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The aim of this article is to show that, just as in recent years Cobreros, Egré, Ripley and van Rooij have provided a non-transitive counterpart of classical logic (i.e. one in which all classically acceptable inferences are valid but Cut and other metainferences are not), the same can be done for every Tarskian logic, with full generality. To establish this fact, a semantic approach is taken by showing that appropriate structures can be devised to characterize a non-transitive counterpart of every Tarskian logic, starting from the logical matrices that are usually taken to render them. [ABSTRACT FROM AUTHOR]

We investigate the class of all pure three-valued logics that result from choosing the eight subsets of |$\{0, 1, \frac {1}{2}\}$| as designated values on the strong Kleene schema, including the sets that are not (order) filters. We present some of their main characteristics and show some formal relations between these logics. We also suggest a recipe to build philosophical interpretations for most of these logics and show why it is not easy to apply this account to the last two logics in the list. [ABSTRACT FROM AUTHOR]

This paper discusses two revisionary views about substructurality. The first attempts to reduce the structural features of a logic to properties of its logical vocabulary. It will be found to be untenable. The second aims to separate the structural features of a logic from the properties of logical consequence and to reinterpreted them as sui generis proof resources. I will argue that it is a viable path for a renewed understanding of substructurality. [ABSTRACT FROM AUTHOR]

Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is 'semantically laden' and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in general and Frege's philosophy in particular. [ABSTRACT FROM AUTHOR]

This article presents and discusses a prima facie counterexample to modus ponens. To appropriately theorize the case, I argue for conceptualizing the notions of logical consequence and logical commitment in "normative" terms, so that logical commitment does not attach to the premises of a spurious dominance argument—and, more generally, does not attach to unreasonable decision states, or to syntactically specified classes thereof. I also suggest that there is a logical motivation for the restriction to "well-formed" decision states that is characteristic of Savage-style logics of decision. [ABSTRACT FROM AUTHOR]

Aristotle's notion of deduction (syllogism) differs from the conception of logical consequence in classical logic in two essential features, which are required by Aristotle's definition of syllogism and are incorporated into his formalisation of deduction: in addition to the standard necessary truth-preservation, Aristotle requires relevance of premises for the conclusion and non-repetition of premises in the conclusion. These requirements, together with Aristotle's conception of simple propositions, lead to the result that valid deductive steps (syllogisms) must have very specific forms, namely the well-known syllogistic shape. All other kinds of deduction lacking this shape, such as "syllogisms based on a hypothesis", can be considered "syllogisms" only in a relative sense: they are based on an assumption of the existence of genuine syllogistic deductions in the syllogistic shape. Aristotle's demands should cover all kinds of deduction: all valid deduction must be relevant and non-repetitive. This brings Aristotle's definition much closer to the intuition associated with the notion of logical consequence. [ABSTRACT FROM AUTHOR]

One of the solutions to Bernardete’s paradox and a number of analogous paradoxes is based on the idea that there is a special type of causality — logical causality. This solution was proposed by Hawthorne and modified by Uzquiano. The paper presents a criticism on it. I put forward objections against Uzquiano’s modification of Hawthorne theory as well as against the very idea of logical causality. The conclusion is to the effect that, unless other reasons for the idea of logical causality are present, this idea either is trivial or lacks sufficient reason.

We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as infinitely many ways that a sentence might receive both classical truth values in the latter. In order to obtain deductive systems that are very nearly classical, we need to utilize different conditionals (and different negations) in each logic. [ABSTRACT FROM AUTHOR]

According to Tarski's model-theoretic analysis of logical consequence, the sentence X is a logical consequence of a set of sentences Γ if and only if any model for Γ is also a model for X. Etchemendy, however, does not accept the analysis and critiques it. According to Etchemendy, Tarski’s analysis 1- involves a conceptual mistake: confusing the symptoms of logical consequence with their cause; 2- cannot properly explain the necessity of logical consequence; 3- faces the problem of overgeneration; and 4- faces the problem of undergeneration. In the present article, by evaluating these critiques and examining the effectiveness of some of the answers presented in defense of Tarski's analysis, we try to show that among these critiques, only the problem of undergeneration is not acceptable. According to our common sense understanding, if an argument is valid, it is truth-preserving, and by assuming the truth of the premises, the conclusion will be true as well. But it does not mean that we can reduce the logical consequence relation to truth preservation. This flaw leads Tarski’s analysis to be an unacceptable analysis of logical consequence.

