by sentences of different languages, it is also usually taken to be language independent. The most basic reason to favor propositions as truth bearers is that truth seems to be a property of what is said, rather than the result of a merely syntactic business. However, although propositions are the natural candidate for truth bearers, and they are often considered the obvious choice, they are not unproblematic. The main difficulty is understanding what propositions are. This complication constitutes the main disadvantage with respect to sentences. Many different accounts of propositions have been proposed, diverging on crucial issues such as, for instance, whether propositions are structured or not. For present purposes and the sake of brevity, I restrict attention to three main proposals: a deflationary, a Russellian and a Fregean account.

2.3 Deflationary propositions

A minimalist account of propositions is a minimally committed and possibly deflationary one. According to this view a proposition is whatever entity corresponds to what is expressed by a that-clause.¹⁹ Beside that, the view refrains from saying more and specifying what the nature of such entities is. The idea is that a minimal understanding of propositions is enough for various purposes and in particular for developing a theory of truth.²⁰ This minimally committed view could be turned into a full fledged deflationary account of propositions by explicitly holding that there is no more to propositions than that. The metaphysical nature of propositions would indeed be quite shallow.²¹ This metaphysical lightness of propositions could be further specified by extending Lewis’ distinction between sparse and abundant properties to propositions. Sparse properties are those corresponding to objective similarities and playing causal-explanatory roles, whereas abundant properties correspond to any predicate whatsoever, irrespective of being joint-carving or not.²² A deflationary conception of propositions can apply this distinction to propositions understanding them as 0-place relations and holding that propositions are merely abundant.²³ Propositions would correspond to that-clauses applied to declarative sentences whatsoever, without any need to posit a substantial common nature. Such a substantial nature would indeed be excluded. Propositions would be the mere by-product of linguistic constructions that are useful for certain expressive functions but lack serious metaphysical significance.²⁴

What conception of truth is naturally supported by such a deflationary view of propositions? Given the abundance of propositions, that-clauses would not capture a substantial class of entities. Hence, if the bearers of truth are understood in a deflationary and abundant way, it is natural to expect that many of their properties would also turn out to be similarly abundant. The property of truth, in particular, can be naturally held to be an insubstantial and abundant property of such abundant propositions. After all, if truth was a robust property, it would be at least puzzling if it characterized insubstantial bearers. If truth were substantial, then at least true propositions would form a uniform sparse class of entities. Consequently, if a deflationary view of truth is to be defended (according to which a truth predicate is to be admitted only for expressive purposes and the property attached to it is a mere by-product of grammar with no metaphysical substantial import), then a deflationary account of propositions seem to fit the project nicely. Again, I am not claiming that the combination of a deflationary view of propositions and deflationary truth is mandatory, since other conceptions of truth could be viable. Nonetheless the two are apparently very well suited to go together.²⁵

