This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. I provide a counter-example to epistemic closure for reductio proofs. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

The anti-exceptionalist debate brought into play the problem of what are the relevant data for logical theories and how such data affects the validities accepted by a logical theory. In the present paper, I depart from Laudan's reticulated model of science to analyze one aspect of this problem, namely of the role of logical data within the process of revision of logical theories. For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of several (...) distinct methodologies for logical theories. The resulting picture is coherent with the Laudanean view that agreement and disagreement between scientific theories take place at different levels. From this perspective, one is able to articulate other kinds of divergence that considers not only the inferential aspects of a given logical theory, but also the epistemic aims and the methodological choices that drive its development. (shrink)

Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations for (...) an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem, and explore some versions of anti-exceptionalism about abstraction. I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V. I finally consider how the abstractionist can compare between competing criteria, and argue that anti-exceptionalists should be pluralists about abstraction. (shrink)

Philosophical arguments usually are and nearly always should be abductive. Across many areas, philosophers are starting to recognize that often the best we can do in theorizing some phenomena is put forward our best overall account of it, warts and all. This is especially true in esoteric areas like logic, aesthetics, mathematics, and morality where the data to be explained is often based in our stubborn intuitions. -/- While this methodological shift is welcome, it's not without problems. Abductive arguments involve (...) significant theoretical resources which themselves can be part of what's being disputed. This means that we will sometimes find otherwise good arguments which suggest their own grounds are problematic. In particular, sometimes revising our beliefs on the basis of such an argument can undermine the very justification we used in that argument. -/- This feature, which I'll call self-effacingness, occurs most dramatically in arguments against our standing views on the esoteric subject matters mentioned above: logic, mathematics, aesthetics, and morality. This is because these subject matters all play a role in how we reason abductively. This isn't an idle fact; we can resist some challenges to our standing beliefs about these subject matters exactly because the challenges are self-effacing. The self-effacing character of certain arguments is thus both a benefit and limitation of the abductive turn and deserves serious attention. I aim to give it the attention it deserves. (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)

I investigate syntactic notions of theoretical equivalence between logical theories and a recent objection thereto. I show that this recent criticism of syntactic accounts, as extensionally inadequate, is unwarranted by developing an account which is plausibly extensionally adequate and more philosophically motivated. This is important for recent anti-exceptionalist treatments of logic since syntactic accounts require less theoretical baggage than semantic accounts.

Anti-realism about the foundations of logic are curiously absent from the literature. This is especially striking given natural analogies with moral anti-realis.

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

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 is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the (...) meta-rules impose unreasonable cognitive demands on reasoning and underestimate her challenge. (shrink)

The debate between exceptionalists and anti-exceptionalists about logic is often framed as concerning whether the justification of logical theories is a priori or a posteriori (for short: whether logic is a priori or a posteriori). As we substantiate (S1), this framing more deeply encodes the usual anti-exceptionalist thesis that logical theories, like scientific theories, are abductively justified, coupled with the common supposition that abduction is an a posteriori mode of inference, in the sense that the epistemic value of abduction is (...) (and, indeed, must be) a posteriori. In past work, however, we have argued that this common supposition is incorrect: abduction is an a priori mode of inference, in the sense that the epistemic value of abduction is (and indeed, must be) a priori (Biggs and Wilson 2017a, 2017b, 2019). After sketching our two main argumentative strategies for this conclusion (S2), we go on (S3) to consider its import on the proper understanding of anti-exceptionalism about logic. (shrink)

Many advocates of non-classical logic for reasons external to mathematics claim that their proposed revisions are consistent with the use of classical logic within pure mathematics. Doubts are raised about such claims, concerning the applicability of pure mathematics to natural and social science. -/- .

_ doi:10.1093/analys/anx072 _, published: 27 June 2017.

Anti-exceptionalism about logic takes logical theories to be continuous with scientific theories. Scientific theories are subject to criteria of theoretical equivalence. This article compares two types of theoretical equivalence – one syntactic and one semantic – in the context of logical anti-exceptionalism, and argues that the syntactic approach leads to undesirable consequences. The anti-exceptionalist should therefore take a semantic approach when evaluating whether logical theories, understood as scientific theories, are equivalent. This article argues for a particular semantic approach, in terms (...) of categorical equivalence, to determine whether logical theories are equivalent. (shrink)

Thought: A Journal of Philosophy, EarlyView.

