Diversity Reading List

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.

Abstract: I propose a model on which epistemic frameworks are understood in terms of not only beliefs, but also sets of evidential support relations. We are generally responsive to multiple frameworks, some more compatible than others.The model allows for prioritizing certain frameworks by drawing on van Benthem and Pacuit's work on logics for evidence-based belief. This prioritization allows us to capture the idea that some epistemic frameworks are "held come what may" with nuance and complexity.

Abstract:

How does being a woman affect one’s epistemic life? What about being black? Or queer? Standpoint theorists argue that such social positions can give rise to otherwise unavailable epistemic privilege. “Epistemic privilege” is a murky concept, however. Critics of standpoint theory argue that the view is offered without a clear explanation of how standpoints confer their benefits, what those benefits are, or why social positions are particularly apt to produce them. But this need not be so. This article articulates a minimal version of standpoint epistemology that avoids these criticisms and supports the normative goals of its feminist forerunners. With this foundation, we develop a formal model in which to explore standpoint epistemology using neighborhood semantics for modal logic.

Abstract:

How many logics do logical pluralists adopt, or are allowed to adopt, or ought to adopt, in arguing for their view? These metatheoretical questions lurk behind much of the discussion on logical pluralism, and have a direct bearing on normative issues concerning the choice of a correct logic and the characterization of valid reasoning. Still, they commonly receive just swift answers – if any. Our
aim is to tackle these questions head on, by clarifying the range of possibilities that logical pluralists have at their disposal when it comes to the metatheory of their position, and by spelling out which routes are advisable. We explore ramifications of all relevant responses to our question: no logic, a single logic, more than one logic. In the end, we express skepticism that any proposed answer is viable. This threatens the coherence of current and future versions of logical pluralism.

Abstract: This article offers a logical, linguistic, and philosophical account of modern quantification theory. Contrasting the standard approach to quantifiers (according to which logical quantifiers are defined by enumeration) with the generalized approach (according to which quantifiers are defined systematically), the article begins with a brief history of standard quantifier theory and identifies some of its logical, linguistic, and philosophical strengths and weaknesses. It then proceeds to a brief history of generalized quantifier theory and explains how it overcomes the weaknesses of the standard theory. One of the main philosophical advantages of the generalized theory is its philosophically informative criterion of logicality. The paper describes the work done so far in this theory, highlights some of its central logical results, offers an overview of its main linguistic contributions, and discusses its philosophical significance.

From the Introduction: "Modern mathematics is based on the axiomatic method. We choose axioms and a deductive system---rules for deducing theorems from the axioms. This methodology is designed to guarantee that we can proceed from "obviously" true premises to true conclusions, via inferences which are "obviously" truth-preserving. [...] New and interesting questions arise if we give up as myth the claim that our theorizing can ever be separated out from the complex dynamic of interwoven social/political/historical/cultural forces that shape our experiences and views. Considering mathematics as a set of stories produced according to strict rules one can read these stories for what they tell us about the very real human desires, ambitions, and values of the authors (who understands) and listen to the authors as spokespersons for their cultures (where and when). This paper is the self-respective and self-conscious attempt of a mathematician to retell a story of mathematics that attends to the relationships between who we are and what we know."

Abstract:

Despite emerging attention to Indigenous philosophies both within and outside of feminism, Indigenous logics remain relatively underexplored and underappreciated. By amplifying the voices of recent Indigenous philosophies and literatures, I seek to demonstrate that Indigenous logic is a crucial aspect of Indigenous resurgence as well as political and ethical resistance. Indigenous philosophies provide alternatives to the colonial, masculinist tendencies of classical logic in the form of paraconsistent—many-valued—logics. Specifically, when Indigenous logics embrace the possibility of true contradictions, they highlight aspects of the world rejected and ignored by classical logic and inspire a relational, decolonial imaginary. To demonstrate this, I look to biology, from which Indigenous logics are often explicitly excluded, and consider one problem that would benefit from an Indigenous, paraconsistent analysis: that of the biological individual. This article is an effort to expand the arenas in which allied feminists can responsibly take up and deploy these decolonial logics.

Abstract:

Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and intensionality. The relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes.

Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.

Publisher’s Note:

Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

From the Introduction: "Anne Waters shows how nondiscrete nonbinary ontologies of being operate as background framework to some of America’s Indigenous languages. This background logic explains
why and how gender, for example, can be understood as a non-essentialized concept in
some Indigenous languages of the Americas. [...] The Indigenous understanding that all things interpenetrate and are relationally interdependent embraces a manifold of complexity, resembling a world of multifariously associated connections and intimate fusions Such a nondiscretely aggregate ontology ought not to be expected to easily give way to a metaphysics of a sharply defined discretely organized binary ontology. From an Indigenous ontology, some multigendered identities may be more kaleidoscopic and protean concepts than Euro-American culture has yet to imagine."