PLURALISM AND NORMATIVITY IN TRUTH AND LOGIC

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and Restall (2006), Field (2009), Lynch (2009), and Sher (2016a). Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. I. Pluralism in Truth and Logic The relation between truth-pluralism and logical pluralism has been discussed by a number of philosophers. A natural link between the two is the fact that the main logical (or rather, meta-logical) relation, logical consequence, is defined in terms of truth. A classical reference is Tarski (1936), according to which the sentence X is a logical consequence of the set of sentences K iff (if and only if) in every model in which all the sentences of K are true X is true too. It is common to say that logical consequence is defined in terms that significantly include preservation or transmission of truth. Now, if truth is plural—that is, there are different types of truth—then the preservation (transmission) of different types of truth might be based on different principles, giving rise to, or requiring, a plurality of logics. This potential connection is laid down in Lynch (2009) and Pedersen (2014), and I share their view. But whether this potential connection materializes depends on what truth-pluralism is and what is required for the transmission of different types of truth. If the plurality of truth is so deep that it allows both realist and antirealist conceptions of truth, and if transmission of realist truth requires, say, a bivalent logic while the transmission of antirealist truth requires a non-bivalent logic, then logic in some fields is bivalent, in others non-bivalent, i.e., there are different types of logic for different fields. But if truth, as truth, is essentially (hence, always) realist and its plurality is limited to variations within the domain of realist truth (e.g., truth is always based on correspondence but the patterns of correspondence vary in, say, physics and mathematics), then the plurality of truth, by itself, would not lead to logical pluralism in the way delineated above. This, however, does not rule out other connections between truth-pluralism and logical pluralism. For example, both truth and logic might share some traits, or combinations of traits, that are potentially conducive to This content downloaded from 70.179.3.18 on Sun, 18 Oct 2020 01:46:55 UTC All use subject to https://about.jstor.org/terms 338 / AMERICAN PHILOSOPHICAL QUARTERLY pluralism. And indeed, they both share such a combination of traits, e.g., the combination of having a highly broad and a highly diverse scope. Both apply to many fields of knowledge, including fields that vary in their subject-matter and degree of abstractness. This opens up the possibility of pluralism for both. But diversity and breadth by themselves do not necessitate pluralism. In this paper I would like to explore a pair of other factors that correlate with pluralism and its opposite, monism, factors whose correlation with pluralism and monism in truth and logic has not been examined before. These factors pertain to our attitude to, or conception of, truth and logic, specifically, whether it is deflationist or substantivist. Starting with truth, I will examine whether and how deflationism and substantivism, as well as variations within substantivism, lead to different views on pluralism with respect to truth. Before turning to this question, however, let me briefly clarify the “level” on which I will speak on truth in this paper, for example, whether I will talk about the concept of truth or about the property of truth. This distinction plays a significant role in some philosophers’ thinking about truth, but it plays a less significant role in my own thinking about it. One reason is that for me philosophically important concepts are denoting concepts, so that given the philosophical importance of the concept of truth (in my view), truth is not just a concept. Another is that it is not automatically the case that if the concept of truth denotes something, it denotes a property. A further alternative is that the concept of truth denotes a norm, and there are other options as well. For reasons that I will explain below, I regard truth itself (what the concept of truth stands for) primarily as a norm and secondarily as a property—the property of satisfying the norm of truth. So, for me, talking about the concept, norm, and property of truth are all significant. Very often in this paper, though, I use “truth” to talk about the subject-matter of philosophical investigations and theories of truth. Although different philosophers have different views about what this subject-matter is, there is a certain family resemblance between the range of views discussed in the philosophical literature, and it is our familiarity with (more or less) the same literature that enables us to talk to each other about truth even when our answers to the question “What is truth?” differ significantly. A. Pluralism and Monism with Respect to Truth One well-known “manifesto” of truthdeflationism (often called “alethic deflationism”) is Horwich (1990). Horwich uses the term “minimalism” for his particular version of deflationism, but here I will treat this version as representative of the deflationist approach. It is easy to see that deflationism is associated with, or leads to, monism with respect to truth. According to deflationism, there is very little to truth: truth is a very thin property, concept, or predicate, and all there is to it is fully captured by the equivalence schema, formulated by Horwich as: (E) It is true that p if and only if p. [Horwich 1990, 7] Now, because this understanding of truth is both minimalist and exhaustive, it leaves no room for pluralism with respect to truth. Suppose there were some significant differences between truth in physics and truth in mathematics. These differences would concern features of truth other than (E), but deflationism does not recognize any such features. From the deflationist’s perspective, either there cannot be such differences or, if there could be, they would be irrelevant to our understanding of truth. The result is monism with respect to truth. Given any two fields of knowledge in the scope of truth, K1 and K2, their concept of truth is exhausted by (E). This content downloaded from 70.179.3.18 on Sun, 18 Oct 2020 01:46:55 UTC All use subject to https://about.jstor.org/terms PLURALISM AND NORMATIVITY / 339 Deflationism is too undiscerning to discern differences between fields of truth. Instead of looking and seeing whether truth behaves in the same way in all fields, deflationists limit their attention to a single, minimalistic test, one that is blind to any potential differences between truths in different fields. Generalizing, we may say that an easy way to impose unity (monism) on truth is to limit our attention to a very thin common denominator of all truths (e.g., (E)). But this way is too easy. One problem with the monistic conception of truth arrived at in this way is that it is blind to philosophically significant differences between truths. One example of such a difference is the difference between material truth (truth simpliciter) and logical truth. The difference between these two types of truth is difficult to ignore, but from a deflationist perspective, which takes only the material (E) schema into account, there is no room for two types of truth. Horwich (1990) does not say anything about logical truth, but he does say that “a central tenet of the point of view advanced here is that the theory of truth and the theory of logic have nothing to do with one another” (Horwich 1990: 76–77). This suggests that he does not recognize logical truth as a specific type of truth. In contrast to Horwich, Wright (1992), Lynch (2009), and I (2016a) are all substantivists with respect to truth. By “substantivist” I mean an advocate of a substantive theory (of any subject-matter), and by “substantive” I understand, in addition to “non-deflationist,” also having such traits as “informative,” “explanatory,” “deep,” “important,” “significant,” “theoretically grounded,” “subject to high standards of discovery and justification,” “rigorous,” “systematic,” “thorough,” “of intellectual interest,” and so on. Non-deflationism by itself may be viewed as weak substantivism; the aggregation of all or most of the traits noted above is strong substantivism. Wright’s, Lynch’s, and my substantivism about truth explains (at least in part) our attention to the plurality of truth. If truth is not exhausted by a single and simple principle, if there is more to truth than the equivalence schema, then there is room for multiple principles of truth, including principles that vary in scope. Some principles may hold in all domains of truth, others may be specific to particular domains (clusters of domains). Given the breadth of truth and the diversity of fields of truth, substantivism is open to the possibility of multiple types of truth with principled differences between them. For example, some principles governing truth in everyday physics (the physics of mid-size, observable objects) might not govern truth in mathematics, and vice versa. The acceptance of plurality by any theory, however, requires a balance between unity and diversity (disunity). And one way to introduce such a balance is to include both general and particular (global and local) principles. The former unify the theory, the latter dive