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Chapter Four addresses colonizing governmental discourses surrounding the Dawes Act of 1887 and the identity constructions that arose as the nation edged ever closer to removed Native communities in the West. The chapter, particularly, argues that the U.S. government transformed the paternal relationship it employed in the 1830s to exclude Natives into a rhetorical strategy of assimilation. In the process, American Indians were constituted as dependent and yet civilized enough for agricultural production as a key contribution to the U.S. nation-state. This illustrated a commodification of Native communities through republicanism. And, the government constructed itself as a republican father that would train American Indians for possible citizenship through the allotment policy’s insistence on yeoman farming. The late nineteenth century promises of citizenship pointed to the possibility that American Indians could exist as equals within the civis. However, the colonizing Dawes Act continued to distance American Indians from the U.S. nation. This conflation of assimilation and segregation underscored the identity duality of U.S. nationalism. But, the possibility that citizenship was feasible acted as a decolonial rupture that American Indians worked through to petition for both U.S. citizenship and separate sovereignty.

Chapter Five analyzes the fashion in which American Indians decolonially challenged the allotment policy, and did so in part by restructuring their dependent – and the government’s self-professed paternal and controlling – identities codified in the Dawes Act. American Indians crafted their rebukes to the policy through petitions, memorials, biographical and literary works and public speeches that served to interrogate the identity duality that was entrenched in the allotment scheme. Specifically, the chapter argues that American Indians gave voice to this dualism and these identity constructions, signifying both the hybrid relationship between the U.S. government and Native communities and the decolonizing power of indigenous voice in exposing the government’s contradictions. That is, Dawes era Native discourses pierced the mythos of republicanism and paternalism that the government imbricated, thus revealing the incongruence of the allotment policy’s promises of citizenship combined with further exclusion.

The conclusion considers the exchanges of governmental and American Indian discourses in the first third of the twentieth century in a colonizing context. Here, the passage of the Indian Citizenship Act of 1924 and the Indian New Deal of 1934 culminated from a merging of governmental and indigenous voices, thereby exhibiting a hybridity present in the residues of their nineteenth century exchanges. Both of the outwardly emancipating acts were symbolic of the decolonizing power of Native agency over the course of the removal and allotment eras. Seemingly, integrationist American Indians would achieve the U.S. citizenship they had striven for throughout the allotment era through the Indian Citizenship Act. Likewise, separatist Natives would attain independence through the Indian New Deal, which allowed for tribal restructuring. However, the acts also pointed to the ways that the U.S. government retained its colonial control over American Indians by reifying the identity duality of U.S. nationalism. That is, the acts granted American Indian communities a controlled citizenship and a controlled sovereignty. In the end, both U.S. governmental and American Indian voices were blended into the resulting twin legislation that capped the cultural exchanges extant in nineteenth century U.S.-Native relations.

That Obligatory Control (OC) is fundamentally a dual phenomenon is an old theme in generative grammar, which appears in different guises: VP vs. NP complements, PRO vs. deleted reflexive, predication vs. coindexing, functional vs. anaphoric control, restructuring vs. non-restructuring, property-denoting vs. propositional complements, etc. Most of these divisions are regretfully based on the availability of an English-specific construction, the for-infinitive. This study offers a new take on this old theme. The duality of OC we pursue is firmly grounded in the semantic type of the matrix predicate: attitude vs. nonattitude predicates. We will also see that it has syntactic consequences for the categorial size of the clausal complement. Our starting point will be the empirical landscape of clausal complementation described in Landau’s Agree model.

This chapter discusses transformation and duality in pornographic adaptations of Dr. Jekyll and Mr. Hyde. Hardcore adaptations of Robert Louis Stevenson’s Dr. Jekyll and Mr. Hyde utilize the concept of dual selves to explore crises in queer sexual subjectivity and female sexual desire. Through an analysis of the gay comedies Heavy Equipment (1977) and Dr. Jerkoff and Mr. Hard (1997), and the Vivid Video hetero drama Jekyll and Hyde (1999), this chapter demonstrates the different ways gay and straight pornographers draw on the erotic pleasures of transformation as a way of exploring sexual crisis and a desire to break free from rigid and illusory formulations of identity and desire.

Chapter 4 discusses how the immediacy of language processing provides a fundamental constraint on theories of language acquisition and evolution. Language happens in the here-and-now. Because memory is fleeting, new material will rapidly obliterate previous material, creating a Now-or-Never bottleneck. To successfully deal with the continual deluge of linguistic information, the brain must compress and recode its input into “chunks” as rapidly as possible. It must deploy all available information predictively to ensure that local linguistic ambiguities are dealt with Right-First-Time; once the original input is lost, there is no way to recover it. Similarly, language learning must also occur in the here-and-now. This implies that language acquisition involves learning how to process linguistic structure, rather than inducing a grammar. Incoming language is recoded incrementally into chunks of increasing granularity, from sounds to constructions, and beyond. Importantly, several key properties of language follow naturally from this perspective, including the local nature of linguistic dependencies, the quasi-regular nature of linguistic structure, multiple levels of linguistic representation, and duality of patterning (i.e., that meaningful units are composed of smaller elements).

