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UConn Conference on Truth Pluralism and Logical Pluralism Abstracts

Friday, April 17th

Nikolaj J.L.L. Pedersen (Yonsei) – “Strong Alethic Pluralism”

Alethic pluralism is the view that there are different ways of being true. Propositions about riverbanks might be true because they correspond with reality whereas propositions about the law might be true because they cohere with the body of law. Recently, alethic pluralism has attracted considerable attention in the literature. Authors with pluralist sympathies have taken on the positive task of spelling out the different aspects of alethic pluralism in greater detail. As a result, different versions of the view have emerged. Strong alethic pluralists give up on the idea of truth-as-such. They deny that there is a single truth property applicable across all truth-apt domains of discourse. Truth is Many, not One. Moderate alethic pluralists, on the other hand, hold on to the idea of truth-as-such. The property is generic or applies across all truth-apt discourse. However, propositions belonging to different domains may possess this generic truth property in virtue of having distinct properties such as correspondence or coherence. The Many ground the One. In this sense truth is both One and Many. This paper has two aims. The first aim is to present and develop a version of strong alethic pluralism in some detail. This task has been somewhat neglected in the literature, one major reason being that strong pluralism is widely regarded as a non-starter due to a battery of seemingly devastating objections leveled against it. Among these objections the problem of mixed compounds is regarded as being particularly pressing—and difficult—for the strong pluralist to deal with. The second aim of the paper is to give a strongly pluralist response to the problem of mixed compounds. [This is joint work with Seahwa Kim.]

Neil Tennant (Ohio State) – “Truthmaking and Truth-Transmission: How to Determine the Right Logic”

This study shows how an inferentialist can arrive at the right logic. We begin with the inferences that are involved in determining the truth value of a sentence when it is interpreted in a model. The rules governing these inferences allow one to define, co-inductively, the notions ‘V is a verification of p in the model M’ and ‘F is a falsification of p in the model M’. These notions embody a strong relation of relevance (of salient facts to truth-value determinations). The existence of an M-relative verification of p is equivalent to the sentence p’s being true-in-M in the sense of Tarski. Verifications and falsifications are relevantly from, or relative to, a set of literals expressing some of the atomic information in the model. But a system of deduction needs to provide, in general, proofs of p from (finite sets of) complex premises. Such proofs are model-independent. We investigate how the model-relative rules of verification and falsification can morph into introduction and elimination rules, respectively, that are model-independent but that preserve M-relative verifiability from premises to conclusions. The deductive rules thus arrived at preserve the strong relation of relevance—arguably, one that is the strongest possible. These rules form the system of Core Logic. Pacete all pluralists present, I shall argue that Core Logic is the right logic, for a host of orthogonal but intersecting reasons.

Paul Horwich (NYU) – “Is TRUTH a Normative Concept?”

My answer will be ‘no’. And I’ll defend it by: (i) distinguishing a concept’s having normative import from its being intrinsically normative; (ii) sketching a method for telling whether or not a concept is of the latter sort; (iii) responding to the anti-deflationist, Dummettian argument (extended in different directions by Crispin Wright, Huw Price, and Michael Lynch) in favor of the conclusion that TRUTH is intrinsically normative; (iv) proceeding to address a less familiar route to that conclusion — one that’s consistent with my deflationism about TRUTH, but that depends on the further assumption that MEANING is intrinsically normative; and (v) arguing that this further assumption is mistaken.

Saturday, April 18th

Dorit Bar-On (UConn) & Keith Simmons (UConn) – “Truth: One or Many?”

Truth pluralism is a metaphysical theory of the nature of truth. The pluralist rejects the deflationist claim that truth is at best a ‘shallow’, insubstantial property. Indeed, the pluralist embraces a plurality of truth properties (such as correspondence, superassertibility, coherence), each appropriate to a different domain (or domains) of discourse. On the face of it, the pluralist will inherit all the main problems of the various traditional substantivist theories of truth. In addition, a strong pluralist, who only recognizes a plurality of truth properties (so that truth emerges not as one but only many), faces a number of problems, such as the problem of mixed discourse. But the moderate pluralism, who acknowledges that there is, in addition to diverse truth properties, a single property of truth (so that truth emerges as both one and many), faces problems of her own. After raising specific difficulties we see with moderate pluralism, we propose a less extravagant way to preserve the metaphysical intuitions that motivate pluralism.

Teresa Kouri (Ohio State) – “Connective Meanings in Beall and Restall’s Logical Pluralism”

I will show that there is a problem with the meanings of the connectives as presented in Beall and Restall’s Logical Pluralism. In their system, they claim that negation (¬) in constructive logic and negation (¬) in relevant logic are one and the same. I show this cannot be, given how they have defined the meaning of a logical connective. I suggest that this type of problem is typical of a certain way of thinking about the meanings of connectives, and gesture towards an alternate route to logical pluralism which does not encounter such problems.