This paper sharpens the distinction between inferential and logcon arguments. Inferential arguments represent possible inferences, logcon ones need not. This distinction clarifies the roles that arguments play in accounting for the normativity of validity for inferential reasoning and in establishing the theoretical connection between validity and logical consequence. There are two related takeaways. First, the normativity of validity for inferential reasoning is grounded on the notion of an inferential argument. This will account for the use of validity to judge inference in the face of well‐known skepticism that a theory of validity has any special relevance to inferential reasoning. Second, a valid logcon argument needn't be an inferential argument. Accordingly, the normativity of validity for inferential reasoning doesn't require that every valid logcon argument be an inferential argument. The takeaways harmonize the use of validity to evaluate inferential reasoning with the use of the concept of logical consequence to characterize validity. [ABSTRACT FROM AUTHOR]

This paper proves a precisification of Hume's Law—the thesis that one cannot get an ought from an is—as an instance of a more general theorem which establishes several other philosophically interesting, though less controversial, barriers to logical consequence. [ABSTRACT FROM AUTHOR]

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction (e.g. ‘Snow is white. Grass is green. Therefore, snow is white and grass is green’) and Identity (e.g. ‘Snow is white. Therefore, snow is white’). 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 (SOPL), designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. [ABSTRACT FROM AUTHOR]

Classical and intuitionistic logic both validate Ex Contradictione Quodlibet (ECQ), according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil (ECN). It addresses the key arguments – model-theoretic, proof-theoretic, meaning theoretic and holist – deployed by proponents of ECQ against their standard opponents, and shows that each can be defeated from a position of support for ECN. In the course of answering these arguments, some understanding is developed of possible motivations for ECN and a solid case is built that ECN deserves further investigation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 (and hence methodologically idle) 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 (and thus immune to Quinean criticism of basing logic on explicit conventions). 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 (independent of us) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper clarifies, revises, and extends the account of the transmission of truthmakers by core proofs that was set out in chap. 9 of Tennant (2017). Brauer provided two kinds of example making clear the need for this. Unlike Brouwer's counterexamples to excluded middle, the examples of Brauer that we are dealing with here establish the need for appeals to excluded middle when applying, to the problem of truthmaker-transmission, the already classical metalinguistic theory of model-relative evaluations. [ABSTRACT FROM AUTHOR]

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.

In this paper, we evaluate Button's claim that knot is a nasty connective. Knot's nastiness is due to the fact that, when one extends the set { ¬ , ∨ , ∧ , → } with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk's nastiness, knot's nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as validity-preserving, we are inclined to conclude that there, knot is not that nasty. However, since motivating non-reflexivity is harder than motivating non-transitivity, we also acknowledge that disagreement with our conclusion is possible. [ABSTRACT FROM AUTHOR]

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but also on what we call Gentzen-regular connectives (including negation, conjunction, and disjunction). For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations. [ABSTRACT FROM AUTHOR]

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper. [ABSTRACT FROM AUTHOR]

Standard definitions of logical consequence for formal languages are atomistic. They take as their starting point a range of possible assignments of semantic values to the extralogical atomic constituents of the language, each of which generates a unique truth value for each sentence. In modal logic, these possible assignments of semantic values are generated by Kripke-style models involving possible worlds and an accessibility relation. In first-order logic, they involve the standard structures of model theory, as sets of objects from which the extralogical symbols of the language receive their denotations. I argue that there is an alternative, holistic, approach to the task of defining logical consequence for a formal language. It specifies necessary and sufficient conditions for an assignment of truth values to all the sentences of the language to be compatible with the intended interpretation of its logical constants. It achieves this without invoking possible assignments of semantic values to the extralogical atomic constituents of the language, or the formal resources that are employed to generate these. I show how this approach can be successfully applied to modal propositional logic and to first-order logic, modal as well as nonmodal. I show that the holistic definitions of logical consequence that I supply for these languages are equivalent to the standard atomistic definitions. [ABSTRACT FROM AUTHOR]

