As the foundation of our rationality, logic has traditionally been considered fixed, stable and constant. This conception of the discipline has been challenged recently by the plurality of logics and in this book, Pavel Arazim extends the debate to offer a new view of logic as dynamic and without a definite, specific shape. The Problem of Plurality of Logics examines the origins of our standard view of logic alongside Kant's theories, the holistic view, the (...) class='Hi'>issue of logic's pragmatic significance and Robert Brandom's logical expressivism. Arazim then draws on proof-theoretical approaches to present a convincing argument for a dynamic version of logical inferentialism, which opens space for a new freedom to modify our own logic. He explores the scope, possibilities and limits of this freedom in order to highlight the future paths logic could take, as a motivation for further research. Marking a departure from logical monism and also from the recent doctrine of logical pluralism in its various forms, this book addresses current debates concerning the expressive role of logic and contributes to a lively area of discussion in analytic philosophy. (shrink)

Pluralism is relevant to conceptual engineering in many ways. First of all, we face the issue of pluralism when trying to characterise the very object(s) of conceptual engineering. Is it just concepts? Could concepts be pluralistically conceived for the purposes of conceptual engineering? Or rather, is it concepts and other representational devices as well? Second, one may wonder whether concepts have only one function in our mental life (representation) or, rather, a plurality of functions (including non-representational (...) ones). Third, it is a contended question whether conceptual engineering projects should pursue only one set of values and goals (epistemic ones) or, rather, a variety of values and goals, including non-epistemic ones. Finally, the engineering of a concept may result in a form of “local” conceptual pluralism, which gives rise to its own ontological and semantic challenges. Having explored the various ways in which pluralism becomes important for conceptual engineers, this contribution presents and summarizes the articles published in this special issue. (shrink)

This chapter contains sections titled: Introduction Logical Consequence Logical Pluralism Applications of Logic Conclusion References.

In this article, I address some higher-order issues involving the concept of God that arise within a pluralistic context: the problem of conceptual unity, the problem of unicity of extension and the problem of homogeneity/heterogeneity. My proposal to solve these questions involves a special hybrid theory of concepts, called the theory of ideal concepts. I argue that when associated with a pluralistic vision of concepts, and formalized within a possible world structure, such theory provides a satisfactory answer to these problems. (...) The formalization is based on a specific version of the Simplest Quantified Modal Logic (SQML), and its presentation is exclusively semantic, keeping technical details to a minimum. (shrink)

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions. (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If (...) logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s official answer to these questions centers on three distinctions: general versus particular logic; pure versus applied logic; pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, I argue, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined ‘transcendental logic’ while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, I reassess the place of Kant’s theory in the history of philosophy of logic and highlight certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism. In Chapter 1, “Kant and a Philosophical History of Logic – Methodological Reflections,” I discuss certain exegetical challenges posed by Kant’s logic corpus and argue for a “history of philosophical problems” method by which to reconstruct a Kantian theory of logic. In Chapter 2, “The Nature and Place of Logic – A History of Controversies,” I construct a partial history of philosophy of logic that revolves around the (supposedly) scientific status of logic on the one hand and its value or utility on the other. In Chapter 3, “The Making of a Scientific Logic from Bacon to Wolff,” I examine how four representative early modern philosophers – Francis Bacon, John Locke, G.W. Leibniz, and Christian Wolff – approached the four questions mentioned above. In Chapter 4, “Kant on the Way to His Own Philosophy of Logic,” I consider how Kant, in the decade between around mid-1760s and mid-1770s, navigated between existing accounts of logic until he finally found his own voice. I highlight the breakthroughs that would mark his critical departures from previous views and pave the way for the final articulation of his own view. In Chapter 5, “Logic and the Demands of Kantian ‘Science’,” I zero in on Kant’s official theory of logic in his monumental publication, Critique of Pure Reason. I foreground both what makes the theory original and what leaves it vulnerable to criticisms from post-Kantian thinkers. (shrink)

