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Conclusion

Anandi Hattiangadi

in Oughts and Thoughts: Scepticism and the Normativity of Meaning

This concluding chapter synthesizes the arguments presented in the preceding chapters. It is argued that although we may not yet have an adequate theory of representation, we have no reason to ... More

This concluding chapter synthesizes the arguments presented in the preceding chapters. It is argued that although we may not yet have an adequate theory of representation, we have no reason to believe that none will be forthcoming. The incoherence of the sceptical conclusion gives us some reason to believe that a fully adequate theory of intentionality will be forthcoming.Less

Some calculations of L-groups

Stanley Chang and Shmuel Weinberger

in Quantum Mechanics

This chapter discusses some of the techniques that enter into L theory. The nature of L groups for groups π‎ is very different if π‎ is finite or if π‎ is torsion-free. The latter case seems to be ... More

This chapter discusses some of the techniques that enter into L theory. The nature of L groups for groups π‎ is very different if π‎ is finite or if π‎ is torsion-free. The latter case seems to be governed by rigidity phenomena and is conjecturally very closely related to group homology. Finite groups, however, are studied algebraically. The chapter then explains some of the mathematics that surround the calculation of L groups, looking at connections to Witt theory, algebraic K theory, and representation theory. The connection to representation theory motivates Dress induction. The chapter considers Shaneson's thesis which shows that the Farrell fibering theorem is equivalent to a calculation of L groups.Less

Causally Driven Analogs

Karen Neander

in A Mark of the Mental: In Defense of Informational Teleosemantics

In chapter 8, the author brings causal, teleosemantic and resemblance theories of content together by extending CT (as presented in chapter 7) to explain how homomorphism (more specifically, analog ... More

In chapter 8, the author brings causal, teleosemantic and resemblance theories of content together by extending CT (as presented in chapter 7) to explain how homomorphism (more specifically, analog relations, or second-order similarity relations) can play a content-constitutive role. While the idea that some systems have the function to model the world might explain why a natural representational system counts as a representational system, it is neutral between iconic mental representation and a more language-like version of Mentalese. The author then addresses traditional objections to resemblance theories of content, to show how they can now be met. She argues that sensory-perceptual systems can have functions to produce inner state changes that are caused by and the analogs of their contents, and that this casts light on the intuitive appeal of resemblance theories of mental representation, and that it permits some sensory-perceptual simples to represent novel and non-existent contents. Chapter 8 also addresses the fourth and fifth content-determinacy challenges: why does R have the content there’s C and not there’s Q, when (iv) C is a determinate of Q, or (v) C is a determinable for Q? In the last few sections, Berkeley’s problem of abstraction and two contemporary strategies for its solution are discussed, insofar as it concerns the representation of perceptible properties (e.g., shape and color).Less

A Crash Course in Representation Theory

Loring W. Tu

in Introductory Lectures on Equivariant Cohomology: (AMS-204)

This chapter studies representation theory. In order to state the equivariant localization formula of Atiyah–Bott and Berline–Vergne, one will need to know some representation theory. Representation ... More

This chapter studies representation theory. In order to state the equivariant localization formula of Atiyah–Bott and Berline–Vergne, one will need to know some representation theory. Representation theory “represents” the elements of a group by matrices in such a way that group multiplication becomes matrix multiplication. It is a way of simplifying group theory. The chapter provides the minimal representation theory needed for equivariant cohomology. A real representation of a group G is a group homomorphism. Every representation has at least two invariant subspaces, 0 and V. These are called the trivial invariant subspaces. A representation is said to be irreducible if it has no invariant subspaces other than 0 and V; otherwise, it is reducible.Less

Type A Weyl Group Multiple Dirichlet Series

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are ... More

This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are introduced: Φ‎, a reduced root system; n, a positive integer; F, an algebraic number field containing the group μ‎₂ₙ of 2n-th roots of unity; S, a finite set of places of F containing all the archimedean places, all places ramified over a ℚ; and an r-tuple of nonzero S-integers. In the language of representation theory, the weight of the basis vector corresponding to the Gelfand-Tsetlin pattern can be read from differences of consecutive row sums in the pattern. The chapter considers in this case expressions of the weight of the pattern up to an affine linear transformation.Less

Event Structure and Morphosyntax in Navajo

CARLOTA S. SMITH

in The Syntax of Aspect: Deriving Thematic and Aspectual Interpretation

Event structure in Navajo presents a challenge to generative linguistic analysis. The Navajo verb word has a complex structure with an abstract stem and prefixes that appear in fixed positions. The ... More

Event structure in Navajo presents a challenge to generative linguistic analysis. The Navajo verb word has a complex structure with an abstract stem and prefixes that appear in fixed positions. The positions are traditionally represented by a template. This chapter determines how information about event structure is conveyed in the Navajo verb, and considers how best to represent such structure in a linguistic account. It discusses two different approaches: that of semantically-based syntax, and the surface-structure interpretation of Discourse Representation Theory. It is argued that the latter is preferable on grounds of simplicity and adequacy.Less

Are We Ever Conscious of Concepts?

