The aim of this paper is threefold. Firstly, §1 and §2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, §3 and §4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel’s Second Incompleteness Theorem (...) it’s shown that either we must be agnostic about the consistency of Peano Arithmetic or akratic in our arithmetical theorizing. If successful, these sections will underscore the pertinence and persistence of akrasia in arithmetic (by appeal to Gödel’s seminal work). Thirdly, §5 concludes by suggesting a way of translating the dilemma of arithmetical akrasia into a case of regular epistemic akrasia; and further how one might try to escape the dilemma when it’s framed this way. (shrink)

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)

This paper discusses the Uniqueness Thesis, a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement. Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such formalizations, (...) and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be One True Logic is noncognitive. The same may be true of monism about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)

It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...) antecedents at some world, the same worlds are deemed as relevant for all occasions of utterance. But surely this is inadequate, if shifts of contexts between occasions are to be accounted for. Both the linguistic and logical implications of this defect are discussed, and in order to overcome it a modification of David Lewis’ ordering semantics for counterfactuals is developed for a modified language. I follow Lewis by letting contexts determine comparative similarity assignments, and show that the addition of syntactic context parameters (context indices) to the language gives the freedom required to switch between sets of relevant antecedent worlds from occasion to occasion by choosing the corresponding similarity assignment accordingly. Thus an account that extends Lewis’ analysis of a language containing a single counterfactual connective > to a language containing infinitely many counterfactual connectives >_c, each indexed by a different context name c, overcomes the limitations of traditional analyses. Finally it is also shown that these traditional accounts can be recovered from the modified account if certain contextual restrictions are in place. -/- . (shrink)

Talk of metaphysical modality as “absolute” is ambiguous, as it appears to convey multiple ideas. Metaphysical possibility is supposedly completely unrestricted or unqualified; metaphysical necessity is unconditional and exceptionless. Moreover, metaphysical modality is thought to be absolute in the sense that it’s real or genuine and the most objective modality: metaphysical possibility and necessity capture ways things could and must have really been. As we disentangle these ideas, certain talk of metaphysical modality qua “absolute” turns out to be misguided. Metaphysical (...) possibility isn't completely unrestricted or most inclusive compared to the other modalities; metaphysical necessity, like all kinds of necessities, is relative to or conditional upon a specific framework of reference. Still, metaphysical modality captures how things could and must have really been most generally because it deals with reality and the nature of things or their essence. That’s the chief interest of metaphysics. Arguments against the alleged absoluteness of metaphysical modality may not thereby undermine its philosophical significance. (shrink)

This paper discusses the uniqueness thesis, a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement. Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

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?

It is often remarked that first-order Peano Arithmetic is non-categorical but deductively well-behaved, while second-order Peano Arithmetic is categorical but deductively ill-behaved. This suggests that, when it comes to axiomatizations of mathematical theories, expressive power and deductive power may be orthogonal, mutually exclusive desiderata. In this paper, I turn to Hintikka’s :69–90, 1989) distinction between descriptive and deductive approaches in the foundations of mathematics to discuss the implications of this observation for the first-order logic versus second-order logic divide. The descriptive (...) approach is illustrated by Dedekind’s ‘discovery’ of the need for second-order concepts to ensure categoricity in his axiomatization of arithmetic; the deductive approach is illustrated by Frege’s Begriffsschrift project. I argue that, rather than suggesting that any use of logic in the foundations of mathematics is doomed to failure given the impossibility of combining the descriptive approach with the deductive approach, what this apparent predicament in fact indicates is that the first-order versus second-order divide may be too crude to investigate what an adequate axiomatization of arithmetic should look like. I also conclude that, insofar as there are different, equally legitimate projects one may engage in when working on the foundations of mathematics, there is no such thing as the One True Logic for this purpose; different logical systems may be adequate for different projects. (shrink)

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (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)

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)

How many correct logics are there? Monists endorse that there is one, pluralists argue for many, and nihilists claim that there are none. Reasoning about these views requires a logic. That is the meta-logic. It turns out that there are some meta-logical challenges specifically for the pluralists. I will argue that these depend on an implicitly assumed absoluteness of correct logic. Pluralists can solve the challenges by giving up on this absoluteness and instead adopt contextualism about correct logic. This contextualism (...) is naturalistically appealing. (shrink)

In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and (...) argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+. (shrink)

The article is centered on the question of how best to understand the logical pluralism/logical monism debate. A number of suggestions are brought up and rejected on the ground that they re...

