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)

By playing a crucial role in settling open issues in the philosophical debate about logical consequence, logical evidence has become the holy grail of inquirers investigating the domain of logic. However, despite its indispensable role in this endeavor, logical evidence has retained an aura of mystery. Indeed, there seems to be a great disharmony in conceiving the correct nature and scope of logical evidence among philosophers. In this paper, I examine four widespread conceptions of logical evidence to argue that all (...) should be reconsidered. First, I argue that logical apriorists are more tolerant of logical evidence than empiricists. Second, I argue that evidence for logic should not be read out of natural language. Third, I argue that if logical intuitions are to count as logical evidence, then their evidential content must not be propositional. Finally, I argue that the empiricist proposal of treating experts' judgments as evidence suffers from the same problems as the rationalist conception. (shrink)

This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked in most discussions on (...) the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism. (shrink)

Inferentialism has brought important insights into the nature of meanings. It breaks with the representationalist tradition that sees meanings as constituted primarily by representing some extra-linguistic reality. Yet the break with tradition should be pursued further. Inferentialists still regard meanings as static, and they still do not entirely abandon the idea of fully determined meaning. Following Davidon’s ideas about meanings as constituted only in the course of a specific conversation, I propose a dynamic account of what meanings are. They are (...) described as entities belonging to the dynamic realm of Henri Bergson’s duration. The inhabitants of this realm live in constant movement and development which is more essential to them than the stages that this development goes through. My account brings about a rejection of the notion of the strict literal meaning and therewith also of the contrasting notions such as ambiguity. Meaning is understood as a dynamic entity that is characterized rather by its history than by its nature. (shrink)

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

Western contemporary logic has been used to advance the field of Islamic philosophical theology, which historically utilised Aristotelian-Avicennian logic, on grounds of there being an inherent normativity in logic. This is in spite of the surrounding controversy on the status of logic in the Islamic theological tradition. The normative authority of logic means that it influences the content of what we ought to believe and how we ought to revise those beliefs. This paper seeks to demonstrate that, notwithstanding the incompatible (...) differences between the two systems, the underlying feature of both Western contemporary logic and Aristotelian- Avicennian logic is logical normativity. It then argues that an inherent normativity of logic in the Islamic theological/philosophical tradition is unmotivated. Instead, it proposes to reinstate logic as anti-exceptional within the Islamic theological/philosophical tradition as a viable alternative. (shrink)

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...) logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction. (shrink)

Zapadna suvremena logika korištena je za unapređenje islamske filozofske teologije, koja je povijesno koristila aristotelovsko-avicenovsku logiku, na temelju toga što se logika shvaćala kao inherentno normativna. To je usprkos kontroverzama o statusu logike u islamskoj teološkoj tradiciji. Normativni autoritet logike znači da ona utječe na sadržaj onoga u što bismo trebali vjerovati i na to kako bismo trebali revidirati ta uvjerenja. Ovaj rad nastoji pokazati da je, bez obzira na nekompatibilne razlike između dvaju sustava, temeljna značajka zapadne suvremene logike i (...) aristotelovsko-avicenovske logike njihova normativnost. Zatim se tvrdi da je inherentna normativnost logike u islamskoj teološkoj/filozofskoj tradiciji nemotivirana. Umjesto toga, kao održivu alternativu rad predlaže ponovno uspostavljanje logike kao anti-ekscepcionalističke unutar islamske teološke/filozofske tradicije. (shrink)

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should be replaced (...) by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (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)

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

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (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)

_T__S_ is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce _T__S_ _ω_, a logic without metainferential validities. Notwithstanding, _T__S_ _ω_ is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [_T__S_ _ω_, _S__T_ _ω_ ], a logic without validities and antivalidities. Nevertheless, [_T__S_ _ω_, _S__T_ _ω_ ] is still informative, because it has many contingencies. The three-standard logic [ \(\mathbf {TS}_{\omega (...) }, \mathbf {ST}_{\omega }, [{\overline {\emptyset }}{\emptyset }, {\emptyset } {\overline {\emptyset }}]\) ] that we will further introduce, has no validities, no antivalidities and also no contingencies whatsoever. We will also present two more validity-empty logics. The first one has no supersatisfiabilities, unsatisfabilities and antivalidities ∗. The second one has no invalidities nor non-valid-nor-invalid (meta)inferences. All these considerations justify thinking of logics as, at least, three-standard entities, corresponding, respectively, to what someone who takes that logic as correct, accepts, rejects and suspends judgement about, just because those things are, respectively, validities, antivalidities and contingencies of that logic. Finally, we will present some consequences of this setting for the monism/pluralism/nihilism debate, and show how nihilism and monism, on one hand, and nihilism and pluralism, on the other hand, may reconcile—at least according to how Gillian Russell understands nihilism, and provide some general reasons for adopting a multi-standard approach to logics. (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)

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)

According to a widely shared generic conception of inferential justification—‘the standard conception’—an agent is inferentially justified in believing that p only if she has antecedently justified beliefs in all the non-redundant premises of a good argument for p. This conception tends to serve as the starting-point in contemporary debates about the nature and scope of inferential justification: as neutral common ground between various competing, more specific, conceptions. But it’s a deeply problematic starting-point. This paper explores three questions that haven’t been (...) given the attention they deserve, that complicate the application of the standard conception to cases, and that reveal it to be underspecified at the core—in ways that aren’t resolved but inherited by more specific (extant) versions of it. The goal isn’t to answer the questions, but to articulate them, explain what turns on them, and invite a critical re-examination of the standard conception. (shrink)

Logical pluralism is the view that there is more than one right logic. A particular version of the view, what is sometimes called domain-specific logical pluralism, has it that the right logic and connectives depend somehow on the domain of use, or context of use, or the linguistic framework. This type of view has a problem with cross-framework communication, though: it seems that all such communication turns into merely verbal disputes. If two people approach the same domain with different logics (...) as their guide, then they may be using different connectives, and hence talking past each other. In this situation, if we think we are having a conversation about “¬A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lnot A$$\end{document}”, but are using different “¬\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lnot $$\end{document}”s, then we are not really talking about the same thing. The communication problem prevents legitimate disagreements about logic, which is a bad result. In this paper I articulate a possible solution to this problem, without giving up pluralism, which requires adopting a notion of metalinguistic negotiation, and allows people to communicate and disagree across domains/contexts/frameworks. (shrink)

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds (...) that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)

As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one (...) can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens. (shrink)

In support of logical nihilism, according to which there are no logical laws, Gillian Russell offers purported counterexamples to two laws of logic. Russell’s examples rely on cleverly constructed predicates not found in ordinary English. I show that similar apparent counterexamples to the same logical laws can be constructed without exotic predicates but using only what ordinary language provides. We correctly analyze such arguments so that they do not actually constitute counterexamples to any logic laws. I claim that we can (...) and should do the same for Russell’s arguments. (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)

I offer here a critical assessment of Beall and Ficara’s most recent take on Hegelian contradictions. By interpreting differently some key passages of Hegel’s work, I favor, unlike them, a no-gaps approach which leads to a different logic.

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.

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)

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)

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)