Olliz Boyd’s essay examines Blackness in the Latin American literary practices with the aim of showing its centrality to Latin American cultures. He argues that the African heritage of Latin America has been erased as a result of Eurocentric mestizaje. Olliz Boyd first examines this erased heritage in the understanding of race in Latin America and its peculiar processes of racialization, before moving on to centring the analysis on aesthetic practices and literature in particular. Olliz Boyd’s essay examines the erasure of Afro-Latininidad from a perspective that differs from Hooks’ analysis of the erasure of self-identified Afro-Latin communities. He argues that mestizos in general have mixed-race roots that include not just European and Indigenous ancestry, but African as well. The erasure of Afro-Latininidad is, thus, more radical as it involves the negation of an Afro-Latin reality at the heart of mestizaje.
La Negra as Metaphor in Afro-Latin American Poetry
Carter examines the anti-Black sentiment in Latin American culture and pays particular attention to how, even in negrista poetry aimed at contributing to the fight against oppression of Black people, Black women are used as a symbol of sensuality and primitiveness. The paper argues that when Black women feature in poetry in the figure of la mulata, they are associated with nature and portrayed as inherently evil, sensual and primitive. Moreover, while representations of Black men evolved to focus on their inner consciousness, rather than on their physical attributes, and to combat oppressive imagery and symbolism, la mulata continued being used as a satire aimed at inviting Afro-Latin communities to take positive steps towards improving their social conditions. They were used to advance a criticism for how the anti-Black sentiment at the heart of popular conceptions of mestizaje ends up being internalized by members of Afro-Latin communities, so that Black women are represented as renouncing Blackness and engaging in a “whitening” process.
Indigenous Inclusion/Black Exclusion: Race, Ethnicity, and Multicultural Citizenship in Latin America
This article analyses the causes of the disparity in collective rights gained by indigenous and Afro-Latin groups in recent rounds of multicultural citizenship reform in Latin America. Instead of attributing the greater success of indians in winning collective rights to differences in population size, higher levels of indigenous group identity or higher levels of organisation of the indigenous movement, it is argued that the main cause of the disparity is the fact that collective rights are adjudicated on the basis of possessing a distinct group identity defined in cultural or ethnic terms. Indians are generally better positioned than most Afro-Latinos to claim ethnic group identities separate from the national culture and have therefore been more successful in winning collective rights. It is suggested that one of the potentially negative consequences of basing group rights on the assertion of cultural difference is that it might lead indigenous groups and Afro-Latinos to privilege issues of cultural recognition over questions of racial discrimination as bases for political mobilisation in the era of multicultural politics.
Seven Interpretative Essays on Peruvian Reality
In this essay, Mariátegui offers an analysis of Peruvian literary practices and a criticism of some of its central figures. He argues that what has been construed as a “national literature” erases the contributions of Indigenous cultures to Peruvian identity, and, in doing so, it partly contributes to the marginalization of Indigenous Peruvians.
The Inner Life of Mestizo Nationalism
Tarica examines Rosario Castellanos’ Indigenism in her literary work, particularly in her fictional autobiography Balún Canán (The Nine Guardians). Tarica argues that the novel is an examination of the interaction of Castellanos’ mestiza and female identities, and that it concludes with the constitution of an “utterly lonely figure”. Nevertheless, Tarica argues that the inclusion of other protagonists, such as the protagonist’s Mayan nanny, allow for Castellanos to examine the coloniality of power and the appropriation of indigenous identities. According to Tarica, this allows Castellanos to present the protagonist not as a heroine, but as an antiheroine that offers an “absolutely partial version of national events”, and who manages to affirm herself only in “a place of solitary wandering: Uranga’s Nepantla as in-betweenness.
Intellectual Generosity and the Reward Structure of Mathematics
Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood’s (2007) analysis of intellectual generosity. By appealing to Thurston’s own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood’s analysis nicely captures the sense in which he was intellectually generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress.
The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning
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.
A Group Theory of Group Theory: Collaborative Mathematics and the ‘Uninvention’ of a 1000-page Proof
Over a period of more than 30 years, more than 100 mathematicians worked on a project to classify mathematical objects known as finite simple groups. The Classification, when officially declared completed in 1981, ranged between 300 and 500 articles and ran somewhere between 5,000 and 10,000 journal pages. Mathematicians have hailed the project as one of the greatest mathematical achievements of the 20th century, and it surpasses, both in scale and scope, any other mathematical proof of the 20th century. The history of the Classification points to the importance of face-to-face interaction and close teaching relationships in the production and transformation of theoretical knowledge. The techniques and methods that governed much of the work in finite simple group theory circulated via personal, often informal, communication, rather than in published proofs. Consequently, the printed proofs that would constitute the Classification Theorem functioned as a sort of shorthand for and formalization of proofs that had already been established during personal interactions among mathematicians. The proof of the Classification was at once both a material artifact and a crystallization of one community’s shared practices, values, histories, and expertise. However, beginning in the 1980s, the original proof of the Classification faced the threat of ‘uninvention’. The papers that constituted it could still be found scattered throughout the mathematical literature, but no one other than the dwindling community of group theorists would know how to find them or how to piece them together. Faced with this problem, finite group theorists resolved to produce a ‘second-generation proof’ to streamline and centralize the Classification. This project highlights that the proof and the community of finite simple groups theorists who produced it were co-constitutive–one formed and reformed by the other.
Mathematical Practice, Crowdsourcing, and Social Machines
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend.
The Study of Mathematical Practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice – for example the community question-answering system mathoverflow contains around 40,000 mathematical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of “soft” aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal.
Crowdsourced mathematical activity is an example of a “social machine”, a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.
Reassembling Mathematical Practices: a Philosophical-Anthropological Approach
In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.