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)

Logical pluralism is a general idea that there is more than one correct logic. Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence. The authors appeal to this epistemic interpretation to briefly motivate a kind of logical pluralism: “different accounts of logical consequence may preserve different properties of propositions”. The aim of this paper is to study the prospect of (...) a logical pluralism based on different interpretations of logical systems. First, we give our analysis of what it means to interpret a logic – and make some hopefully useful distinctions along the way. Second, we present what we call an interpretational logical pluralism: there is more than one correct logic and a logic is correct only if it has some adequate interpretation. We consider four variants of this idea, bring up some possible objections, and try to find plausible solutions on behalf of the pluralist. We will argue that interpretations of logical systems provide a promising – albeit not unproblematic – route to logical pluralism. (shrink)

According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria. In this paper, I analyze some important discussions in the philosophy of logic, and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. (...) I argue that, rather than having a specific methodology such as abductivism, logic can be characterized by methodological pluralism. This position can also be seen as the application of scientific pluralism to the realm of logic. (shrink)

This paper compares two ways of holding that logic is special among the sciences in that it has no restricted class of entities as its subject matter, but instead concerns all entities alike. One way is Williamson’s explanation of how inquiry into logical consequence and logical truth only superficially concerns the linguistic or conceptual entities that bear these properties. Williamson draws on ideas familiar from deflationism about truth, and his account has been called “deflationary.” I argue that the analogy is (...) misleading. While there’s a broad sense in which Williamson offers a deflationary account of logical inquiry, his view differs from deflationism about truth in being best understood as a form of instrumentalism. By contrast, I elaborate a deflationism about logical properties modeled on deflationism about truth. I defend this expressive device deflationism as an explanation of our use of logical predicates. (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)

A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good (...) Company Problem for neo-logicists recently raised by Paolo Mancosu (2016), concerning the existence of rival abstractive definitions of cardinal number which are nonetheless equally able to reconstruct Peano Arithmetic. We survey Mancosu’s envisaged possible replies to this predicament, and suggest as a further path the adoption of some form of mathematical pluralism concerning abstraction principles. We then explore three possible ways of substantiating such pluralism—Conceptual Pluralism, Domain Pluralism, Pluralism about Criteria—showing how each of them can be related to analogous proposals in the philosophy of logic. We conclude by considering advantages, concerns, and theoretical ramifications for these varieties of mathematical pluralism. (shrink)

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum (...) logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages. (shrink)

The background of this paper (section 1) consists in a new account to foundation‐theoretic epistemology characterized by two features: (i) All beliefs are to be justified by deductive, inductive or abductive inferences from a minimalistic class of unproblematic (introspective or analytic) basic beliefs. (ii) Higher‐order justifications for these inferences are given by means of the novel method of optimality justifications. Optimality justifications are a new tool for epistemology (section 2). An optimality justification does not attempt todemonstratethat a cognitive method is (...) reliable (which is impossible), but pursues the more modest goal of demonstrating that the method isoptimalamong all accessible alternative methods for the given epistemic goal. The reasoning from the established optimality of a method to the acceptability of a particular belief generated by the method is accomplished by so‐called optimality principles. In sections 3–5, the method of optimality justifications is carried out in detail for three fundamental problems: justifying induction, logic, and theory‐generating abduction. (shrink)

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, (...) can be translated into classical logic by introducing additional intensional operators into the language. Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic. (shrink)

‘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)

This essay offers a conception of logic by which logic may be considered to be exceptional among the sciences on the backdrop of a naturalistic outlook. The conception of logic focused on emphasises the traditional role of logic as a methodology for the sciences, which distinguishes it from other sciences that are not methodological. On the proposed conception, the methodological aims of logic drive its definitions and principles, rather than the description of scientific phenomena. The notion of a methodological discipline (...) is explained as a relation between disciplines or practices. Logic serves as a methodological discipline with respect to any theoretical practice, and this generality, as well as logic’s reflexive nature, distinguish it from other methodological disciplines. Finally, the evolution of model theory is taken as a case study, with a focus on its methodological role. Following recent work by John Baldwin and Juliette Kennedy, we look at model theory from its inception in the mid-twentieth century as a foundational endeavour until developments at the end of the century, where the classification of theories has taken centre-stage. (shrink)

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)

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)

Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as ‘classical recapture’. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The goal of the paper is (...) to address this problem. First, I discuss a number of different ways to characterize the idea of classical recapture and I examine how far it can be pushed. Secondly, I argue that a palatable form of classical recapture is given by the thought that classical logic can be retained for statements that are grounded (in Kripke’s sense). To substantiate this view I provide a formal fixed‐point semantics for a language containing a predicate standing for the concept of groundedness and I address a couple of objections that have been deployed against the claim that classical recapture can aid the non‐classical logician’s cause. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalism are, and they are at odds with naturalist philosophers of (...) logic, who may have seemed like natural allies. Moreover, those internal battles concern well-trodden philosophical issues, and there is no hint as to how they are to be resolved on broadly scientific grounds. We close by looking at three of the founders of logic who may have seemed like obvious enemies of anti-exceptionalism—Aristotle, Frege, and Carnap—and conclude that none of their positions is clearly at odds with at least some of the main themes of anti-exceptionalism. We submit that, at least at present, anti-exceptionalism is too vague or underspecified to characterize a coherent conception of logic, one that stands opposed to more traditional approaches. (shrink)

El objetivo del presente trabajo es evaluar si el problema de la adopción supone un obstáculo real para la revisión de la lógica. En este marco, defendemos una posición antiexcepcionalista de la lógica y examinamos la posibilidad de modificar las prácticas inferenciales a raíz de una modificación en la teoría lógica. Aun cediendo el punto central del problema, argumentamos que no solo puede salvaguardarse la posibilidad de modificar racionalmente nuestra teoría lógica, sino también la de razonar deductivamente siguiendo nuevos patrones (...) inferenciales. Es decir, consideramos que el dilema kripkeano alcanza únicamente para rechazar la posibilidad de adoptar ciertos principios lógicos, así como de razonar de acuerdo a ellos según una noción específica de “adopción”, pero no anula la posibilidad de adquirirlos mediante otros mecanismos a los que llamamos “adquisición por inmersión” y “adquisición por decodificación”. (shrink)

Anti-exceptionalism about logic is the doctrine that logic does not require its own epistemology, for its methods are continuous with those of science. Although most recently urged by Williamson, the idea goes back at least to Lakatos, who wanted to adapt Popper's falsicationism and extend it not only to mathematics but to logic as well. But one needs to be careful here to distinguish the empirical from the a posteriori. Lakatos coined the term 'quasi-empirical' `for the counterinstances to putative mathematical (...) and logical theses. Mathematics and logic may both be a posteriori, but it does not follow that they are empirical. Indeed, as Williamson has demonstrated, what counts as empirical knowledge, and the role of experience in acquiring knowledge, are both unclear. Moreover, knowledge, even of necessary truths, is fallible. Nonetheless, logical consequence holds in virtue of the meaning of the logical terms, just as consequence in general holds in virtue of the meanings of the concepts involved; and so logic is both analytic and necessary. In this respect, it is exceptional. But its methodologyand its epistemology are the same as those of mathematics and science in being fallibilist, and counterexamples to seemingly analytic truths are as likely as those in any scientic endeavour. What is needed is a new account of the evidential basis of knowledge, one which is, perhaps surprisingly, found in Aristotle. (shrink)

In this paper we put forward and defend a view of the nature of logic that we call moderate anti-exceptionalism. In the first part of the paper we focus on the problem of genuine logical validity and consequence. We make use of examples from current debates to show that attempts to pinpoint the one and only authentic logic inevitably either yield irrefutable theories or lead to dead ends. We then outline a thoroughly naturalist account of logical consequence as grounded in (...) rules implicit in human linguistic practices. We insist that there are only two existing kinds of language: natural languages, and artificial languages that have been forged by us. There is thus no room for a "genuine" language and hence for "genuine" logic. We conclude that though logical theories are established—and are liable to criticism—in a similar fashion as those of the sciences, and in this sense logic is not exceptional, to fulfill its mission logic must lay a claim to normative authority over our argumentation and reasoning, which makes its methodology somewhat special. Logical theory is not meant to provide just an explanation, the standards it establishes serve also as a tool, providing for a reinforcement of our rational communication. (shrink)