David Kemmerer

in Concepts in the Brain: The View From Cross-linguistic Diversity

This final chapter addresses the following question: Do the highest levels of mental representation—in particular, concepts and the thoughts they enter into—ever achieve consciousness when activated? ... More

This final chapter addresses the following question: Do the highest levels of mental representation—in particular, concepts and the thoughts they enter into—ever achieve consciousness when activated? Two competing positions have been taken on this issue. The liberal view holds that the contents of experience include not only sensory, motor, and affective states, but also whatever concepts happen to be engaged. In contrast, the conservative view maintains that concepts lack intrinsic qualia and always perform their functions beneath the surface of awareness. This chapter argues that the conservative view is more plausible than the liberal view, and that this has significant implications for three contemporary neuroscientific theories of consciousness. Specifically, it shows that the conservative view raises serious problems for Stanislas Dehaene’s Global Neuronal Workspace Theory and Giulio Tononi’s Integrated Information Theory, but is consistent with Jesse Prinz’s Attended Intermediate-Level Representation Theory.Less

Judgment Alone: Cloven Citizenship in the Era of the Internet

Nadia Urbinati

in Creating Political Presence: The New Politics of Democratic Representation

The generally suspicious way in which democratic citizens tend to look at representation derives from the fact that, no matter how political representation is structured, it can greatly affect their ... More

The generally suspicious way in which democratic citizens tend to look at representation derives from the fact that, no matter how political representation is structured, it can greatly affect their lives. This is due to the fact that the decisions that result from the process of representation are engrafted in state institutions. Yet in politics, representation is not simply what representation does. The phenomenology of representation as the making of claims that represents what we are and want is an important part, although only one part, of the representative game. The other part is the process of decision-making that our electoral choices initiate. This chapter shows how the dual-face of representation displays different conceptions of democracy, which can be grouped in two broad procedural families, one more traditional and minimalist, and the other more deliberative. The parallel analysis of these two families introduces the chapter’s main argument: privileging representation as a practice of informal participation (claim-making in all its complexity) prefigures a kind of democratic citizenship that, thanks also to the internet, breaks down the diarchy of claim-making and decision-making, magnifying the mistaken belief that only the former consists of a more genuine, powerful and richer form of participation.Less

Modular Categories

MICHAEL MÜGER

in Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse

This is a review article on modular categories, and related mathematical subjects such as representation theory of loop groups and of quantum groups at root-of-unity deformation parameter. These ... More

This is a review article on modular categories, and related mathematical subjects such as representation theory of loop groups and of quantum groups at root-of-unity deformation parameter. These represent one of the most fruitful places of interaction of ‘pure’ mathematics and mathematical physics.Less

Selected Theorems by Eli Stein

Charles Fefferman

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

This chapter is an overview of the scope and originality of Eli Stein's contributions to analysis. His work deals with representation theory, classical Fourier analysis, and partial differential ... More

This chapter is an overview of the scope and originality of Eli Stein's contributions to analysis. His work deals with representation theory, classical Fourier analysis, and partial differential equations. He was the first to appreciate the interplay among these subjects, and to perceive the fundamental insights in each field arising from that interplay. No one else really understands all three fields, hence the need for this chapter. However, deep understanding of three fields of mathematics is by no means sufficient to lead to Stein's main ideas. Rather, at crucial points, Stein has shown extraordinary originality, without which no amount of work or knowledge could have succeeded.Less

Dragons and Kasha

Tanya Khovanova

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

This chapter begins with the following teaser about hungry dragons stealing kasha from one another. “Suppose a four-armed dragon is sitting on every face of a cube. Each dragon has a bowl of kasha in ... More

This chapter begins with the following teaser about hungry dragons stealing kasha from one another. “Suppose a four-armed dragon is sitting on every face of a cube. Each dragon has a bowl of kasha in front of him. Dragons are very greedy, so instead of eating their own kasha, they try to steal kasha from their neighbors. Each minute, every dragon extends four arms to the four neighboring faces on the cube and tries to get the kasha from the bowls there. As four arms are fighting for every bowl of kasha, each arm manages to steal one-fourth of what is in the bowl. Thus, each dragon steals one-fourth of the kasha of each of his neighbors, while at the same time all of his own kasha is stolen. Given the initial amounts of kasha in every bowl, what is the asymptotic behavior of the amounts of kasha?” It then arrives at a branch of mathematics called representation theory.Less