RESUMEN Este trabajo pretende relacionar dos debates emparentados sobre cómo la lógica y el lenguaje influyen sobre el pensamiento. Existe un eje de discusión en relación a si hay una pluralidad de lógicas o un único sistema lógico como criterio de evaluación para cualquier contexto de razonamiento. En lingüística, el debate surgido a partir de las interpretaciones fuertes y débiles de la hipótesis Sapir-Whorf ha centralizado la discusión en torno al grado de influencia o determinación del lenguaje sobre el pensamiento. (...) Desde perspectivas y marcos teórico-conceptuales diferentes, lógica y lingüística delimitan y problematizan un campo de indagación y reflexión. El artículo, desde una mirada transdisciplinar, pretende dar cuenta y postular vasos comunicantes entre estos debates atendiendo a los matices de cada enfoque, así como proponer una hipótesis propia sobre la problemática planteada. ABSTRACT This paper aims to relate two debates about how logic and language influence thought. There is an axis of discussion about whether there exists a plurality of logic or a single logical system as an evaluation criterion for any reasoning context. In linguistics, the debate arising from the strong and weak interpretations of the Sapir-Whorf hypothesis has centralized the discussion around the degree of influence or determination of language on thought. From different perspectives and theoretical-conceptual frameworks, logic, and linguistics delimit and problematize a field of inquiry and reflection. The article, from a transdisciplinary perspective, intends to account for and postulate communicating vessels between these debates, considering the nuances of each approach. It also seeks to propose its own hypothesis on the problem raised. (shrink)

In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding validity in (...) those different domains. Indeed, as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

This paper examines the metaphysical status of Ezumezu logic in the direction of logical realism. While presenting Ezumezu logic as a prototype of African logic, Chimakonam makes statements that somewhat entail logical monism. Using the method of critical analysis of related literature, the paper argues that presenting Ezumezu logic as one of the prototypes of African logic while at the same time making claims that elevate it to a hegemonic status, gives rise to (...) what is regarded in the paper as the monist-pluralist paradox. Drawing lessons from Abakedi’s ID paradox, the paper argues that a monist logical foundation for African logic cannot be consistently defended without paradoxes. The paper proposes that different African philosophies should be grounded by different African logics such that one need not be trained in one particular prototype such as Ezumezu logic or argue in conformity to it to qualify as an African professional or scholar. (shrink)

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a (...) correct logic, since linear logic is useful for studying natural language syntax. I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular concatenation. I end by explaining why this is a feature rather than a bug. (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)

I criticize conceptual pluralism, as endorsed recently by John Dupre and Philip Kitcher, for failing to supply strategies for demarcating science from non-science. Using creation-science as a test case, I argue that pluralism blocks arguments that keep creation-science in check and that metaphysical pluralism offers it positive, metaphysical support. Logical empiricism, however, still provides useful resources to reconfigure and manage the problem of creation-science in those practical and political contexts where pluralism will fail.

This paper examines the questions on how conflicts within and across religious practices could be understood. This paper specifically concerns with the debates around perspectives, both monolithic and plural encountered within the field of religious discourses and at the current juncture provides a way to intervene in the monism-pluralism debate in ethics. The various arguments proposed by John Hick, W.T Stace and Keith E. Yandell’s pluralistic approach have been analysed for examining the discourses more closely. The aim has been (...) to provide a comparative and critical approach towards monism and pluralism. (shrink)

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens (...) and Universal Instantiation. I show this through a detailed analysis of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. (...) ‘Some philosophers wrote Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (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)

Many philosophers have argued that logical pluralism is not compatible with the normativity of logic. They developed different versions of the collapse argument: if two logics are correct, then the weaker one will be normatively irrelevant. In this paper, I argue that the collapse argument is based on a controversial premise: the assumption that every logic can be characterized by the same bridge principle. I provide a solution to the collapse argument based on the modification of (...) this premise, maintaining both logical pluralism and the normativity of logic. (shrink)

In recent times, the American Philosophical Association has been exposed in a serious way to the issue of pluralism in philosophy curriculums in the departments of philosophy of American universities and colleges. This conversation brings to the fore the fact that what is at issue in the prospect of pluralizing American philosophy departments is not merely the matter of deciding the discipline's boundaries of intellectual formation relative to the current generation of students, but the unforeseeen consequences of (...) pluralism which challenge both 'the American canon' and the profession's self-understanding vis-à-vis a 'Western' intellectual heritage that distinguishes the 'essential' from the 'marginal' by privileging essential figures, problems, and time-honored methodological commitments. Yet, to the degree that there is a quest for relation of differences, this need not presuppose the universality of philosophical discourse, comparative philosophy moving inevitably within a logic of opposition rather than a logic of mutuality. Our thinking is surely problematic if at this World Congress we find an occasion for a confrontation between 'the West' and 'the margin,' the latter construed negatively as a 'mute, growing and menacing pressure.'. (shrink)

