Elements of ∞-Category Theory

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Mobilizing knowledge

Many linguistic studies have analyzed the ways in which reported speech is used to mobilize knowledge in academic writing, but there have been far fewer such studies of knowledge mobilization in non-academic genres. This study analyzes the functions of reported speech in a Canadian quasi-judicial public inquiry report, a genre that is intertextually situated between research genres (through academic expert witnesses) and policy genres (through its role in making policy recommendations to the government). All instances of explicitly marked citation and reported speech in the commission report were identified and coded by function. The findings show citation and reported speech had specific functions that contributed to knowledge mobilization by discursively creating evidence, transporting worldviews and values, and changing knowledge status in the legal genres. The analysis also raises theoretical questions in linguistics, resulting in the argument that reported speech is not a static, formal category but a discursive status negotiated by the participants.

Variable subject pronoun expression in Cabo-Verdean Creole

The Cabo-Verdean Creole (CVC) subject domain has clitic and tonic pronouns that often amalgamate in double subject pronoun constructions; the possibility of a zero-subject and the formal category underlying subject clitics are disputed (Baptista 1995, 2002; Pratas 2004). This article discusses five variable constraints that condition subject expression across three descriptive and inferential analyses of a corpus of speech collected from 33 speakers from Santiago and Maio. Double subject pronoun constructions and zero-subjects were promoted by a persistence effect, though for the former this applied across nonadjacent clauses since double subject pronoun constructions are switch reference and contrastive devices resembling the doubling of agreement suffixes by independent pronouns in languages traditionally classified as pro-drop. Zero-subjects were favored in third-person contexts as previously observed by Baptista and Bayer (2013), and when a semantically referentially deficient (Duarte & Soares da Silva 2016) DP antecedent was in an Intonational Unit that was prosodically and syntactically linked to the Intonational Unit containing the target anaphor (Torres Cacoullos & Travis 2019). Results support reclassification of CVC subject clitics as ambiguous person agreement markers (Siewierska 2004) and suggest that CVC is developing a split-paradigm for person marking and subject expression (Wratil 2009; Baptista & Bayer 2013).

Residential Education for Disadvantaged Girls: An Alternate Field?

In this article, we engage with the experiences of students in a government-run residential secondary school that enrols girls primarily from disadvantaged socio-economic backgrounds. Through an exploration of the history of the programme, secondary evaluations conducted over the years and a month-long engagement with one such residential school, we probe how the categories of disadvantage—caste and gender— continue to operate, even as the state tries to obliterate them in this space. Drawing on Bourdieu’s theorization of ‘practices’, we describe daily informal interactions in the space, highlighting their role in reinforcing and sometimes challenging extant social differences. Drawing attention to the diversity that lies even within the formal category of ‘disadvantaged’, we describe the potential and the limitations of targeted residential schooling. Our work points to the need for greater sensitivity in the planning and implementation of state-run programmes targeted at the most marginalized and a re-imagination of efforts to offer an ‘alternate field’.

Prolegomena to a theory of chorophorics

The goal of this paper is to offer a theoretical analysis of chorophorics, a recently proposed pro-formal category that can refer either to “places”, or to locations as arguments of spatial relations. It is suggested that chorophorics are a common category that displays heterogeneous morphological properties but homogeneous syntactic distribution and semantic interpretation. Evidence supporting this argument is offered via eight genetically unrelated languages. The evidence shows that at least three different types of chorophorics can be individuated across languages: chorophorics as a sub-type of prepositions, of case-marked nouns or of postpositions. A formal account is offered, based on a Lexical Syntax analysis. The account shows that chorophorics share a similar distribution with prepositional phrases and receive their “place” sense from their distribution in discourse contexts.

Creation and the Transcategorial Phenomenal

This chapter considers the concept of ineffability. Has this concept been monopolized by pluralists who use it to provide an object that is sufficiently mystical and unfathomable to accommodate religious differences? Does the ineffable do any work in their systems other than provide a formal category of ultimacy? The chapter seeks to investigate this by evaluating the use of ineffability, or the transcategorial, by advocates of the pluralist view of religions. In the second part, the chapter seeks to bring the analytic tradition into dialogue with the phenomenological tradition and particularly with the work of Jean-Luc Marion. Marion highlights the given-ness or excess of experiences that do not rely on metaphysical grounds. The chapter suggests an alternative account of ‘the Real’ as an experience of excess (the ‘transcategorial phenomenal’) that takes place in the midst of the event of interreligious encounter. ‘The Real’ from the ground-up.

The Emergence of the Formal Category “Symmetry” in a New Sign Language

Logical properties such as negation, implication, and symmetry, despite the fact that they are foundational and threaded through the vocabulary and syntax of known natural languages, pose a special problem for language learning. Their meanings are much harder to identify and isolate in the child’s everyday interaction with referents in the world than concrete things (like spoons and horses) and happenings and acts (like running and jumping) that are much more easily identified, and thus more easily linked to their linguistic labels (spoon, horse, run, jump). Here we concentrate attention on the category of symmetry [a relation R is symmetrical if and only if (iff) for all x, y: if R(x,y), then R(y,x)], expressed in English by such terms as similar, marry, cousin, and near. After a brief introduction to how symmetry is expressed in English and other well-studied languages, we discuss the appearance and maturation of this category in Nicaraguan Sign Language (NSL). NSL is an emerging language used as the primary, daily means of communication among a population of deaf individuals who could not acquire the surrounding spoken language because they could not hear it, and who were not exposed to a preexisting sign language because there was none available in their community. Remarkably, these individuals treat symmetry, in both semantic and syntactic regards, much as do learners exposed to a previously established language. These findings point to deep human biases in the structures underpinning and constituting human language.

Jesus Christ

Around 1915 Barth saw in the name of Jesus Christ the unity of a God we do not have, with a human being that we are not. In both editions of his Epistle to the Romans, this intuition was expressed, but not yet thought through. When Barth became acquainted with post-Reformation orthodoxy in Göttingen, however, he discovered a way to understand his intuitions in light of the doctrinal decisions of the early church. From Christological debates between the Lutherans and the Reformed, he learned in the 1930s that there cannot be just one representation of the overwhelming reality of the Lord, and that a theologian needs to argue along several different lines. In his doctrine of reconciliation, Barth sketched these different lines in discrete part-volumes. The more formal category of the Word gave way to the all-embracing presence of the Lord Jesus Christ.