Word Order, Information Structure, and Discourse Relations: A Study of Old and Middle English Verb-Final Clauses

Kristin Bech

in Information Structure and Syntactic Change in the History of English

This chapter explores the connection between word order and discourse relations in Old English (OE), while also taking information structure into account. The focus is on verb-final declarative ... More

This chapter explores the connection between word order and discourse relations in Old English (OE), while also taking information structure into account. The focus is on verb-final declarative clauses. It first introduces framework for the analysis of discourse relations and then presents data showing the development of verb-final word order from Old to Middle English. It then outlines the relation between verb-final word order and information structure. Finally, it analyzes and studies the discourse relations of verb-final clauses in some detail, with reference to the distinction between coordinating and subordinating discourse relations as outlined in Segmented Discourse Representation Theory. The basic idea is that some parts of the text play a subordinate role relative to other parts. The chapter shows that verb-final main clauses in OE are primarily associated with discourse coordination rather than subordination. In other words, verb-final clauses do not contrast with V2 clauses with respect to discourse relations, and it therefore remains unclear whether discourse relations play a role in word order variation in Old English.Less

Introduction

Jessica Smartt Gullion

in Fracking the Neighborhood: Reluctant Activists and Natural Gas Drilling

This chapter provides an overview of the theoretical and methodological approaches that were used to conduct an ethnographic study of natural gas drilling activism in the Barnett Shale, a natural gas ... More

This chapter provides an overview of the theoretical and methodological approaches that were used to conduct an ethnographic study of natural gas drilling activism in the Barnett Shale, a natural gas field located beneath the populated Dallas Fort Worth Metroplex. Included is discussion of conceptualizations of the environment and how those conceptualizations impact human relationships in the natural environment. Also included are details about the ethnographic practice of this project, data collection and analysis, reflexivity, and the ethical considerations that went in to this work.Less

Complement Focus and Reference Phenomena

Anthony J. Sanford and Linda M. Moxey

in The Processing and Acquisition of Reference

This chapter presents the results of various experiments that investigated how different determiners and quantifiers make different sets of entities available for reference. It also reviews numerous ... More

This chapter presents the results of various experiments that investigated how different determiners and quantifiers make different sets of entities available for reference. It also reviews numerous accounts of a phenomenon known as complement set reference (compset reference) and shows that it is part of a cluster of phenomena related to negative and positive quantifiers. It then considers various attempts to explore the phenomenon in the context of discourse semantics and presents a number of psychological experiments linking the phenomenon to aspects of negativity and denial of a supposition. It shows that negative quantifiers such as few appear to allow reference to a complement set, contrary to Discourse Representation Theory.Less

From Mission to Electoral Strategy

Heath Brown

in Immigrants and Electoral Politics: Nonprofit Organizing in a Time of Demographic Change

This chapter operationalizes the grounded theoretical model discussed in the previous chapter with an empirical measurement of the various factors it focuses on. It explains the survey methodology ... More

This chapter operationalizes the grounded theoretical model discussed in the previous chapter with an empirical measurement of the various factors it focuses on. It explains the survey methodology used to field a questionnaire to eleven hundred nonprofit organizations in the six states, then analyzes the data collected from survey respondents with a particular focus on the first part of the theory of immigrant-serving nonprofit engagement. The evidence shows that aspects of mission, organizational resources, and policy relate to which electoral tactics an immigrant-serving nonprofit makes use of. Most significantly, the new law to tighten voting procedures in Florida reduced the likelihood that organizations in that state held voter registration drives.Less

Pride and shame in the creation of child and family social work

Matthew Gibson

in Pride and Shame in Child and Family Social Work: Emotions and the Search for Humane Practice

This chapter considers the role of pride and shame in creating, maintaining and disrupting practices that have resulted in child and family social work. As people sought to develop ways of addressing ... More

This chapter considers the role of pride and shame in creating, maintaining and disrupting practices that have resulted in child and family social work. As people sought to develop ways of addressing social issues related to children and families, different discourses on children, families and social issues provided competing and conflicting messages about what was praiseworthy and shameful behaviour. Different representations of social work practice can, therefore, be seen to have been constructed within these competing discourses. This chapter outlines these representations as social administration, social policing, activism, therapy and practical help, demonstrating how pride and shame were central components in how these practices were institutionalised. This chapter then analyses how a discourse of neoliberalism has sought to change the boundaries for praiseworthy and shameful behaviour to reconfigure professional practice.Less