Se aborda la cuestión de la racionalidad desde la justificación de la lógica, considerando la existencia de sistemas alternativos. Delimito este tema a la justificación de nuestros criterios de racionalidad, centrándome en la racionalidad inferencial. Ante esto, sugiero una solución a posteriori para reconocer sistemas lógicos como razonables, dada la inexistencia de una noción infalible de racionalidad. Esta propuesta es pluralista, reconociendo múltiples sistemas válidos, y normativa, estableciendo que no todos tienen el mismo valor: algunos son más aptos para inferencias (...) que otros. (shrink)

Anti-exceptionalists about logic maintain that it is continuous with the empirical sciences. Taking anti-exceptionalism for granted, we argue that traditional approaches to explanation are inadequate in the case of logic. We argue that Andrea Woody's functional analysis of explanation is a better fit with logical practice and accounts better for the explanatory role of logical theories.

As a response to the semantic and logical paradoxes, theorists often reject some principles of classical logic. However, classical logic is entangled with mathematics, and giving up mathematics is too high a price to pay, even for nonclassical theorists. The so-called recapture theorems come to the rescue. When reasoning with concepts such as truth/class membership/property instantiation, (These are examples of concepts that are taken to satisfy naive rules such as the naive truth schema and naive comprehension, and that therefore are (...) compatible with a solution to paradox cast in the logics considered below. Other notions of similar kind can be added to the list.) if one is interested in consequences of the theory that only contain mathematical vocabulary, nothing is lost by reasoning in the nonclassical framework. This article shows that this claim is highly misleading, if not simply false. Under natural assumptions, some well-established approaches to recapture are incorrect. (shrink)

Drawing on the epistemology of logic literature on anti-exceptionalism about logic, we set out to investigate the following metaphilosophical questions empirically: Is philosophy special? Are its methods (dis)continuous with science? More specifically, we test the following metaphilosophical hypotheses empirically: philosophical deductivism, philosophical inductivism, and philosophical abductivism. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we searched through a large corpus of philosophical texts mined from the JSTOR database (N = 435,703) to find patterns of (...) argumentation. The results of our quantitative, corpus-based study suggest that deductive arguments are significantly more common than abductive arguments and inductive arguments in philosophical texts overall, but they are gradually and steadily giving way to non-deductive (i.e. inductive and abductive) arguments in academic philosophy. (shrink)

The most serious objection to Beall and Restall’s case-based logical pluralism is the so-called collapse argument. According to the collapse argument, logical pluralism is not genuinely pluralistic and collapses into a single privileged relation of logical consequence. In response, Caret offered an account of logical contextualism that supposedly maintains the merits of Beall and Restall’s case-based logical pluralism while circumventing the collapse argument. In this paper, I first point out a gap in the collapse argument in that it does not (...) affect pluralists who assume that there is no uniquely strongest admissible consequence relation. This gap, then, is closed by an improved version of the collapse argument, which makes use of Eklund’s classification of types of pluralism. Finally, I discuss how Caret’s logical contextualism cannot hold up against this new formulation of the collapse argument unless implausible assumptions about the contents of normative operators are made. Moreover, by reformulating the collapse argument, I determine the extent to which logical monism and pluralism oppose each other, paving the way for fruitful future discussion. (shrink)

Philosophers of science often assume that logically equivalent theories are theoretically equivalent. I argue that two theses, anti-exceptionalism about logic (which says, roughly, that logic is not a priori, that it is revisable, and that it is not special or set apart from other human inquiry) and logical realism (which says, roughly, that differences in logic reflect genuine metaphysical differences in the world), make trouble for both this commitment and the closely related commitment to theories being closed under logical consequence. (...) I provide three arguments. The first two show that anti-exceptionalism about logic provides an epistemic challenge to both the closure and the equivalence claims; the third shows that logical realism provides a metaphysical challenge to both the closure and the equivalence claims. Along the way, I show that there are important methodological upshots for metaphysicians and philosophers of logic. In particular, there are lessons to be drawn about certain conceptions of naturalism as constraining the possibilities for metaphysics and the philosophy of logic. (shrink)

Abstract‘Logical Realism’ is taken to mean many different things. I argue that if reality has a privileged structure, then a view I call metaphysical logical realism is true. The view says that, first, there is ‘One True Logic’; second, that the One True Logic is made true by the mind‐and‐language‐independent world; and third, that the mind‐and‐language‐independent world makes it the case that the One True Logic is better than any other logic at capturing the structure of reality. Along the way, (...) I discuss a few alternatives, and clarify two distinct kinds of metaphysical logical realism. (shrink)

