Diversity Reading List

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:
This chapter reviews the book A Mind of One's Own: Feminist Essays on Reason and Objectivity (1993), by Louise B. Antony and Charlotte Witt. The appeal to reason and objectivity amounts to a request that the observer refuses to be intimidated by habit, and look for cogent arguments based on evidence that has been carefully sifted for bias. In our own society the arguments of feminists make such appeals to reason and objectivity all the time, and in a manner that closely resembles Platonic arguments. And yet today reason and objectivity are on the defensive in some feminist circles. We are frequently told that reason and objectivity are norms created by "patriarchy," and that to appeal to them is to succumb to the blandishments of the oppressor. We are told that systems of reasoning are systems of domination, and that to adopt the traditional one is thus to be co-opted. A Mind of One's Own is a collection of essays by women who are prominent in philosophy today and who wish to confront recent feminist criticisms of philosophy. Most of the contributors are under fifty and widely respected; most grew up with strong political ties to feminism.

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.

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:
Hass examines chapters devoted to Aristotle in a recent, prominent, and controversial feminist critique of logic, Andrea Nye's Words of Power: A Feminist Reading of the History of Logic. Hass shows that Nye's criticisms of logic in general and of Aristotle in particular are misplaced. What is crucial in Nye's attack are alleged problems caused by overzealous "abstraction." But Hass argues that abstraction is not problematic; instead, it is crucial (and empowering) for feminist political theory. Although she rejects Nye's form of feminist logic critique, Hass finds more that is worthwhile in the criticisms of logic advanced by Luce lrigaray and Val Plumwood. These thinkers call for feminist alternatives to what has come to be standard deductive logic - and interestingly enough, their call is echoed in other contemporary criticisms from within the field of logic itself, for example, from intuitionist or entailment logics. The logical schemes envisaged by lrigaray and Plumwood would encompass more situated and fluid ways of using formal systems to describe and analyse reality and diverse experiences. Hass argues that, in Aristotle's case, we can glimpse something of such an alternative by looking to his account of negation, which is richer and more complex than that allowed by most contemporary formal systems.

Abstract:

Hass examines chapters devoted to Aristotle in a recent, prominent, and controversial feminist critique of logic, Andrea Nye's Words of Power: A Feminist Reading of the History of Logic. Hass shows that Nye's criticisms of logic in general and of Aristotle in particular are misplaced. What is crucial in Nye's attack are alleged problems caused by overzealous "abstraction." But Hass argues that abstraction is not problematic; instead, it is crucial (and empowering) for feminist political theory. Although she rejects Nye's form of feminist logic critique, Hass finds more that is worthwhile in the criticisms of logic advanced by Luce lrigaray and Val Plumwood. These thinkers call for feminist alternatives to what has come to be standard deductive logic - and interestingly enough, their call is echoed in other contemporary criticisms from within the field of logic itself, for example, from intuitionist or entailment logics. The logical schemes envisaged by lrigaray and Plumwood would encompass more situated and fluid ways of using formal systems to describe and analyse reality and diverse experiences. Hass argues that, in Aristotle's case, we can glimpse something of such an alternative by looking to his account of negation, which is richer and more complex than that allowed by most contemporary formal systems.

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:

‘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:

This entry presents the framework of « dialogical logic » in the initial Lorenzen and Lorenz tradition. The rules for the game and for building strategies are provided with step by step examples, helping the reader understand how the dialogue tables reflect a dynamic process of interaction between the players. Various logics are presented within this pluralistic framework: intuitionist logic, classical logic, and modal logics, with references to various other logics. In a second part of the entry, objections against the framework are considered, together with answers provided by the « Immanent Reasoning » variant, which stays within the Lorenzen and Lorenz tradition, and by the « Built-In Opponent » variant first developed by Catarina Dutilh Novaes, which develops a different dialogical tradition.

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.