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)

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

The notion of ontology originates in philosophy. It has been recently employed in computer science and information technology for representing knowledge. In the first part of the paper, I argue that there is a significant overlap in these notions of ontology. Utilizing this overlap, I show in the second part that ontologies can be used for developing a new powerful heuristic method for resolving verbal disputes in philosophy. Verbal disputes can be defined in terms of ontologies: A dispute over two (...) texts P and S is verbal if and only if both of them can be mapped into the same ontology. In the appendix, I analyze the dispute over logical pluralism and indicate how my method of resolving verbal disputes can be employed. (shrink)

How many logics do logical pluralists adopt, or are allowed to adopt, or ought to adopt, in arguing for their view? These metatheoretical questions lurk behind much of the discussion on logical pluralism, and have a direct bearing on normative issues concerning the choice of a correct logic and the characterization of valid reasoning. Still, they commonly receive just swift answers – if any. Our aim is to tackle these questions head on, by clarifying the range of possibilities that logical (...) pluralists have at their disposal when it comes to the metatheory of their position, and by spelling out which routes are advisable. We explore ramifications of all relevant responses to our question: no logic, a single logic, more than one logic. In the end, we express skepticism that any proposed answer is viable. This threatens the coherence of current and future versions of logical pluralism. (shrink)

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 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)

It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (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)

This paper aims to call into question the customary division of logically revisionary responses to the truth-theoretic paradoxes into those that are “substructural” and those that are “ structural.” I proceed by examining, as a case study, Beall’s recent proposal based on the paraconsistent logic LP. Beall formulates his response to paradox in terms of a consequence relation that obeys all standard structural rules, though at the price of the language’s lacking a detaching conditional. I argue that the same response (...) to paradox can be given using a consequence relation that preserves detachment rules for a conditional, though at the price of restricting structural rules. The question “Is paradox being blocked by invoking a substructural consequence relation?” is thus ill-posed. The lesson of this example, I conclude, is that there is no useful explication of the idea of a substructural approach to paradox. (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...) view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

Some philosophers have argued that putative logical disagreements aren't really disagreements at all since when you change your logic you thereby change the meanings of your logical constants. According to this picture classical logicians and intuitionists don't really disagree, they just mean different things by terms like “not” and “or”. Quine gave an infamous “translation argument” for this view. Here I clarify the change of logic, change of meaning (CLCM) thesis, examine and find fault with Quine's translation argument for the (...) thesis, offer a modified translation argument in its stead, defend my modified argument from a crucial objection, discuss where the CLCM thesis leaves logical disputes, and discuss if and how the thesis coheres with Quine's influential view of logic. (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)

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)

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)

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)

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)

In early Buddhist logic, it was standard to assume that for any state of a ff airs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time mak­ing sense of this, but it makes perfectly good sense in the se­mantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest (...) that none of these options , or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate. (shrink)

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of (...) contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively . I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between P and (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory. (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)

En esta nota crítica (i) se hace una breve descripción de cada uno de los artículos que componen Orayen: de la forma lógica al significado, (ii) se señalan algunas cuestiones que no están claras en ellos o en las réplicas de Orayen y, (iii) en la medida de lo posible, se indica si los autores desarrollan ulteriormente los problemas abordados en sus artículos. The aim of this critical note is threefold: (i) it briefly describes and comments on each of the (...) articles of Orayen: de la forma lógica al significado; (ii) identifies some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen's replies; (iii) as far as possible, it refers to further studies made by the authors themselves on the same, or quite related, subjects addressed by them in their papers. (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)

A common and much-explored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...) and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present. The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3. (shrink)

According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...) I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view. (shrink)

At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some (...) other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection. (shrink)

