The Subject Matter of Logic: Explaining what logic is about

<p><b>Logics are formal systems with many different applications. The boundary between logics and other formal systems, like mathematics, is unclear. One way of clarifying this boundary is by appealing to the subject matter; defining their purpose, for instance, showing how the truth of the premises guarantees the conclusion, demonstrating reasoning, or modelling an argument. </b></p><p>There are two contemporary philosophical debates where the subject matter of logic is relevant. The first is that of logical pluralism, which needs a way to determine whether a logic is correct. The second is the argument that the normativity of logic supplies a mechanism for determining whether a logic is correct. In these debates, the subject matter of logic is relevant, but not discussed. And it does not need to be because the participants implicitly agree that the answer is validity. They also agree that this does not advance the debate. </p><p>Validity is a dead-end because it only transforms the question. Logicians clarify validity by giving a definition. But it is a well-established fact that there is more than one way of defining a relation of logical consequence. So, how does one determine whether a given definition is correct? Or to put it another way, how does one know whether that definition captures validity? On this point, opinions are deeply divided. Moreover, there is no clear strategy for resolving the difference of opinion. MacFarlane comments that appeals to intuitions about validity are prevalent in these debates. Furthermore, he remarks, these intuitions are a product of education. </p><p>In many parts of the advanced literature, logicians agree that the subject matter of logic is validity. But this explanation won't do as an introduction for a beginner. As Newton-Smith says, this 'has the fault of explaining the obscure in terms of the equally obscure.' Instead, teachers must give what Mates calls 'an informal and intuitive account of the matters with which logic is primarily concerned.' </p><p>The constraints on introductory explanations provide an opportunity to investigate the subject matter of logic in a novel way and perhaps reveal the source of intuitions about validity, which might, in turn, shed light on questions of pluralism and normativity. My thesis examines the way that teachers introduce the subject matter of logic to beginners. </p><p>I begin by exploring a slice of history and a tradition of logic instruction. I argue that a reliance on this tradition leads to flawed teaching in the modern context. After that, I examine modern introductory texts and the strategies they use to present the subject matter of logic. I draw several lessons from this examination. </p><p>I conduct three interviews with Gillian Russell, Dave Ripley, and Johan van Benthem in which I ask philosophic and pedagogic questions directed by each of their interests. These dialogues are illuminating on their own. But brought together they show the interaction between the teacher's theory of the subject matter of logic and the practice of introductory logic teaching. </p><p>After this investigation into modern logic pedagogy, I present a framework for a solution to the pedagogic problem. It is a framework because there is no single best way to introduce logic to a beginner. But it is possible to develop a guiding structure. The solution which I present relies on a widely accepted 'trivial' form of pluralism and a kind of relativism which I introduce, and argue for, in this thesis. This discussion also includes practical suggestions for developing introductory logic courses.</p>

The Subject Matter of Logic: Explaining what logic is about

<p><b>Logics are formal systems with many different applications. The boundary between logics and other formal systems, like mathematics, is unclear. One way of clarifying this boundary is by appealing to the subject matter; defining their purpose, for instance, showing how the truth of the premises guarantees the conclusion, demonstrating reasoning, or modelling an argument. </b></p><p>There are two contemporary philosophical debates where the subject matter of logic is relevant. The first is that of logical pluralism, which needs a way to determine whether a logic is correct. The second is the argument that the normativity of logic supplies a mechanism for determining whether a logic is correct. In these debates, the subject matter of logic is relevant, but not discussed. And it does not need to be because the participants implicitly agree that the answer is validity. They also agree that this does not advance the debate. </p><p>Validity is a dead-end because it only transforms the question. Logicians clarify validity by giving a definition. But it is a well-established fact that there is more than one way of defining a relation of logical consequence. So, how does one determine whether a given definition is correct? Or to put it another way, how does one know whether that definition captures validity? On this point, opinions are deeply divided. Moreover, there is no clear strategy for resolving the difference of opinion. MacFarlane comments that appeals to intuitions about validity are prevalent in these debates. Furthermore, he remarks, these intuitions are a product of education. </p><p>In many parts of the advanced literature, logicians agree that the subject matter of logic is validity. But this explanation won't do as an introduction for a beginner. As Newton-Smith says, this 'has the fault of explaining the obscure in terms of the equally obscure.' Instead, teachers must give what Mates calls 'an informal and intuitive account of the matters with which logic is primarily concerned.' </p><p>The constraints on introductory explanations provide an opportunity to investigate the subject matter of logic in a novel way and perhaps reveal the source of intuitions about validity, which might, in turn, shed light on questions of pluralism and normativity. My thesis examines the way that teachers introduce the subject matter of logic to beginners. </p><p>I begin by exploring a slice of history and a tradition of logic instruction. I argue that a reliance on this tradition leads to flawed teaching in the modern context. After that, I examine modern introductory texts and the strategies they use to present the subject matter of logic. I draw several lessons from this examination. </p><p>I conduct three interviews with Gillian Russell, Dave Ripley, and Johan van Benthem in which I ask philosophic and pedagogic questions directed by each of their interests. These dialogues are illuminating on their own. But brought together they show the interaction between the teacher's theory of the subject matter of logic and the practice of introductory logic teaching. </p><p>After this investigation into modern logic pedagogy, I present a framework for a solution to the pedagogic problem. It is a framework because there is no single best way to introduce logic to a beginner. But it is possible to develop a guiding structure. The solution which I present relies on a widely accepted 'trivial' form of pluralism and a kind of relativism which I introduce, and argue for, in this thesis. This discussion also includes practical suggestions for developing introductory logic courses.</p>

