Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed...

On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful examination, the strongest (...) Dummettian arguments for anti-realism of this sort fail to secure intuitionistic logic as the single, correct logic for anti-realist discourses. Instead, antirealists are placed in a situation where they fail to be justified in asserting monism (that intuitionistic logic is the unique correct logic). Thus, antirealists seem forced either to accept pluralism (i.e. one or more intermediate logic is at least as `correct’ as intuitionistic logic–an option I take to be unattractive from the anti-realist perspective), or they must be anti-realists about the realism/anti-realism debate (and, in particular, must refuse to assert the instance of excluded middle equivalent to logical monism or logical pluralism). (shrink)

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

Telic monism in logic is the thesis that there is one single philosophically primary goal to logic. A different way to put it is that there is only one canonical application to logic. This thesis is widely present—implicitly or more explicitly—in the literature on the philosophy of logic, yet has not been examined nor argued for extensively. In this paper I will present and critically examine telic monism. One prominent candidate for the canonical application of logic, namely the formal codification (...) of logical consequence in natural language, will be challenged directly. The critique will then be generalized by appealing to a practice-based philosophy of logic. The general argument I put forth here claims that we have no principled reason to assume there to be just one primary goal to logic. Rather, I claim that it is more plausible that there actually is a variety of goals, purposes and applications to logic, without one of them enjoying primacy over the others. If this argument succeeds, at least one of the consequences is that it allows for a kind of logical pluralism that has previously been deemed insignificant, namely logical instrumentalism. (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)

Moral relativism is an attractive position, but also one that it is difficult to formulate. In this paper, we propose an alternative way of formulating moral relativism that locates the relativity of morality in the property that makes moral claims true. Such an approach, we believe, has significant advantages over other possible ways of formulating moral relativism. We conclude by considering a few problems such a position might face.

The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory.

Logical pluralism is the view that there is more than one correct logic. A key objection to logical pluralism is that it collapses into monism. The core of the Collapse Objection is that only the pluralist’s strongest logic does any genuine normative work; since a logic must do genuine normative work, this means that the pluralist is really a monist, who is committed to her strongest logic being the one true logic. This paper considers a neglected question in the collapse (...) debate: what is it for a logic to do genuine normative work? As well as having wider upshot for the connection between logic and normativity, grappling with this question provides a new response to the Collapse Objection on behalf of the pluralist. I suggest that we should allow logics to generate pro tanto reasons in a way that bears not just on combinations of attitudes but on how an agent’s attitudes are based on one another. This motivates adopting normative principles that allow the pluralist’s weaker logics to earn their normative keep. Rather than being ad hoc, these principles capture a sense in which good reasoning goes beyond the consistency of an agent’s attitudes. Good reasoning is also concerned with how an agent’s attitudes are based on one another. (shrink)

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. (shrink)

After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, (...) non-classical logics and cognitive science. (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)

Paul Thagard’s theory of deductive coherence, as set out in his Coherence in Thought and Action, faces a regress objection. Thagard’s method of solving deductive coherence problems presupposes some notion of logical consequence. The problem of specifying which logic to use to this end is itself a deductive coherence problem, so we would expect Thagard’s theory to be able to solve it. However, on pain of regress, the theory of deductive coherence cannot reach such a solution.

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove (...) the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values. (shrink)

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)

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)

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)

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)

Ultralogic as Universal was drafted in 1976, appeared in 1977 as ‘Ultralogic as Universal?’ in The Relevance Logic Newsletter, 2 (1–2) and was reprinted as an appendix to Exploring Meinong’s Jungle...

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)

Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...) is ontic, the conventionalist account seems to avoid a convincing objection to other ontic accounts (Kuorikoski 2021). (shrink)

According to the traditional view in the philosophy of logic facts of logic bear normative authority regarding how one ought to reason. Usually this is to mean that the relation of logical consequence between statements has some special relevance for how one’s beliefs should cohere. However, as I will argue in this article, this is just one way in which logic is normative for reasoning. For one thing, belief is not the only kind of mental state involved in reasoning. Besides (...) adopting and revising beliefs, rational agents pose and resolve questions. For another thing, the consequence relation of classical logic can be conservatively extended such that it includes logical relations between questions as well. Therefore, there is an argument to be made that not only the inference of new beliefs from extant beliefs but also the process of raising additional questions falls under the normative authority of logic. Accordingly, a nuanced account of the normativity of logic presents itself, which convincingly deals with problems such as clutter-avoidance and the paradox of the preface. (shrink)