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two (...) uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation. (shrink)

Given the plethora of competing logical theories of validity available, it’s understandable that there has been a marked increase in interest in logical epistemology within the literature. If we are to choose between these logical theories, we require a good understanding of the suitable criteria we ought to judge according to. However, so far there’s been a lack of appreciation of how logical practice could support an epistemology of logic. This paper aims to correct that error, by arguing for a (...) practice-based approach to logical epistemology. By looking at the types of evidence logicians actually appeal to in attempting to support their theories, we can provide a more detailed and realistic picture of logical epistemology. To demonstrate the fruitfulness of a practice-based approach, we look to a particular case of logical argumentation—the dialetheist’s arguments based upon the self-referential paradoxes—and show that the evidence appealed to support a particular theory of logical epistemology, logical abductivism. (shrink)

Many have contended that non-classical logicians have failed at providing evidence of paraconsistent logics being applicable in cases of inconsistency toleration in the sciences. With this in mind, my main concern here is methodological. I aim at addressing the question of how should we study and explain cases of inconsistent science, using paraconsistent tools, without ruining into the most common methodological mistakes. My response is divided into two main parts: first, I provide some methodological guidance on how to approach cases (...) of inconsistent science; and second, I focus on a peculiar type of formal methodologies for the scrutiny of inconsistent reasoning, the _Paraconsistent Alternative Approach_ (henceforth, PAA) and argue that PAA can enhance a more accurate understanding of sensible reasoning in inconsistent contexts. (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)

Considerable attention recently has been paid to anti-exceptionalism about logic, the thesis that logic is more similar to the sciences in important respects than traditionally thought. One of AEL’s prominent claims is that logic’s methodology is similar to that of the recognised sciences, with part of this proposal being that logics provide explanations in some sense. However, insufficient attention has been given to what this proposal amounts to, and the challenges that arise in providing an account of explanations in logic. (...) This paper clarifies these challenges, and shows how the practice-based approach is best placed to meet them. (shrink)

El Anti-Excepcionalismo Lógico afirma que la Lógica es como cualquier otra ciencia. Si esta afirmación es cierta, entonces ella no sólo es revisable, sino que además todo lo que se puede decir sobre las ciencias aplica, mutatis mutandis, para la misma. El propósito de este artículo es explorar esta consecuencia del Anti-Excepcionalismo Lógico, acercando a la Filosofía de la Lógica el marco teórico de las Máquinas Nomológicas de Nancy Cartwright. De acuerdo con esta visión, lo que hay de verdadero en (...) las teorías científicas no está en el mundo sino en sus modelos: sistemas altamente controlados, estables, artificiales y específicos, dentro de los cuales se manifiestan regularidades sistematizables y enseñables. Mi afirmación es que lo mismo puede decirse de la Lógica: ella no captura las Leyes del Pensamiento o de la Razón, porque el pensamiento y la razón no están gobernados necesariamente por leyes. Sobre lo que sí puede decirse que versan las Leyes de la Lógica son metafísicas posibles: historias acerca de qué son las proposiciones, el pensamiento, la verdad y la validez. A fin de ilustrar y defender esta tesis, presento un ejemplo de Máquina Nomológica de la Lógica Clásica, basada en una lectura original del Tractatus de Wittgenstein, e investigo algunas de sus consecuencias. Mi conclusión es que esta imagen de la Lógica impacta en el problema de la revisión de la Lógica Clásica, en la medida en que muestra que dicha revisión no necesariamente responde a un proceso racional de adecuación de la teoría a los hechos porque los “hechos” relevantes no son anteriores a la teoría misma, sino que están moldeados y conducidos por ella. Palabras clave: Anti-Excepcionalismo Lógico, Abductivismo, Máquinas Nomológicas, Revisión Lógica, Filosofía de la Lógica. (shrink)

Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean ‘logic-first’ view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rather than vice versa. In critical views of logic, by contrast, the logical principles (...) that govern some subject matter may depend on the metaphysics of this subject matter or on the semantics of our discourse about it. Space is thereby carved out between a Fregean position on the one hand and thoroughgoing holism à la Quine on the other. (shrink)

Enumeration and explanation in theories of welfare, Analysis, doi.org/10.1093/analys/anx035, published 13 April 2017.