Diversity Reading List

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.

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:

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.

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: In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer - that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, 'What are groups?'

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:

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.

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:

Anti-exceptionalists about formal logic think that logic is continuous with the sciences. Many philosophers of science think that there is feminist science. Putting these two things together: can anti-exceptionalism make space for feminist logic? The answer depends on the details of the ways logic is like science and the ways science can be feminist. This paper wades into these details, examines five different approaches, and ultimately argues that anti-exceptionalism makes space for feminist logic in several different ways.

Abstract:

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and how we ought to reason, so that pluralism about the consequence relation would result in an incoherent or unattractive pluralism about those things. In this paper I argue that logic isn’t normative. I distinguish three different ways in which a theory – such as a logical theory – can be entangled with the normative and argue that logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own. I use this view to show what is wrong with three different arguments for the conclusion that logic is normative.

Abstract:

This chapter asks whether there is any such thing as feminist logic. It defines feminism and logic, and then goes on to present and evaluate four possible views, introducing and critiquing the work of Andrea Nye, Val Plumwood, and Susan Stebbing. It argues that Stebbing’s approach—on which feminism is one among many political applications of logic—is correct, but that feminist logic could do more, by providing a formal framework for the study of social hierarchies, much as it presently provides a formal framework for the study of numbers and similarity rankings among possible worlds.

Abstract:

Logical nihilism can be understood as the view that there are no laws of logic. This paper presents both a counterexample-based argument in favor of logical nihilism, and a way to resist it by using Lakatos' method of lemma incorporation. The price to pay is the loss of absolute generality.

Abstract: Description: Survey article on logical pluralism. The article is divided into three main parts: i) in the first one the author presents the main arguments for logical pluralism with respect to logical consequence; ii) in the second part, the author considers the relation between logical pluralism and Carnap's linguistic pluralism; iii) in the last section, the author considers further kinds of logical pluralism.

Abstract:

This paper uses logic - a formal language with models and a consequence relation - to think about the social and political topics of subordination and subordinative speech. I take subordination to be a matter of three things: i) ranking one person or a group of people below others, ii) depriving the lower-ranked of rights, and iii) permitting others to discriminate against them. Subordinative speech is speech - utterances in contexts - which subordinates. Section 1 introduces the topic of subordination using examples from the 1979 novel Kindred by Octavia Butler. Section 2 uses these examples to clarify and illustrate the definitions of subordination and subordinative speech. Sections 3 and 4 then develop a way of modeling subordination using a system of social spheres, an adaptation of (Lewis, 1973)'s approach to modeling the relation of comparative similarity on worlds for counterfactuals. Section 4 looks at three possible applications for this work: giving truth-conditions for social quantifiers, identifying fallacies involving such expressions, and explaining the pragmatics of subordinative speech. The last section anticipates objections and raises further questions.

Abstract: This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.