The paper argues that much of the difficulty with making progress on the issue of the normativity of logic for thought, as discussed in the literature, stems from a misapprehension of what logic is normative for. The claim is that, rather than mono-agent mental processes, logic in fact comprises norms for quite specific situations of multi-agent dialogical interactions, in particular special forms of debates. This reconceptualization is inspired by historical developments in logic and mathematics, in particular the pervasiveness of such (...) dialogical conceptions in the early days of logic in ancient Greece. The multi-agent, dialogical perspective then allows for the formulation of compelling 'bridge principles’ between the relation of logical consequence and dialogical normative principles, something that is notoriously difficult to achieve in a mono-agent setting pertaining exclusively to thought and belief. The upshot is also that the truth-preserving rules of logic generally do not have a primary normative bearing on mono-agent mental processes, and in this sense the paper sides with Harman's critique of the idea that logic has a normative import for thought and belief. (shrink)

Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some (...) questions for future research. (shrink)

Traditional inflationary approaches that specify the nature of truth are attractive in certain ways; yet, while many of these theories successfully explain why propositions in certain domains of discourse are true, they fail to adequately specify the nature of truth because they run up against counterexamples when attempting to generalize across all domains. One popular consequence is skepticism about the efficaciousness of inflationary approaches altogether. Yet, by recognizing that the failure to explain the truth of disparate propositions often stems from (...) inflationary approaches' allegiance to alethic monism, pluralist approaches are able to avoid this explanatory inadequacy and the resulting skepticism, though at the cost of inviting other conceptual difficulties. A novel approach, alethic functionalism, attempts to circumvent the problems faced by pluralist approaches while preserving their main insights. Unfortunately, it too generates additional problems---namely, with its suspect appropriation of the multiple realizability paradigm and its platitude-based strategy---that need to be dissolved before it can constitute an adequate inflationary approach to the nature of truth. (shrink)

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

We can distinguish two non-equivalent ways in which a natural language argument can be valid: it can be interpretationally or representationally valid. However, there is just one notion of classical first-order validity for formal languages: truth-preservation in all classical first-order models. To ease the tension, Baumgartner suggests that we should understand interpretational and representational validity as imposing different adequacy conditions on formalizations of natural language arguments. I argue against this proposal. To that end, I first show that Baumgartner’s definition of (...) representational validity is extensionally inadequate. I present a number of natural language arguments that we pre-theoretically hold to be representationally valid, but are not representationally valid according to Baumgartner’s definition. I then point to two further untenable features of Baumgartner’s definitions: according to Baumgartner’s definition of a representationally correct formalization, we cannot arrive at formalizations in a recursive way, and Baumgartner’s definition of representational validity is non-monotonic. I conclude that interpretational and representational validity cannot be understood as merely imposing different adequacy conditions on formalizations. If we want to capture our interpretational and representational intuitions, we need two different formal definitions of validity. (shrink)

This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The algebraic structures corresponding to (...) the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm systems and some extensions and neighbors of R satisfy the new relevance principles. (shrink)

This paper first shows that some versions of the logic R of Relevance do not satisfy the relevance principle introduced by Anderson and Belnap, the principle of which is generally accepted as the principle for relevance. After considering several possible (but defective) improvements of the relevance principle, this paper presents a new relevance principle for (three versions of) R, and explains why this principle is better than the original and others.