Many authors show how useful logic can be as a tool for building theories that can account for problems in the philosophy of religion, such as paradoxical assertions. As a consequence, one's philosophy of logic is crucial as well, since it determines which logics, from the set of available and constructible logics, one can use to build a theory. In this paper, we present the relatively recent debate between logical pluralism and monism because the positions in (...) this debate determine which logic(s) can, with justification, be applied to build a theory that addresses problems in the philosophy of religion. We begin by presenting the problem of paradoxical assertions and the debate over logical pluralism that bears on the addressing paradoxical assertions. We then canvass strategies for arguing in favor of logical monism, and pluralism; ultimately, we conclude that the Western tradition has reached a stalemate on this issue. We then turn our attention to the potential for Indian religious traditions to contribute to the debate. We present the five-step-syllogism from Nyāya-Hindu philosophy, the four corners of reasoning from Buddhist philosophy, and the seven-fold theory of predication from Jaina philosophy. The upshot of our presentation is to lay the groundwork for cross-traditional logical debate by identifying the ways in which Indian discussions of debate and dialogue relate to modern approaches to logic and the philosophy of logic. (shrink)

What has become generally known as the Berlin School of Logical Empiricism constitutes a philosophical movement that was erected on foundations laid by Albert Einstein. His revolutionary work in physics had a profound impact on philosophers interested in scientific issues, prominent among them Paul Oppenheim and Hans Reichenbach, the founding fathers of the school, who joined in viewing him as their hero among philosopher-scientists. Overall the membership of this school falls into three groups. The founding generation was linked by (...) the circumstance that both Grelling and Reichenbach were collaborators of Oppenheim; the middle generation by the fact that both Hempel and Helmer were students of Reichenbach's in Berlin; and the younger generation by the fact that all of its members were students and disciples either of Reichenbach's or of Hempel's in the USA. Three stages are at issue: an initial phase in Berlin, a transatlantic migration, and a continuation in the U.S.A.--principally in Pittsburgh. (shrink)

Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence (...) relations in Gentzen systems generates a form of intra-theoretical logical pluralism. (shrink)

In this short paper I am concerned with basically two especially important issues in Oswaldo Chateaubriand’s Logical Forms II; namely, the dispute between first- and higher-order logic and his conception of logical truth and related notions, like logical property, logical state of affairs and logical falsehood. The first issue was also present in the first volume of the book, but the last is privative of the second volume. The extraordinary significance of both issues (...) for philosophy is emphasized and, though there is a basic agreement with Chateaubriand’s views, some critical remarks are interspersed.Neste pequeno artigo considero basicamente duas questões particularmente importantes em Logical Forms II de Oswaldo Chateaubriand; a saber, a disputa entre a lógica de primeira e de segunda ordem e sua concepção de verdade lógica e noções relacionadas, como as de propriedade lógica, estado de coisas lógico e falsidade lógica. A primeira questão também estava presente no primeiro volume do livro, mas a última apenas aparece no segundo volume. Enfatizo o significado extraordinário de ambas as questões para a filosofia e, embora haja uma concordância básica com as visões de Chateaubriand, algumas observações críticas são inseridas. (shrink)

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.

Recent discussions of logical pluralism trace its origins to Rudolf Carnap’s principle of tolerance; indeed, the principle is seen as one of Carnap’s lasting philosophical contributions. In this paper, I will argue that Carnap’s reasons for adopting this principle are not purely logical, but are rather founded in the Vienna Circle’s manifesto—a programmatic document that brings the Circle’s philosophical work together with a program of social change. Building on work by Uebel, Romizi, and others, I argue that (...) we must understand the principle in light of Carnap’s role in writing the manifesto, and thus as integrated into the larger philosophical and political goals of the Circle. This history illuminates the often-ignored relationship between Carnap’s logical pluralism and his political views. Finally, I turn to the political situation of the post-World War 2 period in the United States. During this time, the Circle’s emigres in the USA transitioned their work from active efforts to reform society to the technical work that we recognize as the foundation of American analytic philosophy today. In this final section, I argue that the reasons that Carnap distanced himself from the political foundations of his view were due in large part to McCarthy-era persecution of left-wing academics. (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)

