Diversity Reading List

Introduction: In increasing numbers, philosophers are coming to read Sellars' "Empiricism and the Philosophy of Mind" (1997, hereafter EPM) as having dealt the definitive death blow to the idea that inner states with epistemic authority could have this authority immediately. EPM purportedly proves that instead, such states necessarily show up already embedded within a web of inferentially articulated conceptual knowledge, and that in order for this to be possible,  the epistemic subject must be a negotiator of a normative space in which standards of justification and correctness are already recognized. [...] In this paper I will attempt to show that Sellars' mythical explanations in EPM employ a very specific and rhetorically complex methodology, and likewise that we will not be in a position to critically assess the paper's arguments unless we give careful attention to its overall textual structure and to the nature of the mythical explanations it employs.

Abstract: In this paper I examine some research on how to diminish or eliminate stereotype threat in mathematics. Some of the successful strategies include: informing our students about stereotype threat, challenging the idea that logical intelligence is an 'innate' ability, making students In threatened groups feel welcomed, and introducing counter-stereotypical role models. The purpose of this paper is to take these strategies that have proven successful and come up with specific ways to incorporate them into introductory logic classes. For example, the possible benefit of presenting logic to our undergraduate students by concentrating on aspects of logic that do not result in a clash of schemas.

Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic - what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics - Logicism, Intuitionism, Formalism, Realism - and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.

Abstract: Val Plumwood charged classical logic not only with the invalidity of some of its laws, but also with the support of systemic oppression through naturalization of the logical structure of dualisms. In this paper I show that the latter charge - unlike the former - can be carried over to classical mathematics, and I propose a new conception of inconsistent mathematics - queer incomaths - as a liberatory activity meant to undermine said naturalization.

Abstract:

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.

Abstract:

This paper stresses the importance of identifying the nature of an author’s conception of logic when using terms from modern logic in order to avoid, as far as possible, injecting our own conception of logic in the author’s texts. Sundholm (2012) points out that inferences are staged at the epistemic level and are made out of judgments, not propositions. Since it is now standard to read Aristotelian sullogismoi as inferences, I have taken Alexander of Aphrodisias’s commentaries to Aristotle’s logical treatises as a basis for arguing that the premises and conclusions should be read as judgments rather than as propositions. Under this reading, when Alexander speaks of protaseis, we should not read the modern notion of proposition, but rather what we now call judgments. The point is not just a matter of terminology, it is about the conception of logic this terminology conveys. In this regard, insisting on judgments rather than on propositions helps bring to light Alexander’s epistemic conception of logic.

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.

Abstract:

The chapter is an overview of Indian logic, with a general introduction followed by specialized sections on four different schools: Nyāya logic, Buddhist logic, Jaina logic, and Navya-Nyāya logic.

Publisher’s Note:

This book describes how logical reasoning works and puts it to the test in applications. It is self-contained and presupposes no more than elementary competence in mathematics.

Publisher's Note: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

From the Introduction: "Lynn Hankinson Nelson and Jack Nelson extend the work begun in the former’s book Who Knows: From Quine to a Feminist Empiricism, by showing that a Quinean understanding of logic as an empirical field implies that logic remains open to revision in light of fundamental shifts in knowledge. Nelson and Nelson point to the revisions in scientific understandings made possible by the incorporation of women and women’s lives as emblematic of the possible ways that feminist thought can provide a deep reworking of the structures of knowledge and thus potentially of logic. Although they are cautious of any conclusions that logic must change, their work offers a theoretical ground from which the effects of feminist theorizing on logic can be usefully explored."

From the Introduction: "Andrea Nye is also concerned with the role of logic in science, linking the adequacy of logic with its applicability in a domain of scientific knowledge. Nye argues that the dominant predicate logic cannot adequately represent the issues surrounding attempts to divide organisms into species. Feminist critiques of the extensional theory of meaning lay the ground for alternative theories of categorization. Without renewed models of categorization, Nye submits, science is in danger of becoming a self-enclosed “logical” system, rather than an instrumental model of reality."

Publisher’s Note:

Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well as gender. In a series of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists.

From the Introduction: "Dorothea Olkowski’s chapter offers an analysis of the need to develop a logic of sense. Drawing on the work of Gilles Deleuze, Olkowski defends formal logic against feminist theorists who have urged that we organize thinking around the principles of embodiment. She warns us against the complete merging of bodily functions and sense-making activities. In Olkowski’s view, feminists need to acknowledge the usefulness of logical analyses at the same time that they must insist on formal systems that reflect and are tempered by human and humane values."

Abstract:

¿Seguimos reglas de inferencia al razonar? Por más intuitiva que resulte la respuesta positiva a esta pregunta, hay una serie de dificultades para vincular reglas lógicas y prácticas inferenciales. El Problema de la Adopción de Reglas de Inferencia constituye un desafío para todo aquel que proponga que podemos seguir nuevos patrones inferenciales a partir del reconocimiento de reglas. En esta sección temática se exploran diversos asuntos conectados a si podemos seguir un nuevo patrón inferencial en virtud de una regla.