Aaron Cotnoir (St Andrews) – “Logical Nihilism”

Logical Monism is the view that there is exactly one formal logic that correctly represents natural language inference whereas Logical Pluralism is the view that there is more than one formal logic that correctly represents natural language inference. I defend the neglected third position of Logical Nihilism: there is no formal logic that correctly represents natural language inference. The view might be thought to be self-defeating, but I suggest it is not; indeed there is much to be said in its favor. I present a range of arguments for logical nihilism, and suggest a promising alternative way for philosophers to think about formal logic (just in case any of these arguments turns out to be good).

Andy Yu (Oxford) – “Logic for Alethic Pluralists”

Although the twin challenges for alethic pluralists to maintain standard accounts of the logical operators and of logical consequence were first posed in Williamson (1994); Tappolet (1997, 2000), there have been few attempts to answer them in a sufficiently systematic and precise way. Cotnoir (2013)’s attempt is a notable exception, but focuses only on answering the second challenge, and founders when taken to be an attempt to answer the first challenge. In this paper, I present a logic on behalf of pluralists that answers both challenges in a systematic and precise way.

Chase Wrenn (Alabama) – “A Please for Immodesty: Alethic Pluralism, Logical Pluralism, and Mixed Inferences”

The problem of mixed inferences is a bugbear for alethic pluralism and logical pluralism alike. Michael Lynch’s alethic functionalism aims to solve the problem for alethic pluralists. But, as Lynch observes, it is tempting to combine alethic and at least one sort of logical pluralism, and doing so threatens to reintroduce the problem. Lynch proposes a way out of the problem for alethic cum logical pluralists. I argue that Lynch’s way out is a dead end, and the combination of alethic pluralism with domain-specific logical pluralism is unattractive.

Rosanna Keefe (Sheffield) – “Pluralisms: Logic, Truth and Domain-Specificity”

In this paper I focus on Domain-specific Logical Pluralism, the view that the true logical consequence relation differs between different domains. One, though not the only, possible route to this type of position, is via Pluralism about Truth. If what truth amounts to differs across different domains, then this may suggest differences regarding validity in those different domains. I will explore difficulties for a position combining pluralism about truth with this kind of logical pluralism. I will criticise Cotnoir’s algebraic approach and draw some more general conclusions from this discussion. I then raise further objections to Domain-specific Logical Pluralism, whether or not it is combined with Pluralism about Truth. I finish by suggesting a framework in which we can vindicate the use of different logics in different domains without commitment to more than one true logical consequence relation; this picture employs a notion of relative validity.

Sunday, April 19th

Paul Simard Smith (UConn) – “Between Double Negation Elimination and a Hard Place: A Dilemma for Domain-Specific Logical Pluralism”

The purpose of my talk will be to present a dilemma for a view called domain-specific logical pluralism (DLP). According to DLP different logics govern different domains of discourse. In particular, in domains of discourse in which propositions are true because they correspond to an obtaining state of affairs advocates of DLP regard classical logic as correct. However, in domains in which truth is epistemically constrained and propositions are true in virtue of possessing the property of being superwarranted something akin to intuitionistic logic is correct. The force of the dilemma I pose for DLP arises through consideration of certain dialogues in which, I contend, an inference is made that is both valid and invalid for the same class of statements, but is valid in a different context from the context in which it is invalid. On one horn of the dilemma an advocate of DLP could adopt a more “radical” pluralism in which they can no longer find comfort in a neat and tidy separation of the domains in which a particular logic holds from the domains in which the same logic does not hold. On the other horn of the dilemma the advocate of DLP could reject the notion that intuitionistic logic is the logic of superwarrant or that classical logic is the logic of correspondence abandoning a central tenet of the view.

Nathan Kellen (UConn) – “Logical Consequence as a Functional Concept”

In this paper I develop an approach I call logical functionalism, which treats logical consequence as a functional concept. The benefit of treating logical consequence in this manner is twofold. First, it eliminates possible confusion by defining consequence in terms of its theoretical role, thus providing conceptual clarity to the debate. Secondly, it provides a common framework to analyse and interpret various theories of logical consequence in a neutral framework, in a manner not previously possible. One outcome of treating logical consequence in this way is that the debate pluralists and monists hinges, in part, on whether they see logical consequence as multiply realisable.

Kevin Scharp (Ohio State) – “Logical and Alethic Pluralism”

Aletheic pluralism is the view that there is more than one truth property, and logical pluralism is the view that there is more than one correct logic.  Usually the truth properties described by the aletheic pluralist are familiar ones advocated by parties debating the nature of truth (e.g., the correspondence property, the pragmatic property, and coherence property).  Likewise, the logics described by the logical pluralist are familiar ones advocated by parties debating the nature of logic (e.g., classical, intuitionistic, and relevant).  However, one can be an aletheic pluralist by focusing on properties of truth that result from different approaches to the aletheic paradoxes instead.  And one can be a logical pluralist by focusing on logics that result from different approaches to the aletheic paradoxes as well.  Moreover, one could combine these two alternative pluralisms into a single view according to which the logic and the truth property differ depending on the discourse, but they are coordinated so that in discourses with stronger logics, the truth property is weaker, and in discourses with weaker logics, the truth property is stronger.  I first formulate this combined theory of truth and logic and then evaluate it as a competitor with more traditional approaches to the aletheic paradoxes.