Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all?

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends (...) not on logic’s normativity but on epistemic goals. (shrink)

I distinguish two ways of developing anti-exceptionalist approaches to logical revision. The first emphasizes comparing the theoretical virtuousness of developed bodies of logical theories, such as classical and intuitionistic logic. I'll call this whole theory comparison. The second attempts local repairs to problematic bits of our logical theories, such as dropping excluded middle to deal with intuitions about vagueness. I'll call this the piecemeal approach. I then briefly discuss a problem I've developed elsewhere for comparisons of logical theories. Essentially, the (...) problem is that a pair of logics may each evaluate the alternative as superior to themselves, resulting in oscillation between logical options. The piecemeal approach offers a way out of this problem andthereby might seem a preferable to whole theory comparisons. I go on to show that reflective equilibrium, the best known piecemeal method, has deep problems of its own when applied to logic. (shrink)

I defend the idea that there are universal fictions, and that the Routley-Deutsch-Kapsner way of generating them – namely, with a story including deliberately and explicitly the proposition Everything is true – is still the best one. I reconstruct Wildman and Folde’s Finean criticisms to universal fictions a la Routley-Deutsch-Kapsner based on the idea that the universal quantifier in such fictions may not target the intended range of quantification, that is, all propositions. I show that Wildman and Folde’s argument does (...) not succeed, for they fail to show that every universal sentence has to be understood as involving a restricted quantifier. (shrink)

People cannot contemplate a proposition without believing that proposition. A model of belief fixation is sketched and used to explain hitherto disparate, recalcitrant, and somewhat mysterious psychological phenomena and philosophical paradoxes. Toward this end I also contend that our intuitive understanding of the workings of introspection is mistaken. In particular, I argue that propositional attitudes are beyond the grasp of our introspective capacities. We learn about our beliefs from observing our behavior, not from introspecting our stock beliefs. -/- The model (...) of belief fixation offered in the dissertation poses a novel dilemma for theories of rationality. One might have thought that the ability to contemplate ideas while withholding assent is a necessary condition on rationality. In short, it seems that rational creatures shouldn‘t just form their beliefs based on whatever they happen to think. However, it seems that we are creatures that automatically and reflexively form our beliefs based on whatever propositions we happen to consider. Thus, either the rational requirement that states that we must have evidence for our beliefs must be jettisoned or we must accept the conclusion that we are necessarily irrational. (shrink)

Scientific pluralism is the view according to which there is a plurality of scientific domains and of scientific theories, and these theories are empirically adequate relative to their own respective domains. Scientific monism is the view according to which there is a single domain to which all scientific theories apply. How are these views impacted by the presence of inconsistent scientific theories? There are consistency-preservation strategies and inconsistency-toleration strategies. Among the former, two prominent strategies can be articulated: Compartmentalization and Information (...) restriction. Among the inconsistency-toleration strategies, we have: Paraconsistent compartmentalization and Dialetheism. In this paper, I critically assess the adequacy of each of these four views. (shrink)

Roger Swyneshed, in his treatise on insolubles (logical paradoxes), dating from the early 1330s, drew three notorious corollaries of his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict the Rule of Contradictory Pairs, which requires that in every such pair, one must be true and the other false. Looking back at Aristotle's treatise De Interpretatione, we find that Aristotle himself, immediately after defining the notion of a contradictory (...) pair, gave counterexamples to the rule. Thus Swyneshed's solution to the logical paradoxes is not contrary to Aristotle's teaching, as many of Swyneshed's contemporaries claimed. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. (shrink)

This paper is about the putative theoretical virtue of strength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well-defined property of logical strength is neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic of (...) scientific strength, and the third is that many modern logics are on a par—or can be made to be on a par—with respect to scientific strength. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...) validity of inferences. In order to make sense of this claim, I will appeal to the Madhyamaka Buddhist philosopher Candrakīrti. I will then pose a problem for Priest’s anti-exceptionalism. Finally, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. (shrink)

A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...) recent and popular heterodox logics such as naïve logics of truth. I use this discussion to motivate a constraint—logical partisanhood—on the uses of such methodology: roughly: both the proposed alternative and our actual background logic must be able to agree that moving to the alternative logic is no worse than staying put. (shrink)

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of (...) the connectives or the best logic outside of a specified context are not legitimate questions. (shrink)

The concept of information has well-known difficulties. Among the many issues that have been discussed is the alethic nature of a semantic conception of information. Floridi :197–222, 2004; Philos Phenomenol Res 70:351–370, 2005; EUJAP 3:31–41, 2007; The philosophy of information, Oxford University Press, Oxford, 2011) argued that semantic information must be truthful. In this article, arguments will be presented in favor of an alethically neutral conception of semantic information and it will be shown that such a conception can withstand Floridi’s (...) criticism. In particular, it is argued that an alethically neutral conception of semantic information can manage the so-called Bar-Hillel Carnap paradox, according to which contradictions have maximum informational content. This issue, as well as some of Floridi’s other arguments, is resolved by disentangling the property of being information from the property of being informative. The essay’s final conclusion is that although semantic information is alethically neutral, a veridical conception of semantic information can, and should, be retained as a subconcept of semantic information, as it is essential for the analysis of informativity, which, unlike the property of being information, depends on truth. (shrink)

I argue that code words like “inner city” do not semantically encode hidden or implicit meanings, and offer an account of how they nonetheless manage to bring about the surprising effects discussed in Mendelberg 2001, White 2007, and Stanley 2015 (among others).

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and h...