In the paper the following questions are discussed: What is logical consequence? What are logical constants? What is a logical system? What is logical pluralism? What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out.

Many contemporary logicians acknowledge a plurality of logical theories and accept that theory choice is in part motivated by logical evidence. However, just as there is no agreement on logical theories, there is also no consensus on what constitutes logical evidence. In this paper, I outline Jean Piaget’s psychological theory of reasoning and show how he used it to diagnose and solve one of the paradoxes of material implication. I assess Piaget’s use of psychology as a source of evidence for (...) logical theory in light of reservations raised by psychologism, and I highlight some ramifications for exceptionalism and anti-exceptionalism about logic by considering his use of psychology as logical evidence in the framework of genetic epistemology, Piaget’s research programme. I conclude that Piaget’s psychological theory of reasoning not only plausibly serves as a source of evidence for logical theory but also makes a strong case for anti-exceptionalism about logic. (shrink)

This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The (...) present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data. (shrink)

Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form (...) of intra-theoretical logical pluralism. (shrink)

This paper addresses the question of what is distinctive about classical mathematics. The answer given is that it depends on a certain notion of conditionality, which is best understood as telling us something about the structure of the mathematics in question, and not something about the logical particle ‘if’.

Biological diversity (BD) explored by biological systematics is a complex yet organized natural phenomenon and can be partitioned into several aspects, defined naturally with reference to various causal factors structuring biota. These BD aspects are studied by particular research programs based on specific taxonomic theories (TTs). They provide, in total, a framework for comprehending the structure of biological systematics and its multi-aspect relations to other fields of biology. General principles of individualizing BD aspects and construing TTs as quasi-axiomatics are briefly (...) considered. It is stressed that each TT is characterized by a specific combination of interrelated ontological and epistemological premises most adequate to the BD aspect a TT deals with. The following contemporary research programs in systematics are recognized and characterized in brief: phenetic, rational (with several subprograms), numerical, typological (with several subprograms), biosystematic, biomorphic, phylogenetic (with several subprograms), and evo-devo. From a scientific pluralism perspective, all of these research programs, if related to naturally defined particular BD aspects, are of the same biological and scientific significance. They elaborate “locally” natural classifications that can be united by a generalized faceted classification. (shrink)

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be (...) subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-à-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth. (shrink)

1. This paper addresses the development of mutual relations between two sets of ideas in scholastic logic. First, consider the following statements: (1) It is impossible to encounter a chimera.(2)...

Logical pluralism is the view that there is more than one formal logic that correctly (or best, or legitimately) codifies the logical consequence relation in natural language. This essay provides a taxonomy of different variations on the logical pluralist theme based on a five-part structure, and then identifies an unoccupied position in this taxonomy: perspectival logical pluralism. Perspectival pluralism provides an attractive position from which to formulate a philosophy of logic from a feminist perspective (and from other, identity-based perspectives, such (...) as critical race theory). An example of how such an account might be developed is sketched. The essay concludes by defusing an obvious objection to the perspectival approach: the claim that the correct logic (or logics), in virtue of the formal nature of logic, should be independent of considerations regarding the identity of the reasoner. (shrink)

The author of “Evidence, Explanation, Enhanced Indispensability” advances a criticism to the Enhanced Indispensability Argument and the use of Inference to the Best Explanation in order to draw ontological conclusions from mathematical explanations in science. His argument relies on the availability of equivalent though competing explanations, and a pluralist stance on explanation. I discuss whether pluralism emerges as a stable position, and focus here on two main points: whether cases of equivalent explanations have been actually offered, and which ontological consequences (...) should follow from these. (shrink)

This paper points out a tension between Agustín Rayo's criteria for singulartermhood and his explicit views on the status of Hybrid Identities, that is, identity statements that use singular terms from two different Systems of Representation, such as "7=Julius Caesar" or more suggestively "I am b" where "b" is a singular term referring to my brain. It argues that non-trivial Hybrid Identities are common and important in philosophy and elsewhere, and it suggests a friendly alternative that involves treating Hybrid Identities (...) on the model of Rayo's "Just Is" statements. The last section of the paper points out that even this friendly alternative has counterintuitive consequences when combined with the metaphysical conventionalism that Rayo finds attractive, when it comes to questions of personal identity over time. (shrink)

In the original publication of the article, in Definition 4, the sixth line which reads as.