Diversity Reading List

Abstract:
The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology.

Abstract:
During the 1970s and 1980s, a team of Automated Theorem Proving researchers at the Argonne National Laboratory near Chicago developed the Automated Reasoning Assistant, or AURA, to assist human users in the search for mathematical proofs. The resulting hybrid humans+AURA system developed the capacity to make novel contributions to pure mathematics by very untraditional means. This essay traces how these unconventional contributions were made and made possible through negotiations between the humans and the AURA at Argonne and the transformation in mathematical intuition they produced. At play in these negotiations were experimental practices, nonhumans, and nonmathematical modes of knowing. This story invites an earnest engagement between historians of mathematics and scholars in the history of science and science studies interested in experimental practice, material culture, and the roles of nonhumans in knowledge making.

Publisher's Note: The role of science in policymaking has gained unprecedented stature in the United States, raising questions about the place of science and scientific expertise in the democratic process. Some scientists have been given considerable epistemic authority in shaping policy on issues of great moral and cultural significance, and the politicizing of these issues has become highly contentious.

Since World War II, most philosophers of science have purported the concept that science should be “value-free.” In Science, Policy and the Value-Free Ideal, Heather E. Douglas argues that such an ideal is neither adequate nor desirable for science. She contends that the moral responsibilities of scientists require the consideration of values even at the heart of science. She lobbies for a new ideal in which values serve an essential function throughout scientific inquiry, but where the role values play is constrained at key points, thus protecting the integrity and objectivity of science. In this vein, Douglas outlines a system for the application of values to guide scientists through points of uncertainty fraught with moral valence.

Following a philosophical analysis of the historical background of science advising and the value-free ideal, Douglas defines how values should-and should not-function in science. She discusses the distinctive direct and indirect roles for values in reasoning, and outlines seven senses of objectivity, showing how each can be employed to determine the reliability of scientific claims. Douglas then uses these philosophical insights to clarify the distinction between junk science and sound science to be used in policymaking. In conclusion, she calls for greater openness on the values utilized in policymaking, and more public participation in the policymaking process, by suggesting various models for effective use of both the public and experts in key risk assessments.

Publisher’s Note:
Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.

Publisher’s Note:
This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.

Abstract:

Val Plumwood’s 1993 paper, “The politics of reason: towards a feminist logic” (hence- forth POR) attempted to set the stage for what she hoped would begin serious feminist exploration into formal logic – not merely its historical abuses, but, more importantly, its potential uses. This work offers us: (1) a case for there being feminist logic; and (2) a sketch of what it should resemble. The former goal of Plumwood’s paper encourages feminist theorists to reject anti-logic feminist views. The paper’s latter aim is even more challenging. Plumwood’s critique of classical negation (and classical logic) as a logic of domination asks us to recognize that particular logical systems are weapons of oppression. Against anti-logic feminist theorists, Plumwood argues that there are other logics besides classical logic, such as relevant logics, which are suited for feminist theorizing. Some logics may oppress while others may liberate. We provide details about the sources and context for her rejection of classical logic and motivation for promoting relevant logics as feminist.

Abstract:
The strongest and, until recently, least-explored approach to feminist logic holds that some formal logics have structural features that perpetuate sexism and oppression, whereas other logics are helpful for resisting and opposing these social phenomena. Our choice of logics may not be purely formal on this view: for example, some logics are preferrable to others on the grounds of feminist commitments. This strong account of feminist logic was first articulated by Val Plumwood. We will critically engage salient features of her view, especially her critique of classical logic and the centering and dominating functions she believes classical negation has. We will see that her understanding of classical negation captures neither the development of Intersectional Feminism, nor the position the concept of centering holds in transformative justice. However, Plumwood's critique of classical negation does lead us to a deeper insight regarding which logics to apply in social justice contexts. Robin Dembroff's analysis of genderqueer as a critical gender kind helps us delineate a non-classical context in which a four-valued logic, such as FDE, can structurally account for the critical feature of this gender kind in a way classical logic cannot. We will also observe how four-valued logics precisely capture the destabilization of, and resistance to, the exclusive and exhaustive gender binary categories Dembroff describes.

Summary: Examines the theory of conditionals and whether it's possible to have a unified theory of them.

Abstract:

The chapter is an introduction to logical treatments of indicative conditionals, comparing truth-functional, non-truth-functional, and suppositional approaches. Some of the topics discussed are truth conditions, conditional belief, assertability, and issues with compounds of conditionals.

Abstract:

From the newsletter's introduction: "Lauren Eichler [...] examines the resonances between feminist and Native American analyses of classical logic. After considering the range of responses, from overly monolithic rejection to more nuanced appreciation, Eichler argues for a careful, pluralist understanding of logic as she articulates her suggestion that feminists and Native American philosophers could build fruitful alliances around this topic."