Logical Pluralism

In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations.

This paper develops and refines the suggestion that logical systems are conceptual artefacts that are the outcome of a design-process by exploring how a constructionist epistemology and meta-philosophy can be integrated within the philosophy of logic.

The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...) for belief can be captured. (shrink)

The starting point of this paper is a version of intra-theoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...) move, I explain how a natural generalisation of the notion of synonymy can be used to counter this objection, but I also show how the solution can be turned into an equally devastating ‘one logic after all’ type of objection. Finally, I propose the general diagnosis that these problems could only arise in the presence of conceptual distinctions that are too coarse to accommodate coherent pluralist theses. T.. (shrink)

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- formation (...) doesnt depend on a prior notion of meaning, but is used to naturalize meaning, and informational content is not defined relative to a pre-existing logical space, but that space is constructed relative to the level of abstraction at which information is assessed). In this paper I focus directly on one of the main ideas introduced in that paper, namely the contrast between logical discrimination and deductive strength, and use this contrast to (1) illustrate a number of open problems for an informational conception of logical consequence, (2) review its connection with the dynamic turn in logic, and (3) situate it relative to the research agenda of the philosophy of information. (shrink)

Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.

Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...) of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence. (shrink)

The paper argues that metaphysical thought, or thought in whose context our general framework of sense is under scrutiny, involves, legitimates, and requires a variety of informal analogues of the ‘true contradictions’ supported in some paraconsistent formal logics. These are what we can call informal ‘legitimate logical inadequacies’. These paradoxical logical structures also occur in deeply pluralist contexts, where more than one, conflicting general framework for sense is relevant. The paper argues further that these legitimate logical inadequacies are real or (...) inherent in sense itself rather than conventional, shows how they can feature in argumentative practice in these metaphysical and pluralist contexts, and discusses some of their implications for metaphysical truth and for philosophical inquiry and disagreement. (shrink)

My aim here is a modest one: to note another example in which the theory of validity and the theory of ‘inference’ naturally come apart. The setting is multiple-conclusion logic. At least on one philosophy of multiple-conclusion logic, there are very clear examples of where logic qua validity and logic qua normative guide to inference are essentially different things. On the given conception, logic tells us only what follows from what, what our ‘choices’ are given a set of premises; it (...) is simply silent on which, of the given ‘choices’, we select from the (conclusion) set of options. (shrink)

We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

Within the philosophy of logic there has been an old debate about strengths and weaknesses of so-called “deviant” logics, as compared to standard logic (i.e. First Order Logic with Identity). With the development of a multitude of many-valued and modal logical systems and the various ways they can be employed in various fields of philosophy, linguistics and computer science, former “deviant” logics have become well accepted. Nowadays we seem to have a new and almost contrary debate about whether there is (...) any universal logic at all or only a multitude of systems: logical pluralism. But what does logical pluralism claim? In this paper one prominent version of logical pluralism is the main target of further questions. (shrink)

With their book Logical Pluralism, Jc Beall and Greg Restall have elaborated on their previous statements on logical pluralism. Their view of logical pluralism is centred on ways of understanding logical consequence. The essay tries to come to grips with their doctrine of logical pluralism by highlighting some points that might be made clearer, and questioning the force of some of Beall’s and Restall’s central arguments. In that connection seven problems for their approach are put forth: (1) The Informal Common (...) Core Problem, (2) The Formal Common Core Problem, (3) The Superior Judge Problem, (4) The Problem of the Conditional, (6) The Problem of an Unsettled Concept of Consequence, (7) The Methodological Problem, (8) The General Logical Form Problem. It seems that the case for logical pluralism is far from clear. It is even unclear what exactly logical pluralism is and where is stops. It is also unclear if logical pluralism could be stated as it is, if it were true. So far universalism seems to be the better position to take. (shrink)