In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated (...) interface between metaphysical and formal truth theories, pointing to several promising questions that arise here. (shrink)

This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalized account of rejectivism through close consideration of Mark Textor's arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.

A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay (...) is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes. (shrink)

This paper addresses the problem of judgment aggregation in science. How should scientists decide which propositions to assert in a collaborative document? We distinguish the question of what to write in a collaborative document from the question of collective belief. We argue that recent objections to the application of the formal literature on judgment aggregation to the problem of judgment aggregation in science apply to the latter, not the former question. The formal literature has introduced various desiderata for an aggregation (...) procedure. Proposition-wise majority voting emerges as a procedure that satisfies all desiderata which represent norms of science. An interesting consequence is that not all collaborating scientists need to endorse every proposition asserted in a collaborative document. (shrink)

Islamic theological contradictions are metaphysical contradictions as opposed to logical and semantic ones. I shall demonstrate that if these theological contradictions are tolerable on the theoretical account of metaphysical dialetheism, then logical space, despite being the space of all possibilities, does not accommodate them in virtue of Chalmers’s ‘deep epistemic possibility’. To resolve this issue, I offer a recalibration of the modal concept of possibility. Doing so would redraw a demarcation between what is possible and what is not. Consequently, we (...) can expand logical space, so it is properly inclusive of all possibilities, including metaphysical dialetheism. Expanding logical space in this way would repudiate Chalmers’s ‘deep epistemic possibility’ and make room for Islamic theological contradictions. (shrink)

In this paper, I present a puzzle about epistemic rationality. It seems plausible that it should be rational to believe a proposition if you have sufficient evidential support for it. It seems plausible that it rationality requires you to conform to the categorical requirements of rationality. It also seems plausible that our first-order attitudes ought to mesh with our higher-order attitudes. It seems unfortunate that we cannot accept all three claims about rationality. I will present three ways of trying to (...) resolve this tension and argue that the best way to do this is to reject the idea that strong evidential support is the stuff rationality is made of. In the course of doing this, I shall argue that there is a special class of propositions about the requirements of rationality that we cannot make rational mistakes about and explain how this can be. (shrink)

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

I discuss Greg Restall’s attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to be (...) the most natural minimal way of distinguishing content and form and suggest further problems arising for this route. (shrink)

The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds.

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: identity is presupposed in every conceptual system; identity is required to characterize individuality; identity cannot be defined; the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons to hold that identity is fundamental; in fact, (...) most of the tasks that seem to require identity may be performed without identity. So, in the end, identity may not be a fundamental concept after all. (shrink)

The semantic paradoxes are a family of arguments – including the liar paradox, Curry’s paradox, Grelling’s paradox of heterologicality, Richard’s and Berry’s paradoxes of definability, and others – which have two things in common: first, they make an essential use of such semantic concepts as those of truth, satisfaction, reference, definition, etc.; second, they seem to be very good arguments until we see that their conclusions are contradictory or absurd. These arguments raise serious doubts concerning the coherence of the concepts (...) involved. This article will offer an introduction to some of the main theories that have been proposed to solve the paradoxes and avert those doubts. Included is also a brief history of the semantic paradoxes from Eubulides to Tarski and Curry. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there (...) is a way to handle classical negation. (shrink)

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart (...) from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting.

Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...) restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume.For a recent introduction to non-classical theories of truth and other semantic notions, see the excellent Beall a .. (shrink)

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

Thanks to the work of Kendall Walton, appeals to the notion of pretence (or make-believe) have become popular in philosophy. Now the notion has begun to appear in accounts of truth. My aim here is to assess one of these accounts, namely the ‘constructive methodological deflationism’ put forward by Jc Beall. After introducing the view, I argue that Beall does not manage to overcome the problem of psychological implausibility. Although Beall claims that constructive methodological deflationism supports dialetheism, I argue that (...) it does not, and I show that it in fact provides a classical response to the Liar paradox. (shrink)

Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. (...) I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content. (shrink)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use (...) in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence. (shrink)

Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...) seems now to be at a standoff. I aim, first, to bolster the revenge objections by considering a relation, internalizability, between languages and theories of truth. A theory of truth is internalizable for a language iff there is an extension of that language in which the theory is expressible and for which the theory provides an accurate and complete assignment of semantic values. There are good reasons to think that acceptable theories of truth are internalizable for any language. With this internalizability requirement in hand, I argue that properly formulated revenge objections are decisive and that the replies to them are inadequate. Second, I show that the internalizability requirement can be met by a certain theory of truth. The central claim of this theory is that truth is an inconsistent concept and should be replaced with a pair of consistent concepts that can then be used to provide a semantics for our truth predicates. This theory is compatible with classical logic, does not give rise to revenge paradoxes of any kind, and satisfies the internalizability requirement. (shrink)

In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. Second, that the (...) presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (shrink)

I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but (...) the more general case is also considered. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...) which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any “truly satisfying, consistent solution”. I argue that this conclusion is too strong. Heck's Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke's and Field's. Moreover, the new Liar gives us no reasons to think that (versions of) these (...) principles cannot be consistently retained once the structural rule of contraction is restricted. I suggest that revisionary logicians have independent reasons for restricting such a rule. (shrink)

Philosophers of religion have taken the assumption for granted that the various religious traditions of the world have incompatible beliefs. In this paper, I will argue that this assumption is more problematic than has been generally recognized. To make this argument, I will discuss the implications of internal religious disagreement, an aspect of this issue that has been too often ignored in the contemporary debate. I will also briefly examine some implications of my argument for how one might respond to (...) the existence of religious diversity. (shrink)

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...) logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)