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)

Deleuze never explicitly formulates his philosophy of logical truth‐values. It thus remains an open question as to the number and types he held there to be. Despite his explicit comments on these matters, additional textual evidence suggests that in his thinking on the event, he favored a third truth‐value, holding either the analetheic view that some truth‐bearers can be truth‐valueless or the dialetheic view that some truth‐bearers can be both true and false. I first argue that taking a logical approach (...) to Deleuze's thinking is feasible, despite his and others' claims that might suggest otherwise. Next, I examine his explicit statements to show that they cannot be taken at face value and that, rather, we need to transpose his claims into contemporary terminology in order to accurately assess them. I lastly turn to his Leibniz‐inspired philosophy of time to argue that the affirmations involved in this conception strongly suggest a dialetheic tendency in his thinking. (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)

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)

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)

'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

We observe that Jc Beall’s shrieking and shrugging strategy gives us an opportunity to reflect on the Australian plan for negation in FDE, a basic subclassical logic that is used in Beall’s argument for subclassical logics. An implication of our observation is applied to a recent defense of the Australian plan for negation by Francesco Berto and Greg Restall.

What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I argue, requires that (...) thinkers have general abilities to respond to support and tension among their thoughts. And these abilities are constituted by following logical rules. So thinkers have to follow logical rules. But there isn’t just one correct logic for thinking. I show that my view is consistent with logical pluralism: there are a range of correct logics, any one of which a thinker might follow. A logic for thinking does, however, have to contain certain minimal principles: Modus Ponens and Non-Contradiction, and perhaps others. We follow logical rules by exercising logical capacities, which display a distinctive first-person/third-person asymmetry: a subject can find the instances of a rule compelling without seeing them as instances of a rule. As a result, there are two limits on illogical thinking. First, thinkers have to tend to find instances of logical rules compelling. Second, thinkers can’t think in obviously illogical ways. So thinking has to be logical – but not perfectly so. When we try to think, but fail, we produce nonsense. But our failures to think are often subjectively indistinguishable from thinking. To explain how this occurs, I offer an account of nonsense. To be under the illusion that some nonsense makes sense is to enter a pretence that the nonsense is meaningful. Our use of nonsense within the pretence relies on the role of logical form in understanding. Finally, while the normativity of logic doesn’t fall directly out of logical constitutivism, it’s possible to build an attractive account of logical normativity which has logical constitutivism as an integral part. I argue that thinking is necessary for human flourishing, and that this is the source of logical normativity. (shrink)

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

The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between (...) logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one consequence relation as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation. (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)

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)

There is a strong case to be made for thinking that an obscure logic, KR, is better than classical logic and better than any relevant logic. The argument for KR over relevant logics is that KR counts disjunctive syllogism valid, and this is the biggest complaint about relevant logics. The argument for KR over classical logic depends on the normativity of logic and the paradoxes of implication. The paradoxes of implication are taken by relevant logicians to justify relevant logic, but (...) considerations on the normativity of logic show that only some of the paradoxes of implication are genuine. KR avoids all the genuine paradoxes of implication, unlike classical logic. Overall, KR avoids the genuine paradoxes of implication and avoids the major objection to relevant logics. This combination of features provides strong reason to give KR a place in the conversation about the right logic. (shrink)

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)

In this paper, I respond to what I have called an epistemological objection to a dialetheist approach to the doctrine of the Incarnation, of which one example is Beall’s contradictory Christ. I discuss Anderson’s book Paradox in Christian theology, in which the author claims to account for the rationality of the doctrine of the Incarnation as a merely apparently contradictory doctrine, and I present my model, based on Anderson’s model, according to which the doctrine has the possibility to be rational (...) by understanding it as genuinely contradictory. I show that this model fits perfectly well with the criteria that, according to Anderson, any model for the rationality of a paradoxical doctrine should meet. Beall does not address the problem of the rationality of the doctrine in his works about the contradictory Christ, and he asserts that he is not interested in it. However, I think that if he wants to make his theory more robust, less suspicious, and more convincing for theologians, philosophers, and ordinary people, he should consider this problem. (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)

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)

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.

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.

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 is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...) to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems. (shrink)

The idea of classical recapture has played a prominent role for non-classical logicians. In the specific case of non-classical theories of truth, although we know that it is not possible to retain classical logic for every statement involving the truth predicate, it is clear that for many such statements this is in principle feasible, and even desirable. What is not entirely obvious or well-known is how far this idea can be pushed. Can the non-classical theorist retain classical logic for every (...) non-paradoxical statement? If not, is she forced to settle for a very weak form of Classical Recapture, or are there robust versions of classical recapture available to her? These are the main questions that I will address in this paper. As a test case I will consider a paracomplete account of the truth-theoretic paradoxes and I will argue for two claims. First, that it is not possible to retain the law of excluded middle for every non-paradoxical statement. Secondly, that there are no robust versions of classical recapture available to the paracomplete logician. (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)

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 his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that (...) Beall should consider another weaker subclassical logic as the logic adequate for his project. To this end, we first briefly present Beall’s argument for FDE. Then, we discuss two specific topics that seem to motivate us to weaken FDE. We then introduce a subsystem that will enjoy all the benefits of Beall’s suggestion. (shrink)

The relationship between logics with sets of theorems including contradictions (“inconsistent logics”) and theories closed under such logics is investigated. It is noted that if we take “theories” to be defined in terms of deductive closure understood in a way somewhat different from the standard, Tarskian, one, inconsistent logics can have consistent theories. That is, we can find some sets of formulas the closure of which under some inconsistent logic need not contain any contradictions. We prove this in a general (...) setting for a family of relevant connexive logics, extract the essential features of the proof in order to obtain a sufficient condition for the consistency of a theory in arbitrary logics, and finally consider some concrete examples of consistent mathematical theories in Abelian logic. The upshot is that on this way of understanding deductive closure, common to relevant logics, there is a rich and interesting kind of interaction between inconsistent logics and their theories. We argue that this suggests an important avenue for investigation of inconsistent logics, from both a technical and a philosophical perspective. (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)