2.4 Russellian propositions

Let us now consider a Russellian account of propositions. Although Russell changed his ideas on propositions and judgments several times, we focus here on the view customarily associated with him and usually contrasted with the Fregean view. Both Russell and Frege held that propositions have a substantial nature and, in particular, are structured entities. They are the result of the combination of simpler constituents. The main point of disagreement is what such constituents are. Russell writes: “Whatever may be an object of thought, or may occur in any true or false proposition …I call a term….A man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned, is sure to be a term; and to deny that such and such a thing is a term must always be false.”²⁶ For Russell, the reference of singular terms, even if they are concrete entities like men or mountains, enters the constitution of a proposition. It is perhaps worth mentioning that Russell draws a distinction between naming and denoting expressions. In particular, ordinary names of natural language may not be logically proper names, but a sort of description in disguise, and thus being denoting rather than naming expressions.²⁷ This idea is related to Russell principle of acquaintance, which leads him to consider as genuinely logical names only those standing for certain entities (sense data, universals, relations, oneself). In a strict sense, these are the only constituents of the propositions that we can grasp. On a more relaxed approach, adopted for example by Neo-Russellians, proper names in natural language are also considered genuinely naming expressions, and concrete individuals enter a proposition as constituents.²⁸ Russell himself sometimes also admits such a case with, for example, the striking case of the Mont blanc.²⁹ Once such a reading, on which I focus here, is adopted, a Russellian proposition is identified with the result of the combination of real-world objects, properties and relations.³⁰ Russellian propositions and worldly facts then apparently have the same constituents. The problem of how such elements are taken together in a proposition, the so-called problem of the unity of the proposition, troubled Russell for years. According to an early account, the constituents of a proposition are taken together in the same way in which they are taken together in a fact. The notion of fact is indeed secondary at that point, while that of proposition is the fundamental one, for propositions “are called facts when they happen to be true”.³¹ This approach to the unity of propositions seems to immediately pose a problem for falsity, though. Since also false propositions have some unity, and apparently there cannot be false facts, it is not clear what a false proposition is. These sorts of problems led Russell to abandon his early view and eventually opt for a multi-place relational account of judgements, in which propositions no longer figure.³² Judgements and facts can then share some of the constituents while avoiding the problem of unity. By facilitating a distinction between truth bearers and facts, truth bearers such as judgements, beliefs and sentences also allow to treat a fact as what makes something true, paving the way to a correspondence theory of truth.³³ Russellian early view of propositions, however, has been somehow recovered by Neo-Russellians.³⁴ Since reconstructing the exact evolution of Russell’s thought is not the goal of this paper, for the sake of the argument, henceforth I put such complications aside and assume a Russellian view of propositions in its crude and typical form. Later, however, I will suggest how a pluralistic conception of propositions could help solve the problem of falsity.

So understood, Russellian propositions seem to provide the most straightforward answer to the question of what theory of truth certain truth bearers are well suited to support. Russellian true propositions just seem to be worldly facts, so that they drag us to an identity theory of truth.³⁵ Given the nature of Russellian propositions, being true is being identical to a fact.³⁶ This is indeed a well known case, which provides a clear example of a conception of truth bearers basically imposing a specific conception of truth.³⁷ The connection apparently holds, in an even stricter way, also in the other direction, since an identity theory of truth seems to require an account of truth bearers along Russell lines. If truth is being identical to a fact, what is true must be the same entity that is a fact.

2.5 Fregean propositions

Similarly to Russellian propositions, also Fregean propositions are structured entities, but their components are different. As is well known, Frege held that, for each expression, two dimensions of meaning should be distinguished. The level of reference, namely the entities for which the expression stands and that directly contribute to determining a truth value, and the level of sense, which is, roughly, the mode of presentation of reference. Unlike Russell, Frege takes propositions to be composed by senses, rather than references. A proposition is typically expressed by a declarative sentence³⁸ and it results from the combination of the various senses of the expressions composing the sentence. Since senses are abstract, also the resulting proposition is abstract. Notably, an expression must have a sense but it might lack a reference. For example, the name “Pegasus” has no reference, since Pegasus does not exist, but it has a sense which might be rendered somehow with the description “a winged horse”. The possible discrepancy between the level of reference and the level of sense is what prevents the problem of falsity met with Russellian propositions to arise. Propositions so conceived, or thoughts (Gedanken in German) as Frege calls them, are the bearers of truth.

Although this hasty reminder of Fregean propositions is certainly unable to do justice to Frege’s view, it should be enough for our purposes. In particular, given the separation of the levels of sense and reference, and the claim that propositions are structured senses, the view seems to rule out an identity theory of truth, for which a true proposition is identical with a fact. It would be more natural to think of truth as a kind of match between the descriptive level of proposition and the worldly level of reference. This might lead to some form of correspondence theory of truth. However, a Fregean view seems well suited to support other conceptions of truth as well. Frege himself favored a different conception, arguing against a correspondence theory of truth.³⁹ Primitivists and deflationary views seem viable options too.⁴⁰ Since Fregean propositions look compatible with a wider range of choices, they might somehow vindicate the impression that the role of truth bearers is not decisive in determining a conception of truth in a good number of cases. Note, however, that further constraints might come from reflections on the senses themselves. If there were different possible accounts of the nature of senses and, consequently, different kinds of Fregean propositions, also different conceptions of truth might be implied. This option is discussed below.

