Audrey Yap

Emmy Noether’s name, while often associated with branches of abstract mathematics such as algebra, is not often associated with any particular philosophical view about the nature of mathematics. This chapter will outline the extent to which Noether can be seen as exemplifying a kind of structuralist view of mathematics, namely a methodological structuralism. Such a view, as outlined by some philosophers of mathematical practice, is a view about how mathematics ought to be done—namely by attending to the structural features of objects, using axiomatic methods, and striving for more general perspectives. We will see how Noether in her mathematical work exhibits all of these tendencies, thereby allowing her to be situated in the history of structuralism as someone who fruitfully employed structural methods in her mathematical work. Finally, the chapter will consider the potential connections between Noether’s methodological views and some philosophical structuralist views that seem to fit naturally with her approach to mathematics.

Feminist philosophers Barrett Emerick and Audrey Yap bring theoretical arguments about personhood and moral repair into conversation with the work of activists and the experiences of incarcerated people to make the case that prisons ought to be abolished. They argue that contemporary carceral systems in the United States and Canada fail to treat people as genuine moral agents in ways that also fail victims and their larger communities. Such carceral systems are a form of what Emerick and Yap call “institutionalized moral abandonment”. Instead, they argue that we should create communities of moral solidarity which open up space for wrongdoers to make up for their wrongs. As part of this argument, the book directly addresses one of the paradigm cases of wrongdoing often used to justify carceral systems: rape. Carceral systems that treat perpetrators of sexual violence as irredeemable monsters both obscure the reality of sexual violence and are harmful to everyone involved. As an alternative to carceral systems, Emerick and Yap argue for an orientation towards justice that is grounded in moral repair. This incorporates elements of restorative justice, mutual aid, and harm reduction. Instead of advocating for one specific and universal approach, the authors argue for multigenerational collective action that aims to build resilient communities that support the wellbeing of everyone.

This paper explores a phenomenon that we will call “justified-but-misdirected anger,” in which one’s anger is grounded in or born from a genuine wrong or injustice, but is directed towards an inappropriate target. In particular, we argue that oppressive ideologies that maintain systems of gender, race, and class encourage such misdirection and are thereby self-perpetuating. We engage with two particular examples of such misdirection. The first includes poor white voters who embrace racist and xenophobic politics; they are justified in being angry about their own economic exploitation, but that anger is misdirected in a way that maintains capitalism (which is the appropriate target of their anger). The second includes so-called “incels” who embrace misogyny; they are justified in being angry about unrealistic and unhealthy standards of contemporary masculinity, but that anger is misdirected in a way that maintains patriarchy. One goal of exploring this type of justified-but-misdirected anger is to contribute to an anti-carceral feminism that helps to thread the needle between holding wrongdoers to account while also clearly identifying the oppressive ideologies that influence their actions.

Alan Richardson’s short book on the history and significance of logical empiricism not only illuminates the importance of logical empiricists’ projects, but also tells us something useful about the ways we choose to do philosophy in the first place. The book’s primary task is providing us with a critical re-evaluation of the legacy of logical empiricism; in doing so, it raises several important metaphilosophical questions. In this article, I will outline three such issues that I think Richardson’s piece brings out and consider some of their impacts on philosophical practice. First, there is the question of philosophical canons and how we teach the history of philosophy. A second related question is how we classify and understand philosophical positions and movements. And the last question I will discuss through logical empiricism is the extent to which we should and can view academic work as morally and politically neutral.