Two challenges to the method of reflective equilibrium have been developed in a dispute between Michael D. Resnik and Stewart Shapiro: because the method itself involves logical notions, it can neither be specified in a logic-neutral way nor can it allow logical pluralism. To analyse and answer these claims, an explicit distinction is introduced between judgements held prior to the process of mutual adjustments and judgements in agreement with the systematic principles, which result from the process. It is then argued (...) that from the presystematic perspective, the method of reflective equilibrium permits developing and justifying rival logics, and hence it allows reasonable disagreement about logics; but such pluralism is no longer available from the perspective of fully developed logical systems. (shrink)

Logical pluralism is the view according to which there is more than one relation of logical consequence, even within a given language. A recent articulation of this view has been developed in terms of quantification over different cases: classical logic emerges from consistent and complete cases; constructive logic from consistent and incomplete cases, and paraconsistent logic from inconsistent and complete cases. We argue that this formulation causes pluralism to collapse into either logical nihilism or logical universalism. In its place, we (...) propose a modalist account of logical pluralism that is independently well motivated and that avoids these collapses. (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...) view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

Beall and Restall 2000; 2001; 2006 advocate a comprehensive pluralist approach to logic, which they call Logical Pluralism, according to which there is not one true logic but many equally acceptable logical systems. They maintain that Logical Pluralism is compatible with monism about metaphysical modality, according to which there is just one correct logic of metaphysical modality. Wyatt 2004 contends that Logical Pluralism is incompatible with monism about metaphysical modality. We first suggest that if Wyatt were right, Logical Pluralism would (...) be strongly implausible because it would get upside down a dependence relation that holds between metaphysics and logic of modality. We then argue that Logical Pluralism is prima facie compatible with monism about metaphysical modality. (shrink)

The problem of constraining methodological pluralism is highlighted in a discussion of John Dupr 's The Disorder of Things . Dupr requires limits on what are to count as legitimate scientific methodologies. Although Dupr recognises this requirement, he fails in his attempt to appropriately ground such limitations.

Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...) logical pluralism and evaluating them along the criteria provided by (ii) and (iii). (shrink)

Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...) 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair from 1971to 1975, I spent many hours with him in Buffalo and on professional trips .. (shrink)

WHAT IS LOGICAL PLURALISM? (J.C. BEALL’S AND GREG RESTALL’S STANDPOINT) S u m m a r y C. Beall and Greg Restall are advocates of a comprehensive pluralist approach to logic, which they call Logical Pluralism (LP). According to LP, there is not one correct logic, but many equally acceptable logical systems. The authors share Tarski’s conviction and follow the mainstream in thinking about logic as the discipline that investigates the notion of logical consequence. LP is the pluralism about logical (...) consequence – a pluralist maintains that there is more than one relation of logical consequence. According to LP, classical, intuitionistic and relevant logics are not rivals, but they all are equally correct, they all count as genuine logics. The purpose of this paper is to present some remarks concerning J.C. Beall’s and Greg Restall’s exposition of LP. At the beginning, the definition of the relation of logical consequence, which is central to their proposal, is shown. According to Beall and Restall, argument is valid if, and only if, in every case when the premisses are true, then the conclusion is, too. They argue that by considering different types of cases the logical pluralist obtains different logics. The paper—apart from presenting LP—also gives a critical discussion of this approach. It seems, that the thesis of LP is far from being clear. It is even unclear what exactly LP is and where is stops. It is unclear what “equally good”, “equally correct”, “equally true” mean. It is not clear, how to explain, in scope of logic, that the system of logic, is a model of real logical connections. (shrink)

In this paper I offer a proof-theoretic defence of meaning-invariant logical pluralism. I argue that there is a relation of co-determination between the operational and structural aspects of a logic. As a result, some features of the consequence relation are induced by the connectives. I propose that a connective is defined by those rules which are conservative and unique, while at the same time expressing only connective-induced structural information. This is the key to stabilizing the meaning of the connectives across (...) multiple determinations of the consequence relation. (shrink)

The article is centered on the question of how best to understand the logical pluralism/logical monism debate. A number of suggestions are brought up and rejected on the ground that they render the debate trivial or otherwise philosophically uninteresting. One way to make philosophical good sense of the debate is to find a canonical purpose for logic such that the monist is someone who holds that some unique logic best serves this purpose and the pluralist holds that many logics do. (...) However, in the article, general obstacles to finding such a purpose are discussed. (shrink)