3 Two roads to truth pluralism

The quick survey above has shown that the choice of a certain kind of truth bearer can influence the resulting conception of truth. Some options have a stronger impact, almost determining what truth should be like, others just favor some views. In any case, different truth bearers are best suited to be combined with different truth properties. This means that if a pluralistic view of primary truth bearers were adopted, also pluralism about truth could be supported. The multiplicity of kinds of truth bearers would lead to a multiplicity of ways of being true. The crucial question then is whether there are reasons to admit more than one kind of primary truth bearers. In this and the following section, I argue that there are.

First of all, we should note that truth pluralism has often been motivated by considerations on differences among the subject matter of various domains of discourse. The idea is that different areas of discourse concern different things, whose nature requires different truth properties. Consider, as a toy example, discourse about middle-size concrete objects like tables and chairs. Intuitively, these physical objects present themself as mind-independent entities of an external reality. When we try to represent such entities we can match the way they are or not. If there is a match, the representation is true, otherwise it is false (or not true). From this naive idea, it takes just a further step to claim that truth consists exactly in the match between a truth bearer and the middle-size concrete objects it represents. Namely, truth consists in correspondence between representation and reality. This natural train of thoughts, however, is problematic for discourses concerning subject matters such as arithmetics, ethics or taste.⁴¹ If also arithmetical truth consisted in correspondence to mind-independent facts, we would be dragged to platonism about numbers. While not an absurd view, mathematical realism may be less appealing than realism about physical objects. After all, in mathematics and other areas, discourses do not seem appropriately causally responsive in the way a representationalist view of truth as correspondence may require, since numbers presumably are not objects with which we can causally interact.⁴² Here, however, is where truth pluralists make their move: if numbers conflict with truth as correspondence, the worst for a correspondence view in arithmetical discourse. Physical truths and arithmetical truths can be just true in different ways. This sort of considerations paves the way to a pluralist view about truth. Of course, since mathematical platonism and other forms of realism are nonetheless legitimate theoretical options, such an argument for truth pluralism (and similarly for truth bearers pluralism) is not a conclusive argument per se. The force of the argument is that it has an initial appeal (at least to some) and it provides a theoretical option that was otherwise neglected. Namely a way to keep a realist conception of truth and metaphysics in some area without being dragged to a global realism.⁴³

Similar reasoning can be replicated in other areas of discourse for other truth properties. The crucial point to observe is that pluralism about truth is motivated by differences among the entities the various discourses are about. Entities of various sorts call for truth properties of different kinds.⁴⁴ The overall picture emerging from such considerations is then the following. We have one kind of truth bearers in all domains, for example a certain kind of propositions, which is apt to bear different properties of truth in different domains of discourse, because such discourses are about entities with different natures.⁴⁵ We have uniformity and monism at the level of truth bearers but a plurality of truth properties as a result of the metaphysical and ontological differences of truth makers.⁴⁶