By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar (...) logics. We first study the members of our class semantically, after which we present a uniform sequent calculus that is sound and complete with respect to all of them. Two further sequent calculi and \ calculus) will be considered, which serve the same purpose and which are obtained by applying general methods to construct sequent calculi for many-valued logics. Rules and proofs in the SK calculus are much simpler and shorter than those of the \ and the \ calculus, which is one of the reasons to prefer the SK calculus over the latter two. Besides favourably comparing the SK calculus to both the \ and the \ calculus, we also hint at its philosophical significance. (shrink)

The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...) neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology (...) is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

I argue for a version of logical pluralism based on the plurality of legitimate formalizations of the logical vocabulary. In particular, I argue that the apparent rivalry between classical and relevant logic can be resolved, given that both logics capture and formalize normative and legitimate senses of logical consequence: classical logic encodes “follows from” as truth preservation and captures the truth conditions of the logical constants, while relevant logic encodes a notion of “follows from” which, apart from preserving truth, avoids (...) the violation of certain Gricean maxims and captures a different inferential role for the same logical constants, enriching their meaning pragmatically. (shrink)

One of the popular realist responses to the pessimistic meta-induction is the ‘selective’ move, where a realist only commits to the ‘working posits’ of a successful theory, and withholds commitment to ‘idle posits’. Antirealists often criticise selective realists for not being able to articulate exactly what is meant by ‘working’ and/or not being able to identify the working posits except in hindsight. This paper aims to establish two results: sometimes a proposition is, in an important sense, ‘doing work’, and yet (...) does not warrant realist commitment, and the realist will be able to respond to PMI-style historical challenges if she can merely show that certain selected posits do not require realist commitment. These two results act to significantly adjust the dialectic vis-à-vis PMI-style challenges to selective realism. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

The notion of “bounded rationality” was introduced by Simon as an appropriate framework for explaining how agents reason and make decisions in accordance with their computational limitations and the characteristics of the environments in which they exist (seen metaphorically as two complementary scissor blades).We elaborate on how bounded rationality is usually conceived in psychology and on its relationship with logic. We focus on the relationship between heuristics and some non-monotonic logical systems. These two categories of cognitive tools share fundamental features. (...) As a step further, we show that in some cases heuristics themselves can be formalized from this logic perspective. We have therefore two main aims: on the one hand, to demonstrate the relationship between the bounded rationality programme and logic, understood in a broad sense; on the other hand, to provide logical tools of analysis of already known heuristics. This may lead to results such as the characterization of fast and frugal binary trees in terms of their associated logic program here provided. (shrink)

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent logics is obtained by filtration: adding conditions to the classical consequence operation . We start by surveying the most promising candidates and comparing their strengths. (...) Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a.. (shrink)

Pluralist and eliminativist positions have proliferated within both science and philosophy of science in recent decades. This paper asks the question why this shift of thinking has occurred, and where it is leading us. We provide an explanation which, if correct, entails that we should expect pluralism and eliminativism to transform other debates currently unaffected, and for good reasons. We then consider the question under what circumstances eliminativism will be appropriate, arguing that it depends not only on the term in (...) question, but also on the context of discussion and details of the debate at hand. The resultant selective eliminativism is an appealing compromise for various ‘pluralists’ and ‘eliminativists’ who are currently locking horns. (shrink)

What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic, between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich and by Williamson. My thesis is that while the deviant logician objection falls (...) short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements. (shrink)

The continental philosophy of non-classical logics is a relatively new field that seeks to determine whether any aspects of certain continental philosophers’ thinking can be characterized in terms of non-classical logics. Some of the main figures that have been examined so far are Martin Heidegger, Jacques Derrida, Gilles Deleuze, and François Laruelle. Although many of these studies are grounded in the writings of Graham Priest, who wrote some of the seminal texts in the field, Jc Beall’s work also features prominently (...) in a number of cases. After surveying this field and highlighting Beall’s influence within it, I claim that it can be substantially expanded by making further uses of Beall’s writings, especially ones that introduce non-classical logics in ways that are especially suitable for this particular field of study and also that discuss such topics as negation, subclassical logics, logical pluralism, and glutty futures. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and Restall (...) (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” (...) is itself context-sensitive, depending on the purposes of a given conversation. (shrink)

In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main theme of my (...) ante rem structuralism is that any coherent axiomatization describes a structure, or a class of structures. If one weakens the logic, then more axiomatizations become coherent. (shrink)

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

Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...

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)

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized (...) logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness. (shrink)

Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...) derivations to produce derivations for intuitionistic logic and for dual intuitionistic logic. The result is another way to understand the manner in which we can have different consequence relations in the same language. Furthermore, the proof-theoretic perspective gives us a different explanation of how the one concept of negation can have three different truth conditions, those in classical, intuitionistic and dual-intuitionistic models. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, we posit (...) rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)