The article presents a brief analysis of how the existence of various logics became possi­ble. This is shown on the example of such well-known logical theories as syllogistics, temporal, multivalued, intuitionistic, paraconsistent and quantum logics. Each of them arose not on someone’s whim, but to solve specific problems. They are based on the most general ontological assumptions about the subject area under study. In formal logic onto­logical assumptions are refined in the concept of a model structure. Since (...) it is impossible to talk about logic in isolation from the language used, the most general epistemic as­sumptions about the nature of the relationship of linguistic expressions to those objects of extralinguistic reality that they represent are also accepted. One of the most important of these relationships is the concept of the truth of sentences, which was first formulated by Plato and Aristotle. Taking certain ontological and epistemic assumptions depending on the problem being solved, we obtain different logics. Process logic is primarily char­acterized by special ontological assumptions that are fundamentally different from the as­sumptions of other currently existing logics. The ontology of processes is an ontology of developing processes, not things. Historically, it was most vividly described in the writings of Heraclitus. In the overwhelming majority of modern approaches to the de­scription of processes, we see attempts to reduce them to sequences of states, which de­values the very concept of a process, just as a cinematic picture of the flow of time deval­ues the concept of time. Since logics are built on the basis of various ontological and epistemic assumptions, they are inherently theories of these accepted assumptions, and not universal reasoning tools that don’t depend on the characteristics of the study area and the categories of linguistic expressions. Universal logic is possible if one rises from the level of specific languages to a higher level of sign theory. (shrink)

Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or argument forms. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by (...) claiming that there is more than one way for an argument to be valid. In this book, Erik Stei defends logical monism, the view that there is exactly one correct logic. He provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic. (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)

It is commonly thought that logic, whatever it may be, is normative. While accounting for the normativity of logic is a challenge for any view of logic, in this paper I argue that it is particularly problematic for certain types of logical pluralists, due to what I call the normative problem for logical pluralism. I introduce the NPLP, distinguish it from other problems that logical pluralists may face, and show that it is unsolvable (...) for one prominent type of logical pluralism. (shrink)

This present book explores recent advances in modeling discourse processes, in particular, new approaches aimed at understanding pathological language behavior specific to schizophrenia. The contributors examine the modeling paradigm of formal semantics, which falls within the scope of both linguistics and logic while providing overlapping links with other fields such as philosophy of language and cognitive psychology. This book is based on results presented during the series of workshops on Coherence and Discourse organized by SLAM, a project developed to (...) systemize the study of pathological language processing by taking an overarching interdisciplinary approach combining psychology, linguistics, computer science and philosophy. The principle focus is on conversations produced by people with psychiatric disorders such as schizophrenia and autism. The contributions come from young and experienced researchers, and invited speakers. The book appeals to likeminded students and researchers. (shrink)

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)

Wolff's book defends the Kantian idea of a "general logic" whose principles underlie special systems of deductive logic. It thus undermines "logical pluralism," which tolerates the co-existence of divergent systems of modern logic without asking for consistent common principles. Part I of Wolff’s book identifies the formal language in which the most general principles of logic must be expressed. This language turns out to be a version of syllogistic language already used by Aristotle. The (...) universal validity of logical principles, as well as the translatability of other logical languages into this language, are shown to depend only on the meanings of its logical vocabulary. Part II of the book answers the metalogical question concerning the deductive relation between general logic and special logical systems, which also have their own (less general) principles. This part identifies the rules according to which logical rules can be derived from principles. The main result of the book is that the highest principles of logic and metalogics are provided by the syllogistic, when properly understood. (shrink)

Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a (...) synthesis of both logical pluralism and logical monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to (...) a realm of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (shrink)

Knowledge representation is one way to exploit expertise in a given domain by logical means. But, what kind of knowledge does one acquire from an inference (or inference on a query result over a knowledge base)? Such a question may appear awkward since the answer seems so obvious: from an inference, one simply acquires knowledge. This is undoubtedly the case when only one type of knowledge (for instance, expert knowledge) is involved in an inference. What if several types of (...) knowledge are involved? What type of knowledge can one deduce from a plurality of knowledge types? I claim that reasoning with different knowledge concepts requires a fine-grained representation of knowledge in which every knowledge type finds a singular expression in order to avoid some epistemic equivocity associated with a coarse-grained representation of knowledge. In the first part of the paper, I revisit the Muddy Children Puzzle, which usually serves to illustrate common knowledge in dynamic epistemic logic. I try to show that this problem also shows some sort of epistemic equivocity between concepts of knowledge and, consequently, that the problem calls for some epistemological refinements concerning the representation of the types of knowledge at play in an inference. In the second part, I address this issue from a semantic point of view, and I develop a fragment of epistemic logic capable of providing a solution to the problem of epistemic equivocity. (shrink)

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

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition (...) for granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

This article applies Hilary Putnam’s theory of internal realism to the issue of religious plurality. The result of this application – ‘internalist pluralism’ – constitutes a paradigm shift within the Philosophy of Religion. Moreover, internalist pluralism succeeds in avoiding the major difficulties faced by John Hick’s famous theory of religious pluralism, which views God, or ‘the Real,’ as the noumenon lying behind diverse religious phenomena. In side-stepping the difficulties besetting Hick’s revolutionary Kantian approach, without succumbing (...) to William Alston’s critique of conceptual-scheme dependence, internalist pluralism provides a solution to significant theoretical problems, while doing so in a manner that is respectful of cultural diversity and religious sensitivities. (shrink)

This a special issue of the Journal of Logic Language and Information that I edited.