Beside such a familiar metaphysical and ontological route to truth pluralism, a different motivation can be obtained moving from differences among the kinds of representations involved in different domains, rather than from differences among what is represented. From semantics, rather than metaphysics. Truth pluralism may be the result not of the variety of reality, but of the variety of our language and thought. As an example, take moral discourse. Two main positions rival each other with respect to the semantics of moral discourse. On the one hand, we have a cognitivist view for which moral claims have a descriptive content that represents certain facts and express beliefs. On the other hand, we have an anti-cognitivist view for which moral claims do not have a descriptive content but an expressive and normative function, so that they do not represent facts and do not express beliefs. Non-cognitivism usually holds that the non descriptive profile of moral discourse also implies that moral claims lack a truth value. However, not all non-cognitivists agree on that.⁴⁷ Blackburn, for example, proposed a form of moral expressivism combined with a deflationary conception of truth, in the form of quasi-realism.⁴⁸ One main motivation for such a move is that of solving some issues affecting a non-cognitivist view, like the Frege-Geach problem, without renouncing the non-cognitivist nature of moral discourse. By applying equally across the board, deflationary truth is argued to vindicate the validity of certain valid inferences involving moral terms, which seem otherwise hardly treatable in a non-cognitivist approach.⁴⁹ If ethical expressivism and quasi-realism is accepted, what about discourse in other areas? A possibility is that of extending non-cognitivism and a deflationary conception of truth to all kinds of discourses. This, however, would clearly be an overreaction. Non-cognitivism about concrete objects, for example, is less appealing and unnecessary. Discourse about middle-size concrete objects can be nicely accounted for in a cognitivist way, possibly supporting a substantive theory of truth. The apparent discrepancy between the (meta)semantics of moral and concrete objects discourse might look like a dilemma from a truth monist perspective. A truth pluralist, however, has a prompt solution to it: different (meta)semantics just require different truth properties. We might well have two kinds of discourse, a cognitive and a non-cognitive one, with different ways of representing and thus apt to different ways of being true. The crucial point in this approach is that the plurality of truth properties is no longer obtained from considerations on the metaphysical nature of the entities our discourses are about. Rather, it is motivated by the variegated semantic nature of the discourses themselves, independently of the underlying metaphysics of their subject matter. Of course, this does not mean that a certain semantics does not have a metaphysical side. If, for example, ethical non-cognitivism is embraced, realism about moral facts becomes a pointless option. However, truth pluralism would not be derived from such metaphysical considerations. Indeed, even if there were mind-independent moral facts, as long as ethical discourse does not describe such facts but, for example, just express our moral attitudes, truth pluralism could still be motivated. In such a scenario, a realist conception of truth, like a correspondence theory, would be misplaced not because moral claims would lack a reality to which correspond, but because they would not be apt to correspond at all.

A second, less developed example of a semantic route to truth pluralism may come from studies on lexical competence. It has been argued that lexical competence is to be characterized by two different kinds of abilities, a referential and an inferential one.⁵⁰ The former is basically the capacity of applying a word to a world item and to recover the word when exposed to that item. Referential competence is needed, for example, to successfully follow an instruction like “fetch me a spoon” or to be able to name a cat “cat” when presented one. It is a language-world relation. The latter—the inferential one—is instead the ability to connect a word with other words. For example, to infer “this is an animal” from “this is a cat”. It is a language-language relation. Some results on cognitive neuroscience and neuropsychology seem not only to support such a distinction but also to show that the two kinds of competence are to a large extent independent, as one could lose one ability but not the other as a consequence of a local brain damage. Such a twofold account of lexical competence may then naturally lead to a twofold account of word semantics.⁵¹ Accordingly, the two kinds of lexical competence might be taken to correspond to two kinds of elements determining the correct use of a word. We have correct uses determined by intralinguistic relations with other words, and we have correct uses determined by the relations with extralinguistic items. What is particularly relevant for our purposes is that although mastery of a word typically involves both kinds of competence, not all of them do. In particular, some words only require inferential competence. A word like “rather”, for example, is not intended to be applied to worldly items, and referential competence is not required to be a competent speaker. Since some words are characterized only by intralinguistic relations, their correct use is entirely determined by them.⁵² Thus, the correctness of sentences composed only by, or essentially hinging on such words (like perhaps logical truths), would only depend on interlinguistic relations.⁵³ In this way, a coherence conception of truth may emerge. By contrast, the correctness of sentences relying also on words involving a referential aspect would also be determined by extra-linguistic relations. A realist conception, like a correspondence theory of truth, would be needed.⁵⁴

The discussion of the two cases above—ethical non-cognitivism and, in particular, lexical competence—as examples of possible justifications of alethic pluralism would require much more space to be assessed. Their role here, however, is illustrative rather than justificatory. They are intended to gesture towards potential ways in which a pluralist conception of truth could be reached moving from semantic rather than metaphysical considerations. They prepare the ground for the main thesis of the paper, namely the derivation of truth pluralism from a plurality of truth bearers.