Everyone thinks they know who Prince Zuko is and can be. His father, Fire Lord Ozai, and sister, Azula, think him weak, disobedient, and undeserving of the crown. His Uncle Iroh thinks him good, if troubled, but ultimately worthy of his faith. The kids initially think him a villain, but eventually come to see him as a person – neither monster nor saint – someone who can choose to go in a new way. Zuko himself shows great ambivalence between these conflicting stories about who he is, though each one helps to craft his own self-understanding. In this paper, we apply Hilde Lindemann’s narrative account of the self to explore the ways that others “hold” Zuko in one identity or “let him go” from others. According to Lindemann, our personal identities consist of the first- and third-person stories that cluster around significant acts, relationships, and commitments in our lives. Our identities are fundamentally relational, formed by the interaction between our own self-conception and the ways in which others see us. As such, others’ stories can enable or prevent us from imaginatively projecting ourselves into a particular future. This can lead us to becoming trapped in our identities; without the possibility of being perceived differently by others, we might find ourselves unable to try different ways of being or acting. The converse is also true, in that others can open up new possible identities by seeing things in us that we have trouble seeing in ourselves. If others in our moral community see us as wicked, beyond redemption and unable to repair our wrongs, we are held in the role of the villain and might come to live into that role without question. Zuko’s story is a perfect illustration of Jean Harvey’s reminder that, “it is just not true that once a thief, always a thief” and that agents can choose to go in a new way, can choose to change. How does Zuko change? We argue that Zuko’s redemption is enabled by those in his moral community holding him in identities in which he is a good person, capable and deserving of care, friendship, and love. While the identity he has in relation to his father and sister closes down many possible futures, his uncle Iroh in particular persists in holding him in an identity in which he is loved and worthy of love. And in doing so - in holding this space for him - Iroh opens up a way for Zuko to exercise agency and choose to become a different kind of person than the one he thought he was destined to be.

This paper explores a phenomenon that we call “justified-but-misdirected anger,” in which one’s anger is grounded in or born from a genuine wrong or injustice but is directed towards an inappropriate target. In particular, we argue that oppressive ideologies that maintain systems of gender, race, and class encourage such misdirection and are thereby self-perpetuating. We engage with two particular examples of such misdirection. The first includes poor white voters who embrace racist and xenophobic politics; they are justified in being angry about their own economic exploitation, but that anger is misdirected in a way that maintains capitalism (which is the appropriate target of their anger). The second includes so-called “incels” who embrace misogyny; they are justified in being angry about unrealistic and unhealthy standards of contemporary masculinity, but that anger is misdirected in a way that maintains patriarchy. One goal of exploring this type of justified-but-misdirected anger is to thread the needle between holding wrongdoers to account while also clearly identifying the oppressive ideologies that influence their actions.

Apologies are an important part of moral life and a method by which someone can satisfy their reparative obligations. At the same time, apologies can be used both as a shield to protect the person apologizing and as a weapon against the person to whom the apology is owed. In this paper we unpack both claims. We defend two principles one should employ to try to avoid such bad outcomes: (1) Apologies must be one-sided and nontransactional, and (2) the wrongdoer must be willing to pay what they owe. We argue that these principles require the wrongdoer’s emotional vulnerability. Furthermore, we argue that the duty to be vulnerable in issuing apologies helps to make sense of why apologizing well is so difficult and why members of privileged groups might be especially prone to apologizing badly.

Criticism can sometimes provoke defensive reactions, particularly when it implicates identities people hold dear. For instance, feminists told they are upholding rape culture might become angry or upset, since the criticism conflicts with an identity that is important to them. These kinds of defensive reactions are a primary focus of this paper. What is it to be defensive in this way, and why do some kinds of criticism, or implied criticism, tend to provoke this kind of response? What are the connections between defensiveness, identity, and active ignorance? What are the social, political, and epistemic consequences of the tendency to defensiveness? Are there ways to improve the situation?

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called "Benacerraf's Problem", which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf's problem.