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)

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)

Restall :279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall :475–493, 2000) and in Beall and Restall. What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, (...) one critical component of Restall’s pluralism is that the relevance logic that gets added must have connectives which mean the same thing as the connectives in the already admitted logic. This is what I will show is not possible. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free (...) topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries (...) of theorems with much wider scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

This paper introduces the special issue on the Concept of God of the Journal of Applied Logics (College Publications). The issue contains the following articles: Logic and the Concept of God, by Stanisław Krajewski and Ricardo Silvestre; Mathematical Models in Theology. A Buber-inspired Model of God and its Application to “Shema Israel”, by Stanisław Krajewski; Gödel’s God-like Essence, by Talia Leven; A Logical Solution to the Paradox of the Stone, by Héctor Hernández Ortiz and Victor Cantero; (...) No New Solutions to the Logical Problem of the Trinity, by Beau Branson; What Means ‘Tri-’ in ‘Trinity’ ? An Eastern Patristic Approach to the ‘Quasi-Ordinals’, by Basil Lourié; The Éminence Grise of Christology: Porphyry’s Logical Teaching as a Cornerstone of Argumentation in Christological Debates of the Fifth and Sixth Centruies, by Anna Zhyrkova; The Problem of Universals in Late Patristic Theology, by Dirk Krasmüller; Intuitionist Reasoning in the Tri-unitrian Theology of Nicolas of Cues, by Antonino Drago. (shrink)

Recent years have seen a surge of attention to the problem of logical pluralism; most of which has been a reaction to Beall and Restall’s account of logical pluralism as the existence of more than one equally correct semantic relation of logical consequence. The underlying thesis is that the indeterminacy of the notion of validity goes beyond what the inductive-deductive distinction can precisify. The notion of deductive validity itself is indeterminate as well and this indeterminacy (...) has its roots in the indeterminacy of the more fundamental notion of case. Cases are what make the premisses and the conclusion of an argument true; the most notable example being Tarskian models for classical logic. Deductive validity is the preservation of truth across all cases. This paper argues that unless this account of logical pluralism is supplemented with an argument in favor of the equal legitimacy of the purported cases it becomes merely a semi-controversial exposition of how different logics can be generated. (shrink)

This paper considers the role of constitutivity and normativity in Frege’s conception of logic. It outlines an historical interpretation with two goals. First, it traces these concepts back to their origins in Kant’s philosophy. Second, it considers some of the different ways in which the issue of normativity and its proper grounding was addressed in the neo-Kantian tradition and in early analytic philosophy. Some neo-Kantians worked out an epistemic-normative conception of objective judgment, according to which the objectivity of (...) cognition is constituted by distinctively logical norms. In Frege we find an original and sophisticated version of this line of thought. For Frege, the normative and constitutive roles of logic come to the fore in the articulation of scientific reason which follows the classical model of demonstrative science as cognitio ex principiis. Wittgenstein’s Tractatus then opens up a fresh Kantian perspective on the constitutivity of logic, one that grounds logic in structure rather than norms, and does so in conscious opposition to Frege and his normative science. Logic is transcendental, according to Wittgenstein, being the essence of the world and of all description. Hence, the normative function of logic becomes, in a way, superfluous. (shrink)

This chapter distinguishes between various senses in which one might be a pluralist about logic. In several of these, pluralism is uncontentiously correct. The difficult issue is whether there are different accounts of validity that are equally correct. It argues for logical monism in this regard.

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

A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises (...) issues of ontological multiplicity and relativity encountered in the natural sciences as well. (shrink)

A diagnosis of Fetal Alcohol Spectrum Disorder ascribes cause to developmental disability; however, there are logical issues in causation with ethical implications. This article focuses on the use of fallacious logic in FASD, focusing on the Canadian Guidelines for diagnosis, and knowledge translation issues from science to practice. The clinician’s logical fallacy is an ethical issue of veracity in the clinician–patient relationship; this then leads to issues of nonmaleficence, because the diagnosis in turn blames the mother (...) for her child’s difficulties. Suggestions for revised diagnostic practices that avoid allusions to causation and responsibility are discussed. (shrink)