4 A scope problem for truth bearers

In the previous section I have argued that general semantic considerations may provide another way to support truth pluralism, alternative (although not necessarily in contrast) to a more common metaphysical route. I now proceed in that direction articulating the strategy in more detail by focusing on differences among specific truth bearers, thus specifying and extending the general considerations above. In particular, I suggest that the standard and well known argument for alethic pluralism, resulting from the so called ‘scope problem’,⁵⁵ can somehow be adapted to support a pluralist view of primary truth bearers. Accordingly, a similar scope argument leads to a plurality of primary truth bearers, which, in turn, leads to a plurality of truth properties. Namely, it is shown that a certain kind of truth bearers is particularly well suited in certain domains, but accepting it as primary in all areas of discourse would be problematic. Since different kinds of truth bearers naturally support different ways of being true, the scope problem for truth bearers provides a new strategy to support truth pluralism.

For the sake of clarity, I should note that the approach is not intended to resist the distinction between primary and secondary truth bearers. Secondary truth bearers can be admitted as well. However, the picture proposed here is not the familiar one in which one kind of truth bearers plays the primary role across the board, while other kinds of truth bearers are always relegated to a secondary role at most. This view does not seem to lead to any interesting form of athletic pluralism. The resulting truth pluralism, in fact, could be easily tamed by extending the primary/secondary distinction from bearers to properties, admitting only one primary way of being true and declassifying the others as merely derivative. Such a view would probably count as a form of truth monism, exactly like the admission of primary and secondary truth bearers is pluralistic only in a harmless sense. The view put forward here is different, for it holds that a certain kind of truth bearers can be primary in some areas, while being secondary in others. What truth bearer plays the primary role and what truth bearer steps back varies in different areas. It is this potential variance in the primary truth bearers that supports an interesting form of pluralism about truth, since it leads to a plurality of primary truth properties. Since, given such remarks, secondary truth bearers are arguably irrelevant to establish alethic pluralism in an interesting form, I put them aside and omit the specification ‘primary’ for ease of exposition. In a final comprehensive view, however, secondary bearers could be admitted as well.

Before proceeding, it is also worth stressing that I am not defending the precise picture described below. Rather, I am just illustrating a reasonable way in which a plurality of truth bearers could be arrived at and developed. To this aim, I prefer to present a quite rich option, where all (and only) variants of truth bearers considered so far are involved. Nonetheless, the obtained account could be modified in several ways. The moral of the story I want to convey is only this: by considerations on truth bearers, a plurality of truth bearers and an ensuing plurality of truth properties can be reasonably advocated.

As a first step, consider sentences. A context in which sentences may be particularly attractive as truth bearers is that of a formalist conception of mathematics. According to formalism, mathematics can be accounted for in terms of rules for manipulating strings of symbols without any reference to their meanings, but only based on their form. A formalist account is a prominent anti-realist view alternative to mathematical realism and platonism. By being merely syntactic items, sentences fit the formalist approach because they avoid the problem of what arithmetical expressions are about, and thus the potential commitment to problematic mathematical entities.⁵⁶ A formal theory is usually formulated in terms of a precise formal language equipped with derivation rules or axioms governing its expressions. Think, for example, of Peano Arithmetics, which is a formal theory formulated in first order logic with the addition of axioms for a stock of primitive non logical terms, such as the successor function and zero. Once sentences are adopted as truth bearers, a natural account of arithmetical truth suggests itself. As already mentioned above, an anti-realist conception of truth like coherence is a straightforward choice.⁵⁷ Combined with a formalist view, the arithmetical truth of a sentence of the formal language of Peano Arithmetics can be taken to consist in being provable (in the relevant calculus) from Peano axioms. Note that I am not claiming that such an approach is correct. I am just presenting it as a possible and prima facie reasonable option.⁵⁸ At the same time, here comes the crucial point. Such an attractiveness would immediately fade away if we were to extend a formalist perspective to other areas, such as discourse about middle-size concrete objects. A formalist view in this case would be a non-starter. The demise of formalism would also deprive sentences of their justification for adoption in other areas. Given that the formalist reasons to favor sentences are limited to the mathematical domain, we have a first example of a scope problem for truth bearers. The issue would be serious for a monist, but it is unproblematic for a pluralist who can just take this result as evidence to admit different truth bearers in different areas. That sentences bear truth in a formal setting does not mean that they must be the primary bearers also in other domains. Once such a local scope of sentences is admitted and pluralism about truth bearers accepted, also truth pluralism ensues. Since sentences support a coherentist view, in mathematics truth might be coherence, whereas in other areas, where other truth bearers can be involved, truth may be something else.