Logical empiricism is not frequently associated with social and political philosophy, but several of the logical empiricists were politically active during their earlier careers and did consider the ways in which their scientific philosophy could provide tools for political engagement. The scientific worldview that they explicitly endorsed was intended to be allied with other modernist projects for the improvement of ordinary life. This chapter argues that some of the philosophical tools and frameworks they developed for those ends can be fruitfully reclaimed by contemporary analytic philosophers engaged in thinking about our social world. Rudolf Carnap’s work, for example, is complementary to some contemporary work on conceptual engineering, such as Sally Haslanger’s work on ameliorative concepts. Additionally, Otto Neurath’s holism, and discussion of the work of auxiliary motives, can help us think through situations in which we have competing empirically adequate theories. I will demonstrate the potential benefits of these frameworks by showing how they might be brought to bear on contemporary issues such as misogyny, transphobia, and scientific racism. I do not claim that the logical empiricists can solve those issues for us, but rather that their work is friendly to the work of philosophers trying to deploy analytic philosophy for liberatory ends. In other words, I argue that there are potential benefits for our viewing the contemporary political turn in analytic philosophy as a return to the political in scientific philosophy.

Kate Manne’s Down Girl: The Logic of Misogyny is an accessible and timely exploration of a particular aspect of gendered oppression that has received surprisingly little scholarly treatment. There is a lot of feminist work on sexism, oppression, and patriarchy, but misogyny, as Manne defines it, is distinct from all of these. Her purpose in this book is to describe misogyny as a distinct force present in contemporary society, and to show how it shapes public life. The strength of Manne’s account is that it detaches misogyny from the intentions and attitudes of individual misogynists, showing instead how it is a feature of a patriarchal society.Misogyny, according to Manne, is like the law enforcement arm of a...

Janice Moulton's “The Adversary Method: A Philosophical Paradigm” articulated several criticisms of the popular idea of philosophy as adversarial debate. Moulton criticizes it on epistemic grounds, arguing that philosophy's overreliance on adversarial debate is to the detriment of its goals. Some, notably Trudy Govier, have argued in favor of at least a minimal adversariality, governed by norms of respectful argumentation. This paper suggests that Govier's faith in these norms is misplaced, because it neglects the social circumstances of the arguers. While some authors have argued that politeness and aggression apply differently to those of different genders, this paper extends that analysis to social identities other than gender. In fact, given certain assumptions about the philosophy of language, engagement in polite adversarial debate may not even be possible for people occupying certain social locations.

This book provides theoretical tools for evaluating the soundness of arguments in the context of legal argumentation. It deals with a number of general argument types and their particular use in legal argumentation. It provides detailed analyses of argument from authority, argument ad hominem, argument from ignorance, slippery slope argument and other general argument types. Each of these argument types can be used to construct arguments that are sound as well as arguments that are unsound. To evaluate an argument correctly one must be able to distinguish the sound instances of a certain argument type from its unsound instances. This book promotes the development of theoretical tools for this task.

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches the way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension with the labeled past-operator “ P ϵ ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.

It is a commonly held view that Dedekind's construction of the real numbers is impredicative. This naturally raises the question of whether this impredicativity is justified by some kind of Platonism about sets. But when we look more closely at Dedekind's philosophical views, his ontology does not look Platonist at all. So how is his construction justified? There are two aspects of the solution: one is to look more closely at his methodological views, and in particular, the places in which predicativity restrictions ought to be applied; another is to take seriously his remarks about the reals as things created by the cuts, instead of considering them to be the cuts themselves. This can lead us to make finer-grained distinctions about the extent to which impredicative definitions are problematic, since we find that Dedekind's use of impredicative definitions in analysis can be justified by his philosophical views.

Although women have long been participants in martial arts and other contact sports, the introduction of a women’s division in the Ultimate Fighting Challenge in 2012 brought women in combat sports into the media spotlight in an arguably unprecedented way. Yet, the increasing acceptance of women’s participation in combat sports does not necessarily mean that these sports are equally accessible to people of all genders. This article, extending insights from Iris Marion Young’s “Throwing Like a Girl,” will argue that the modalities of feminine bodily existence pose barriers to women’s success in combat sports. Young discusses ways in...