Emergence of corporate political activities in the guise of social responsibility: dispatches from a developing economy

PurposeThe objective of this paper is to investigate the emergence of corporate political activities (CPAs) in the form of social responsibility in the banking sector in Bangladesh. The use of institutional logics allows the authors to explore not only the motivations underlying this sudden shift in corporate approach towards corporate social reporting (CSR) disclosure but also to investigate whether a logical plurality exists in this new approach.Design/methodology/approachThe analysis is based on 21 in-depth interviews with policymakers, regulatory bodies and top management and members of boards of directors in the banking sector.FindingsThe findings of this study are both consistent with and different to those of Uddin et al. (2018). While their findings show that Bangladeshi companies engage in CSR activities primarily to demonstrate their allegiance with the ruling political regime driven by notions of traditionalism, this study’s findings show the existence of a logical pluralism across industries in the manner they engage with CSR activities and disclosures. In addition to the dominant market logic, the authors also find the co-existence of community and family logics shaping the nature of CSR disclosures made by banking companies in Bangladesh.Originality/valueThe authors contribute to the accounting and management literature by providing first-hand evidence of the motivations underlying the emergence of CPAs in the context of a developing country. The adoption of an alternative theoretical framework allows the authors to identify the multiple logics that dictate corporate attitude towards CSR engagement and disclosure.

Shadows of Syntax

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.

Alternative Conventions, Alternative Logics

Logical conventionalism leads to logical pluralism. The chapter discusses various arguments for pluralism, based on more and less demanding principles of translation. The crucial problem case of a tonk language is discussed in detail and related to various philosophical points and distinctions from the previous chapters. The chapter also provides a general account of logical and conceptual pluralism in terms of structural inferential role or semantic counterparts. This machinery is then applied to give a conventionalist-friendly account of equivalence between logics. The chapter closes by distinguishing between different types of disagreements in the philosophy of logic – descriptive disputes, normative disputes, and metaphysical disputes. Together chapters 3, 4, and 5 constitute a full development of an inferentialist-conventionalist theory of logic.

Heart and Ashes – the ‘Next’ Ciphers

The question “What next?” is a key one to all philosophical theories that consider causality, continuum, discontinuity, potentiality, and, more generally, probability. The notion of "cause" (aitia) and the rigid causality are based on what was said in the Fifth Book of Aristotle's Metaphysics, but ancient atomists, especially Plato, introduced the possibility of free "bifurcation of consequences", of symmetry and asymmetry of "next", which commence from an absolute new beginning. The principle of an absolute new beginning follows the interpretation of the myth of the deluge in De sapientia Veterum (1609) by Francis Bacon. The "logical pluralism" of numerous cause and effect relationships as well as the continuity principle (as formulated by Leibniz) are encompassed in two ciphers in accordance with the classical definition of cipher by Karl Jaspers. The cipher “sameness” and the cipher “change” suggest that we ask ourselves once again about Aristotle's "probable impossibility", and the starting point is the little-known myth of Dionysus, torn to pieces and restored to a new body thanks to his heart, as well as the creation of humanity from the ashes of the stricken Titans.

The Collapse Argument Reconsidered

According to Beall and Restall’s logical pluralism, classical logic, relevant logic, and intuitionistic logic are all correct. On this version of logical pluralism, logic is considered to be normative, in the sense that someone who accepts the truth of the premises of a valid argument, is bound to accept the conclusion. So-called collapse arguments are designed to show the incompatibility of the simultaneous acceptance of logical pluralism and the normativity of logic. Caret, however, by proposing logical contextualism, and Blake-Turner and Russell by proposing telic pluralism, have sought to nullify the collapse problem. In the present article, after setting out these two approaches to the collapse problem, we argue that by using the concept of the ‘rationality of beliefs’ in order to frame the canonical purpose of logic, it can be demonstrated that if logical contextualism and telic pluralism are considered as philosophically significant logical pluralisms, a refined version of the collapse argument is still a threat for both of these kinds of logical pluralism.