Consider next the scenario provided by moral non-cognitivism in the quasi-realist version mentioned above. This view can be substantiated further by means of a specific choice of truth bearers. Given the peculiar features of non-cognitive discourse, a natural suggestion is to saddle a non-cognitivist view with a deflationary conception of propositions. In particular, the distinction between merely abundant and sparse propositions comes in handy. Since the simple denial of moral propositions leads to several problems, a non-cognitivist could articulate her view holding that a moral sentence, lacking a cognitive content, does express a proposition but only in an abundant sense. Attractive as this move could be for moral discourse, however, it would be an overreaction to extend an abundant view of propositions to discourses of any area. The non-cognitivist arguments for abundant propositions are local. Given, for example, the apparent cognitive profile of discourse about middle-size concrete objects, propositions expressed in that area are better suited to be sparse. We then have an example of a certain kind of propositions that fits one area of discourse, but whose generalization to all areas is problematic. As in the case of the scope problem for truth, a truth bearer pluralist has an easy take on this: there is not a unique kind of propositions uniform across different areas of discourse, since different discourses involve different kinds of propositions. In non-cognitive areas (like moral discourse) propositions are abundant, whereas in cognitive areas propositions are sparse. From such a pluralist view of propositions, pluralism about truth also naturally follows. Abundant propositions easily lead to a deflationary conception of truth (thus matching the original plan of the quasi-realist), while sparse propositions can be combined with a substantial conception of truth. The final general result is that we have two classes of propositions, the merely abundant and the sparse ones, paired with a deflationary and a substantial property of truth respectively.

Consider then the sparse propositions just admitted in non moral discourse. Some arguments have been provided in favor of Russellian propositions. For example, it has been argued that indexicals and demonstratives, and perhaps discourse about individuals in general, require the individual referred to be involved in the expressed proposition.⁵⁹ Such arguments, however, do not automatically apply to cases in which indexicality is not involved. Indeed, extending the view to all discourses may even be a source of problems. For example, if Russellian propositions are invoked in arithmetical discourse, then a number should be an element of the propositions. This would lead to some form of mathematical platonism, which may look particularly unattractive to some. Although monists would be forced to either accept Russellian propositions and their consequences across all the board or to reject them completely, a truth bearer pluralist can again circumvent the obstacle by restricting the scope of Russellian propositions. According to the truth bearer pluralist, some propositions are Russellian, whereas others, like those not involving indexicals or terms directly referring to concrete individuals, need not be. These other sorts of propositions may be Fregean propositions, for example. Since Russellian propositions naturally support an identity theory of truth, which is hardly applied to other views of truth bearers, we would again be led to truth pluralism. Indeed, this pluralistic approach could even help solve other problems. As hinted above, a basic difficulty of the Russellian view in its crude form is that of making sense of false propositions. However, this problem only emerges if monism about propositions is endorsed. In the present view, a sentence with a term failing to refer could be taken to express a proposition not in the Russellian sense but, e.g., in the Fregean one.⁶⁰ This way, true singular propositions could be identical to facts, although false singular propositions might instead be, e.g., Fregean propositions that do not correspond to reality.⁶¹

Let us then consider Fregean propositions. Although they could be taken to form a uniform class of propositions, a more complex account might also be viable. By leveraging on considerations on lexical competence, Fregean propositions may be thought to come in two main varieties. Propositions characterized by mere interlinguistic senses and propositions characterized by both interlinguistic and extralinguistic senses. As hinted above, having only one kind of propositions might fail to do justice to data supporting the two faces of lexical competence. The two kinds of Fregean propositions might then support an interlinguistic and anti-realist way of being true, on the one hand, and an extralinguistic and realist way of being true, on the other.⁶²