This article argues, against contemporary experimentalist criticism, that conceptual analysis has epistemic value, with a structure that encourages the development of interesting hypotheses which are of the right form to be valuable in diverse areas of philosophy. The article shows, by analysis of the Gettier programme, that conceptual analysis shares the proofs and refutations form Lakatos identified in mathematics. Upon discovery of a counterexample, this structure aids the search for a replacement hypothesis. The search is guided by heuristics. The heuristics (...) of conceptual analysis are similar to those in other interesting areas of scholarship, and so hypotheses generated by it are of the right form to be applicable to diverse areas. The article shows that the explanationist criterion in epistemology was developed and applied in this way. The epistemic value of conceptual analysis is oblique because it contributes not towards the main purpose of conceptual analysis but towards the reliable development of epistemically valuable hypotheses in philosophy and scholarship. (shrink)

Jaina philosophy provides a very distinctive account of logic, based on the theory of ?sevenfold predication?. This paper provides a modern formalisation of the logic, using the techniques of many-valued and modal logic. The formalisation is applied, in turn, to some of the more problematic aspects of Jaina philosophy, especially its relativism.

Lewisian Genuine Realism about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? Since (...) the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds. (shrink)

There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...) dubious assumption about the linguistic expression of concepts. Successful revenge would require that there be a notion other than truth that plays the same role with respect to concept-expression that truth is naturally thought to play before we are confronted with the Liar paradox. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

According to the trivialist, everything is true. But why would anyone believe that? It turns out that trivialism emerges naturally from a certain inconsistency view of language, and it has significant benefits that need to be acknowledged. But trivialism also encounters some troubles along the way. After discussing them, I sketch a couple of alternatives that can preserve the benefits of trivialism without the corresponding costs.

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

Philosophers debate about which logical system, if any, is the One True Logic. This involves a disagreement concerning the sufficient conditions that may single out the correct logic among various candidates. This paper discusses whether there are necessary conditions for the correct logic; that is, I discuss whether there are features such that if a logic is correct, then it has those features, although having them might not be sufficient to single out the correct logic. Traditional rationalist arguments suggest that (...) the necessary conditions of thought are necessary and sufficient conditions singling out the correct logical and mathematical theories. In the contemporary debate, Chalmers advocates a view along this line. Jago, analogously, suggests that the necessary conditions for thought—or, as he calls them, our basic epistemic expectations—single out a family of logical and mathematical theories. Warren and Williamson, on the other hand, argue that there are no necessary conditions of thought. I argue that there are necessary conditions for thought, and these are necessary but not sufficient conditions to be the correct logic; indeed, these are features that all logics—correct or incorrect—share. No view we can understand is ruled out by the necessary conditions for thought, but we cannot understand quite any view. Human linguistic and conceptual abilities are genetically constrained, and these constraints are our best guide to the boundaries of logic. Arguing for this, I tackle two dogmas of modern rationalism: namely, the view that the biological constraints of human cognition have no bearing on the boundaries of the epistemic space, and the view that the boundaries of thought coincide with the boundaries of language. (shrink)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and abstract sciences. If we wish (...) to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (shrink)

This article focuses on the applications of philosophical logic in the discipline of philosophy of religion of both ‘Eastern’ and ‘Western’ traditions, in which the problem of apparent ontological contradictions can be found. A number of philosophers have proposed using the work of those non-classical logicians who countenance the violation of the law of non-contradiction (LNC) to address this problem. I discuss (1) whether classical or non-classical account of logic is universal in applying to all true theories, and (2) whether (...) there might be extra-logical considerations which affect what is the correct account of logic for the doctrines in question. With regard to Jc Beall’s application of non-classical (FDE) logic to the doctrine of the Incarnation, I argue using the evidence from the writings of church fathers that the meaning of negation found in the core claims of the doctrine of the Incarnation should not be interpreted in accordance with Beall’s FDE account, and that this extra-logical consideration refutes Beall’s project. Moreover, the FDE’s acceptance of the possibility of statements that are both true and false is contrary to what is allowed by the definition of negation in classical logic; therefore (contrary to Beall), Beall is in fact using a different definition of negation compared with the definition used by the classical account. I develop this point in interaction with contemporary philosophy of religion literature and explain its implications and significance for this discipline. (shrink)

In this paper, I discuss Whiting’s (2021) account of rational belief and discuss some unresolved issues arising from its reliance on epistemic possibility and, by extension, perspective-relative aprioricity.