Diversity Reading List

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.

Abstract:

Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems.

Abstract:

The author argues that there is a strong connection between the dualisms that have strengthened and naturalized systematic oppression across history (man/woman, reason/emotion, etc.), and "classical" logic. It is suggested that feminism's response should not be to abandon logic altogether, but rather to focus on the development of alternative, less oppressive forms of rationality, of which relevant logics provide an example.

Introduction: Plumwood’s second essay uses logical distinctions to map the difficult terrain of feminist theories of difference. By carefully distinguishing among forms of difference, Plumwood refutes attempts by some feminist theorists to identify dichotomous thinking with oppressive thinking.

Abstract:

Being a pragmatic and not a referential approach to semantics, the dialogical formulation of paraconsistency allows the following semantic idea to be expressed within a semi-formal system: In an argumentation it sometimes makes sense to distinguish between the contradiction of one of the argumentation partners with himself (internal contradiction) and the contradiction between the partners (external contradiction). The idea is that external contradiction may involve different semantic contexts in which, say A and not A have been asserted. The dialogical approach suggests a way of studying the dynamic process of contradictions through which the two contexts evolve for the sake of argumentation into one system containing both contexts. More technically, we show a new, dialogical, way to build paraconsistent systems for propositional and first-order logic with classical and intuitionistic features (i.e. paraconsistency both with and without tertium non-datur) and present their corresponding tableaux.

Abstract: The present article provides an introduction to classical Chinese logic, a term which refers to ancient discourses that were developed before the arrival of significant external influences and which flourished in China until the first unification of China, during the Qin Dynasty. Taking as its premise that logic implies both universal and culturally conditioned elements, the author describes the historical background of Chinese logic, the main schools of Chinese logical thought, the current state of research in this area and the crucial concepts and methods applied in classical Chinese logic. The close link between Chinese logic and the Chinese language is also stressed

Abstract:

From the introduction: "we argue that the semantics of the first degree paradox-free implication system FD supports the claim it is superior to strict implication as an analysis of entailment at the first degree level. The semantics also reveals that Disjunctive Syllogism, [...] far from being a paradigmatic entailment, is invalid, and allows the illegitimate suppression of tautologies"

Abstract:

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction.

Publisher's Note: Traditionally, philosophers of quantum mechanics have addressed exceedingly simple systems: a pair of electrons in an entangled state, or an atom and a cat in Dr. Schrodinger's diabolical device. But recently, much more complicated systems, such as quantum fields and the infinite systems at the thermodynamic limit of quantum statistical mechanics, have attracted, and repaid, philosophical attention. Interpreting Quantum Theories has three entangled aims. The first is to guide those familiar with the philosophy of ordinary QM into the philosophy of 'QM infinity', by presenting accessible introductions to relevant technical notions and the foundational questions they frame. The second aim is to develop and defend answers to some of those questions. Does quantum field theory demand or deserve a particle ontology? How (if at all) are different states of broken symmetry different? And what is the proper role of idealizations in working physics? The third aim is to highlight ties between the foundational investigation of QM infinity and philosophy more broadly construed, in particular by using the interpretive problems discussed to motivate new ways to think about the nature of physical possibility and the problem of scientific realism.