Laura Helen Marks
- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780252042140
- eISBN:
- 9780252050886
- Item type:
- book
- Publisher:
- University of Illinois Press
- DOI:
- 10.5622/illinois/9780252042140.001.0001
- Subject:
- Film, Television and Radio, Film
This book argues that pornographic film relies on a particular "Victorianness" in generating eroticism—a Gothic Victorianness that is monstrous and restrained, repressed but also perverse, static but ...
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This book argues that pornographic film relies on a particular "Victorianness" in generating eroticism—a Gothic Victorianness that is monstrous and restrained, repressed but also perverse, static but also transformative, and preoccupied with gender, sexuality, race, and time. Pornographic films enthusiastically expose the perceived hypocrisy of this Victorianness, rhetorically equating it with mainstream, legitimate culture, as a way of staging pornography’s alleged sexual authenticity and transgressive nature. Through an analysis of porn set during the nineteenth century and porn adaptations of Lewis Carroll’s Alice books, Robert Louis Stevenson’s The Strange Case of Dr. Jekyll and Mr. Hyde, Oscar Wilde’s The Picture of Dorian Gray, and Bram Stoker’s Dracula, this book shows how these adaptations expose the implicit pornographic aspects of “legitimate” culture while also revealing the extent to which “high” and “low” genres rely on each other for self-definition. In the process, neo-Victorian pornographies draw on Gothic spaces and icons in order to situate itself as this Gothic other, utilizing the Gothic and the monstrous to craft a transformative, pornographic space. These neo-Victorian Gothic pornographies expose the way the genre as a whole emphasizes, navigates, transgresses, and renegotiates gender, sexuality, and race through the lens of history and legacy.Less
This book argues that pornographic film relies on a particular "Victorianness" in generating eroticism—a Gothic Victorianness that is monstrous and restrained, repressed but also perverse, static but also transformative, and preoccupied with gender, sexuality, race, and time. Pornographic films enthusiastically expose the perceived hypocrisy of this Victorianness, rhetorically equating it with mainstream, legitimate culture, as a way of staging pornography’s alleged sexual authenticity and transgressive nature. Through an analysis of porn set during the nineteenth century and porn adaptations of Lewis Carroll’s Alice books, Robert Louis Stevenson’s The Strange Case of Dr. Jekyll and Mr. Hyde, Oscar Wilde’s The Picture of Dorian Gray, and Bram Stoker’s Dracula, this book shows how these adaptations expose the implicit pornographic aspects of “legitimate” culture while also revealing the extent to which “high” and “low” genres rely on each other for self-definition. In the process, neo-Victorian pornographies draw on Gothic spaces and icons in order to situate itself as this Gothic other, utilizing the Gothic and the monstrous to craft a transformative, pornographic space. These neo-Victorian Gothic pornographies expose the way the genre as a whole emphasizes, navigates, transgresses, and renegotiates gender, sexuality, and race through the lens of history and legacy.
Jason Edward Black
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9781628461961
- eISBN:
- 9781626744899
- Item type:
- chapter
- Publisher:
- University Press of Mississippi
- DOI:
- 10.14325/mississippi/9781628461961.003.0005
- Subject:
- History, American History: 19th Century
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 ...
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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.Less
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.
Jason Edward Black
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9781628461961
- eISBN:
- 9781626744899
- Item type:
- chapter
- Publisher:
- University Press of Mississippi
- DOI:
- 10.14325/mississippi/9781628461961.003.0006
- Subject:
- History, American History: 19th Century
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 ...
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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.Less
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.
Jason Edward Black
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9781628461961
- eISBN:
- 9781626744899
- Item type:
- chapter
- Publisher:
- University Press of Mississippi
- DOI:
- 10.14325/mississippi/9781628461961.003.0007
- Subject:
- History, American History: 19th Century
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 ...
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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.Less
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.
S. N. Afriat
- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.003.0026
- Subject:
- Economics and Finance, Microeconomics
This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to ...
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This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to be a special case of convex programming, but is more substantial, and is really an embodiment of the theory of systems of linear inequalities (as reflected here). This chapter initiates the subject with reference to systems of linear inequalities and natural questions about them, and all LP (linear programming) theorems are encountered simply in pursuing those. Theorems about linear inequalities that have uses directly on their own are also derived (and are illustrated in many places in this book). The eight sections of the chapter are: linear inequalities; separation theorems; theorems of alternatives; polyhedra and polytopes; LP Duality Theorem; the pivot operation; the Simplex Algorithm; and BASIC program.Less
This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to be a special case of convex programming, but is more substantial, and is really an embodiment of the theory of systems of linear inequalities (as reflected here). This chapter initiates the subject with reference to systems of linear inequalities and natural questions about them, and all LP (linear programming) theorems are encountered simply in pursuing those. Theorems about linear inequalities that have uses directly on their own are also derived (and are illustrated in many places in this book). The eight sections of the chapter are: linear inequalities; separation theorems; theorems of alternatives; polyhedra and polytopes; LP Duality Theorem; the pivot operation; the Simplex Algorithm; and BASIC program.
Idan Landau
- Published in print:
- 2015
- Published Online:
- January 2016
- ISBN:
- 9780262028851
- eISBN:
- 9780262327251
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028851.003.0001
- Subject:
- Linguistics, Theoretical Linguistics
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 ...
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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.Less
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.
Laura Helen Marks
- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780252042140
- eISBN:
- 9780252050886
- Item type:
- chapter
- Publisher:
- University of Illinois Press
- DOI:
- 10.5622/illinois/9780252042140.003.0005
- Subject:
- Film, Television and Radio, Film
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 ...
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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.Less
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.
D.C. Feeney
- Published in print:
- 1993
- Published Online:
- January 2014
- ISBN:
- 9780859893817
- eISBN:
- 9781781385180
- Item type:
- chapter
- Publisher:
- Liverpool University Press
- DOI:
- 10.5949/liverpool/9780859893817.003.0007
- Subject:
- Classical Studies, Plays and Playwrights: Classical, Early, and Medieval
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 ...
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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.Less
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.
Joan Ramon Resina
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9781846318337
- eISBN:
- 9781846317880
- Item type:
- chapter
- Publisher:
- Liverpool University Press
- DOI:
- 10.5949/liverpool/9781846318337.003.0015
- Subject:
- Society and Culture, Cultural Studies
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 ...
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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.Less
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.
Morten H. Christiansen and Nick Chater
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780262034319
- eISBN:
- 9780262334778
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262034319.003.0004
- Subject:
- Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
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 ...
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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).Less
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).
Niall Rudd
- Published in print:
- 2005
- Published Online:
- January 2014
- ISBN:
- 9781904675488
- eISBN:
- 9781781385043
- Item type:
- chapter
- Publisher:
- Liverpool University Press
- DOI:
- 10.5949/liverpool/9781904675488.003.0006
- Subject:
- Literature, Poetry
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 ...
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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 verseLess
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
Kazimierz Goebel and Stanisław Prus
- Published in print:
- 2018
- Published Online:
- April 2019
- ISBN:
- 9780198827351
- eISBN:
- 9780191866265
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827351.003.0005
- Subject:
- Mathematics, Pure Mathematics
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 ...
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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.Less
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.
Franz J. Wegner
- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785781
- eISBN:
- 9780191827600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785781.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials
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 ...
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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.Less
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.
Tim Button and Sean Walsh
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198790396
- eISBN:
- 9780191863424
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198790396.003.0014
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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.Less
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.