Let me sum up the overall picture emerging from the combination of all the elements presented in this section. If all remarks are accepted, the following scenario is obtained. Different domains are associated with different kinds of truth bearers and, consequently, truth properties. In arithmetics we have sentences as truth bearers and truth as coherence. In moral discourse, we have abundant propositions as truth bearers and a deflationary truth property. In cognitive and realist domains, like discourse about concrete individuals, we have Russellian propositions and identity to facts as truth, at least when indexicality is involved. In the other cases, Fregean propositions and truth as correspondence may be admitted. Finally, one could complicate Fregean propositions further by distinguishing different aspects of senses. The scenario just sketched supports a pluralist view of truth bearers leading to a pluralism of truth properties.

5 Some consequences of truth (bearers) pluralism

The main consequence of truth (bearers) pluralism is a change of perspective on truth pluralism. Inspired by the opening quote of Wittgenstein, the diversity in truth is considered as an effect of the diversity in the representational devices. Rather than motivating alethic pluralism from metaphysical considerations on what discourses are about, pluralism about truth is derived and looked at from the perspective of philosophy of language and semantics. Although the two views are not necessarily in contrast and could be combined, giving priority to the semantic perspective can have some positive effects. For example, the metaphysical support for alethic pluralism has been subject to deep criticisms, intended to show that if we have pluralism about truth makers, then pluralism at the level of truth becomes redundant if not just misplaced.⁶³ After all, the same property (truth), can well be had for different reasons (different truth makers). This kind of criticism, however, seems blocked if a semantic perspective is adopted. If a plurality of kinds of truth bearers is accepted, then a plurality of truth properties is harder to avoid. Given that the entities bearing certain peculiar properties are different sorts of entities, it is just natural that those properties are different as well. Exactly like numbers, chairs and families are apt to have different typical properties.

A second consequence is that truth (bearers) pluralism can provide an alternative way to articulate the problem of generic truth and the relation between moderate and strong truth pluralism. Contrasting strong alethic pluralism, a moderate version holds that beside area-specific truth properties, also a generic truth property covering all domains is to be admitted. A problem for such a moderate view is that of clarifying the relation between the general and the area-specific truth properties. Truth (bearers) pluralism can offer a new option to dissolve the difficulty, since a general property of truth could be vindicated by the admission of a general kind of truth bearer. As pointed out above discussing falsity and Russellian propositions, the possibility of overlapping (primary) truth bearers need not be excluded.⁶⁴ Accordingly, beside area-specific truth bearers, there could also be a general truth bearer that is associated with all areas of discourse. In this case, the relation among the general property of truth and the area-specific truth properties would pose no particular problem, as they would simply be properties of different kinds of entities.⁶⁵

Finally, the admission of a plurality of truth bearers can fit with other forms of pluralism beside truth pluralism. Gillian Russell, for example, defended a form of logical pluralism as the result of having logical validity defined over classes of different truth bearers.⁶⁶ For example, the logic corresponding to necessary truth preservation over propositions is different from the one preserving truth over sentences. Different truth bearers yield different necessarily truth preserving logics. Truth (bearers) pluralism could be combined with this sort of logical pluralism producing an interesting pluralist package.

6 Conclusion

In this paper I presented a new way of defending and articulating a pluralist view about truth. I have promoted a change of perspective, according to which we should look at truth by considering the nature of representation and its semantics, rather than the nature of what is represented and its metaphysics. In particular, focusing on truth bearers sheds new light on truth. I proceeded in two main steps. First, I have argued that different kinds of truth bearers are apt to bear different properties of truth. Second, I have shown that there are reasons to admit a plurality of (primary) truth bearers. Notably, the main traditional argument for truth pluralism, based on the scope problem, can somehow be adapted to support pluralism about truth bearers too. The final result is a view according to which different areas of discourse involve different kinds of truth bearers, which are apt to bear different properties of truth. The view has then been shown to have interesting implications and to bring a new perspective on several topics. Although defending the exact details of the proposal is beyond the scope of this paper, having offered reasons to consider the approach worth exploring in further debates is enough for my present purposes.