In this paper, I try to find a way of dissolving the tension existing between logical pluralism and the normative status of logic. To do this, on the one hand, regarding the normative status of logic, I defend an externalist perspective of normativity as long as logic has a normative role for social practices of rational interaction. On the other hand, regarding the nature of logic, I argue that logic is the result of a process of reflective equilibrium; logical laws are obtained from a process of mutual adjustment and adaptation with argumentative practices. Therefore, different processes of reflective equilibrium give rise to different logical systems. I show that this externalist characterization of the normativity of logic in conjunction with the thesis of reflective equilibrium enables to defend a version of logical pluralism that doesn't enter into conflict with the normativity. [ABSTRACT FROM AUTHOR]

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends not on logic's normativity but on epistemic goals. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

What does it mean that some proposition follows from others? The standard way of spelling out the notion proceeds in modal terms: x follows from y iff necessarily, if y is true, so is x. But although this yields a useful and manageable account of consequence, it fails to capture certain aspects of our pre-theoretical understanding of consequence. In this paper, an alternative notion of logical consequence, based on the idea of grounding, is developed. [ABSTRACT FROM AUTHOR]

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Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. [ABSTRACT FROM AUTHOR]

Copyright of Análisis Filosófico is the property of Sociedad Argentina de Analisis Filosofico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the logical role is merely descriptive. In this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. [ABSTRACT FROM AUTHOR]

In this article, I consider Kant’s dichotomy between general and transcendental logic in light of a retrospective reconstruction of two approaches originating in 14th century scholasticism that are used to demarcate formal and material consequences. The first approach (e. g., John Buridan, Albert of Saxony, Marsilius of Inghen) holds that a consequence is formal if it is valid — because of its form only — for any matter. Since the matter of a consequence is linked to categorematic terms, its formal validity is defined as being invariant under substitutions for such terms. According to the second approach (e. g., Richard Billingham, Robert Fland, Ralph Strode, Richard Lavenham), the validity of a formal consequence stems from the formal understanding of the consequent in the consequence’s antecedent. I put forward the hypothesis that in his logical taxo­nomy, Kant attempted to reconcile the substitutional interpretation of formal consequences and a formal analysis of the transcendental relations of objects of experience. However, if we interpret the limi­tations imposed by transcendental logic on the power of judgement in the spirit of the scholastic ontology of transcendental relations, it would contradict Kant’s critique of dogmatic ontology. Following in Luciano Floridi’s path, I thus propose to consider transcendental logic, not as a system of consequences equipped with ontologically grounded transcendental limitations, but rather as the logic of design. The logic of design has the benefit of enriching traditional logical tools with a series of notions borrowed primarily from computer programming. A conceptual system designer sets out feasibility requirements and defines a system’s functions that make it possible to achieve the desired outcome using available resources. Kant’s project forbids a dogmatic appeal to the transcendental relations and eternal truths of scholasticism. However, the constitutive nature of the rules of transcendental logic in regard to the power of judgement precludes the pluralism of conceptual systems that can be interpreted within possible experience. Thus, the optimisation problem of finding the best conceptual design from all feasible designs is beyond the competence of transcendental logic.

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and how we ought to reason, so that pluralism about the consequence relation would result in an incoherent or unattractive pluralism about those things. In this paper I argue that logic isn't normative. I distinguish three different ways in which a theory – such as a logical theory – can be entangled with the normative and argue that logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own. I use this view to show what is wrong with three different arguments for the conclusion that logic is normative. [ABSTRACT FROM AUTHOR]