This chapter uses an analysis of fictive belief in modern literature, by R. Newson, to interpret ancient thinking on this subject. Newson stresses the idea of duality, or ‘having it both ways’; that is, we believe in the fictional world even as we also believe in the (real) world in which the reading or make-believe take place. The boundaries and interplay between these two types of belief and the worlds involved is complex and porous both in antiquity and the modern world.

In Direcció Lisboa, Josep Pla effects a redistribution of Iberian cultural space. The Civil War had forced him to accept the utopian character of the Iberian federation, and the demise of this political ideal strengthened the certainty of irreducible otherness. It was no longer against the foil of Catalan modernity, but against the sensual and sensible Portuguese way of life that Castile appeared in the light of its barbaric disruption of the Peninsula's diversity. Pla framed his travels to Portugal with the trope of the itinerary. The approximations and separations in space do double duty for the conjunctions and disjunctions in time, collecting the variegated themes and descriptions of the Other into the discourse of “travel narrative” but also subjecting them to the interpretive conventions of historical discourse. If Pla indulges in a detailed representation of Portuguese difference, in turn Portugal allows him to de-familiarize Spain in an Iberian representation that competes with official history through the objectivity of presence.

This reading of Ovid's telling of the myth of Echo and Narcissus (Metamorphosis 3.339-510) highlights the duality of auditory and visual reflection. Reflection, inversion, repetition and chiasmus are key to the effect of Ovid's verse

The aim of the chapter is to present duality between uniform convexity and uniform smoothness. Lindenstrauss formulas relating moduli of convexity and smoothness are discussed as the main tool. A section deals with the notion of noncreasy and uniformly noncreasy spaces.

These lecture notes deal with Ising models with interactions containing products of more than two spins. After a number of examples have been given, some general statements are presented. Of particular interest is a gauge-invariant Ising model in four dimensions. This has important properties in common with models for quantum chromodynamics as developed by Ken Wilson. One phase yields an area law for the Wilson loop, yielding an interaction that increases proportionally to the distance and thus corresponds to quark confinement. The other phase yields a perimeter law allowing for a quark–gluon plasma.

Mathematical tools necessary to the argument are presented and discussed. The focus is on concepts borrowed from the convex analysis and variational analysis literatures. The chapter starts by introducing the notions of a correspondence, upper hemi-continuity, and lower hemi-continuity. Superdifferential and subdifferential correspondences for real-valued functions are then introduced, and their essential properties and their role in characterizing global optima are surveyed. Convex sets are introduced and related to functional concavity (convexity). The relationship between functional concavity (convexity), superdifferentiability (subdifferentiability), and the existence of (one-sided) directional derivatives is examined. The theory of convex conjugates and essential conjugate duality results are discussed. Topics treated include Berge's Maximum Theorem, cyclical monotonicity of superdifferential (subdifferential) correspondences, concave (convex) conjugates and biconjugates, Fenchel's Inequality, the Fenchel-Rockafellar Conjugate Duality Theorem, support functions, superlinear functions, sublinear functions, the theory of infimal convolutions and supremal convolutions, and Fenchel's Duality Theorem.

Competitive equilibria are studied in both partial-equilibrium and general-equilibrium settings for economies characterized by consumers with incomplete preference structures. Market equilibrium determination is developed as solving a zero-maximum problem for a supremal convolution whose dual, by Fenchel's Duality Theorem, coincides with a zero-minimum for an infimal convolution that characterizes Pareto optima. The First and Second Welfare Theorems are natural consequences. The maximization of the sum of consumer surplus and producer surplus is studied in this analytic setting, and the implications of nonsmooth preference structures or technologies for equilibrium determination are discussed.

Types are one of the cornerstones of contemporary model theory. Simply put, a type is the collection of formulas satisfied by an element of some elementary extension. The types can be organised in an algebraic structure known as a Lindenbaum algebra. But the contemporary study of types also treats them as the points of a certain kind of topological space. These spaces, called ‘Stone spaces’, illustrate the richness of moving back-and-forth between algebraic and topological perspectives. Further, one of the most central notions of contemporary model theory—namely stability—is simply a constraint on the cardinality of these spaces. We close the chapter by discussing a related algebra-topology ‘duality’ from metaphysics, concerning whether to treat propositions as sets of possible worlds or vice-versa. We show that suitable regimentations of these two rival metaphysical approaches are biinterpretable (in the sense of chapter 5), and discuss the philosophical significance of this rapprochement.