While the epistemic significance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ‘logical disagreement’. Chapters 1 and (...) 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a specific proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ‘logical disagreement’. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justification for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of one’s background logic and the logical theory one prefers (officially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic significance of central principles from the literature are at best deflated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reflections on the potential epistemic significance of convergence in logical theorizing. (shrink)

Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory of restricted (...) quantification we use is because they are the best way of dealing with these topics from Beall’s theory-building theory picture of logic, establishing a second point of contact with Beall’s work. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism (...) due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

There was a time when both Rudolf Carnap and Jc Beall were thought to be arch logical pluralists. Beall has since renounced his pluralistic views, but Carnap is still largely regarded as a pluralist. In this paper, I will show that there is good reason to think that Carnap is not a logical pluralist, at least in the way he is presented in the literature. Instead, I argue, he can be seen as a Beall-style logical monist at the meta-level, in (...) line with the views expressed in Beall (APHI 14:1–29, 2017 and NOUS 28:30–54, 2018). (shrink)

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...) star semantics for logics whose many-valued semantics include indeterminate. The equivalence of the many-valued semantics and star semantics is established by way of a soundness and completeness proof. The upshot of the novel semantics in terms of the applied semantics of these logics, and specifically infectiousness, is explored, settling on the idea that infectiousness concerns ineffability. (shrink)

I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to (...) solve by abduction. (shrink)

There is a natural story about what logic is that sees it as tied up with two operations: a ‘throw things into a bag’ operation and a ‘closure’ operation. In a pair of recent papers, Jc Beall has fleshed out the account of logic this leaves us with in more detail. Using Beall’s exposition as a guide, this paper points out some problems with taking the second operation to be closure in the usual sense. After pointing out these problems, I (...) then turn to fixing them in a restricted case and modulo a few simplifying assumptions. In a followup paper, the simplifications and restrictions will be removed. (shrink)

This paper presents a simple but, by my lights, effective argument for a subclassical account of logic—an account according to which logical consequence is (properly) weaker than the standard, so‐called classical account. Alas, the vast bulk of the paper is setup. Because of the many conflicting uses of ‘logic’ the paper begins, following a disclaimer on logic and inference, by fixing the sense of ‘logic’ in question, and then proceeds to rehearse both the target subclassical account of logic and its (...) well‐known relative (viz., classical logic). With background in place the simple argument—which takes up less than five pages—is advanced. My hope is that the minimal presentation will help to get ‘the simple argument’ plainly on the table, and that subsequent debate can move us forward. (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)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

Nancy Cartwright's 1983 book How the Laws of Physics Lie argued that theories of physics often make use of idealisations, and that as a result many of these theories were not true. The present paper looks at idealisation in logic and argues that, at least sometimes, the laws of logic fail to be true. That might be taken as a kind of skepticism, but I argue rather that idealisation is a legitimate tool in logic, just as in physics, and recognising (...) this frees logicians up to use false laws where these are helpful. (shrink)

Here, we outline UPJA’s recent developments and the contents of Volume 2, Issue 2.

This paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics.

Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

Justification logics provide frameworks for studying the fine structure of evidence and justification. Traditionally, these logics do not impose any closure requirements on justification. In this paper, we argue that for some applications they should subject justification to closure under some variety of logical consequence. Specifically, we argue, building on ideas from Beall, that the non-classical logic FDE offers a particularly attractive notion of consequence for this purpose and define a justification logic where justification is closed under FDE consequence. We (...) show the resulting logic to be sound and complete. Lastly, we discuss how the closure of justification under FDE ontrasts closure under related non-classical logics and how our approach contrasts with some alternatives. (shrink)

We investigate a hitherto under-considered avenue of response for the logical pluralist to collapse worries. In particular, we note that standard forms of the collapse arguments seem to require significant order-theoretic assumptions, namely that the collection of admissible logics for the pluralist should be closed under meets and joins. We consider some reasons for rejecting this assumption, noting some prima facie plausible constraints on the class of admissible logics which would lead a pluralist admitting those logics to resist such closure (...) conditions. (shrink)