The article is centered on the question of how best to understand the logical pluralism/logical monism debate. A number of suggestions are brought up and rejected on the ground that they render the debate trivial or otherwise philosophically uninteresting. One way to make philosophical good sense of the debate is to find a canonical purpose for logic such that the monist is someone who holds that some unique logic best serves this purpose and the pluralist holds that many logics do. (...) However, in the article, general obstacles to finding such a purpose are discussed. (shrink)

Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it is (...) obscure just what Goldfarb and Ricketts claim about Carnap). Toward the end I critically discuss Michael Friedman's suggestion that Carnap believed in a relative a priori. (shrink)

A convergência de interpretações contemporâneas de Kant (Jacobi) e nossas contemporâneas (Apel e Habermas) na crítica ao monologismo. tanto teorético como prático, inerente à filosofia kantiana, é questionada pela emergência nesta de referências signitlcativas à ordem intersubjectiva, na defesa de um pluralismo lógico. ético e estético que culmina na concepção de uma razão comunicacional. /// La convergence d'interprétations contemporaines de Kant (Jacobi) et nos contemporaines (Apel et Habermas) dans la critique au monologisme. aussi théorétique que pratique, inhérent à la philosophie (...) contemporaine kantienne. est questionnée par l'émergence dans cette philosophie de références significatives à l'ordre intersubjectif. dans la défense d'un pluralisme logique, éthique et esthétique qui culmine dans la conception d'une raison communicationelle. /// The convergence of critical interpretation, offered equally by Kant's contemporaries (Jacobi) and our own (Apel and Habermas). concerning the theoretical and practical monologism inherent in Kantian philosophy is put here under question by the emergency in Kant's philosophy of significant references to the intersubjective order independent of logical, aesthetic, and ethical pluralism, culminating in a conception of communicational reason. (shrink)

There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart (...) from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these. (shrink)

We are told that there are standards of rigour in proof, and we are told that the standards have increased over the centuries. This is fairly clear. But rigour has also changed its nature. In this paper we as-sess where these changes leave us today.1 To motivate making the new assessment, we give two illustra-tions of changes in our conception of rigour. One, concerns the shift from geometry to arithmetic as setting the standard for rig-our. The other, concerns the notion (...) of effective proof or compu-tations. To make the assessment, we look at one motivation for increasing the rigour of a mathematical argument: explicitness and honesty. We then present a standard of rigour by means of a characterisation developed with reference to what we call ‘an account-proof’. We evaluate the standard with reference to the motivation. With the analysis we discover that, regardless of the motivations for rigour, the standard is almost never met, and that the motivations are not all satisfied. It follows that, in some sense, the motivations have misfired. The misfiring suggests to us that we re-assess our notion of rigour. We think of rigour as a relative term. Moreover, the standard for rigour depends on philosophical underpinnings. The strength of the argument of this paper rests on the plausibility of our selection of motivations and on the plausibility of our standard. (shrink)

Much of cognitive science seeks to provide principled descriptions of various kinds and aspects of rational behaviour, especially in beings like us or AI simulacra of beings like us. For the most part, these investigators presuppose an unarticulated common sense appreciation of the rationality that such behaviour consists in. On those occasions when they undertake to bring the relevant norms to the surface and to give an account of that to which they owe their legitimacy, these investigators tend to favour (...) one or other of three approaches to the normativity question. They are the analyticity or truth-in-a-model approach; the pluralism approach; and the reffective equilibrium approach.All three of these approaches to the normativity question are seriously flawed, never mind that the first two have some substantial provenance among logicians and the third has enjoyed a flourishing philosophical career.Against these views, we propose a strong version of what might be called normatively immanent descriptivism. We attempt to elucidate its virtues and to deal with what appears to be its most central vulnerability, embodied in the plain fact that actual human behaviour is sometimes irrational. (shrink)