Beall has given more or less convincing arguments to the effect that neither classical logic, nor K3, nor LP, nor S3 can play the role he expects from logic: to be the basement theory for all true theories, including true theology. However, he has not considered all the pertinent competitors, and he has not given any reassurance that he has not gone too low in the hierarchy of logics to find his desired “universal closure of all true theories”. In this (...) paper, I put forward those additional arguments to show the superiority of FDE with respect to logics that include a detachable conditional but that are very much like FDE otherwise. I also discuss the problem that theological consequence might not contrapose even if theological consequence is supposed to extend FDE consequence and the latter does contrapose. (shrink)

En este artículo discutimos la tesis de Jc Beall según la cual no hay negación lógica. Evaluamos la solidez del argumento con el que defiende su tesis y presentamos dos razones para rechazar una de sus premisas: que la negación tiene que ser excluyente o exhaustiva. La primera razón involucra una presentación alternativa de las reglas de la negación en sistemas de secuentes diferentes al que Beall presupone. La segunda razón establece que la negación no tiene que ser excluyente o (...) exhaustiva. (shrink)

A very natural and philosophically important subclassical logic is FDE. This account of logical consequence can be seen as going beyond the standard two-valued account to a four-valued account. A natural question arises: What account of logical consequence arises from considering further combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different context. In this note we generalize Priest’s result to show (...) that even if one considers ordinal-many combinations of the previous values, for any ordinal, the resulting consequence relation remains FDE. (shrink)

Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.

Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some (...) questions for future research. (shrink)

The continental philosophy of non-classical logics is a relatively new field that seeks to determine whether any aspects of certain continental philosophers’ thinking can be characterized in terms of non-classical logics. Some of the main figures that have been examined so far are Martin Heidegger, Jacques Derrida, Gilles Deleuze, and François Laruelle. Although many of these studies are grounded in the writings of Graham Priest, who wrote some of the seminal texts in the field, Jc Beall’s work also features prominently (...) in a number of cases. After surveying this field and highlighting Beall’s influence within it, I claim that it can be substantially expanded by making further uses of Beall’s writings, especially ones that introduce non-classical logics in ways that are especially suitable for this particular field of study and also that discuss such topics as negation, subclassical logics, logical pluralism, and glutty futures. (shrink)

This paper investigates the meaning of restricted quantification when the embedded conditional is taken as the conditional of some first-order connexive logics. The study is carried out by checking the suitability of RQ for defining a connexive class theory, in analogy to the definition of Boolean class theory by using RQ in classical logic. Negative results are obtained for Wansing’s first-order connexive logic QC and one variant of Priest’s first-order connexive logic QP. A positive result is obtained for another variant (...) of QP. (shrink)

Priest, argues that classical reasoning can be made compatible with his preferred logical theory by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favour of the one in G. Priest, I shall argue that due to the fact that the derivability adjustment theorem holds for several logics of formal consistency, these paraconsistent logics are particularly well suited to accommodate classical reasoning by means of a version of that maxim, (...) yielding thus an enthymematic account of classical recapture. (shrink)

In this paper, I examine the deep theological faultline generated by divergent understandings of the divine attributes among two early antagonistic Muslim groups – the traditionalists (main...

In a recent series of articles, Beall has developed the view that FDE is the formal system most deserving of the honorific “Logic”. The Simple Argument for this view is a cost-benefit analysis: the view that FDE is Logic has no drawbacks and it has some benefits when compared with any of its rivals. In this paper, I argue that both premises of the Simple Argument are mistaken. I use this as an opportunity to further reflect on how such arguments (...) can be bolstered to provide more substantial and productive support for revisionary theses about Logic. (shrink)

In "Semantic paradoxes and abductive methodology", Williamson presents a new Quinean argument based on central ingredients of common pragmatism about theory choice (including logical theory, as is common). What makes it new is that, in addition to avoiding Quine's unfortunate charge of mere terminological squabble, Williamson's argument explicitly rejects at least for purposes of the argument Quine's key conservatism premise. In this paper I do two things. First, I argue that Williamson's new Quinean argument implicitly relies on Quine's conservatism principle. (...) Second, by way of answering his charges against nonclassical logic I directly defend a particular subclassical account of logical consequence. (shrink)

Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is (...) substructural. It is presented as a dialogue for the simple reason that it summarizes a range of dialogues on this subject that the author has had with various folks over the past few years. The method I use to investigate the toolkit is inspired in both philosophical and technical details by Alasdair Urquhart’s work on semantics for relevance logics from the early 1970s. (shrink)