*Frank Arntzenius*

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter discusses the idea that there are no such things as space-time points; the idea that every part of space-time is a finitely extended region. First a number of, prima facie compelling, ...
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This chapter discusses the idea that there are no such things as space-time points; the idea that every part of space-time is a finitely extended region. First a number of, prima facie compelling, arguments in favour of this view are given. Then a mathematically precise topological version of this idea is developed, which is subsequently rejected as inadequate for the purposes of physics. In view of this inadequacy a mathematically precise measure theoretic theory of pointless spaces developed. But it is meekly conceded that, ultimately, pointy spaces are a more plausible setting for physics.Less

This chapter discusses the idea that there are no such things as space-time points; the idea that every part of space-time is a finitely extended region. First a number of, prima facie compelling, arguments in favour of this view are given. Then a mathematically precise topological version of this idea is developed, which is subsequently rejected as inadequate for the purposes of physics. In view of this inadequacy a mathematically precise measure theoretic theory of pointless spaces developed. But it is meekly conceded that, ultimately, pointy spaces are a more plausible setting for physics.

*Mihály Bakonyi and Hugo J. Woerdeman*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128894
- eISBN:
- 9781400840595
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128894.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly ...
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Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.Less

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.

*Jennifer Rose Carr*

- Published in print:
- 2019
- Published Online:
- March 2019
- ISBN:
- 9780198833314
- eISBN:
- 9780191871658
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198833314.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology

On an attractive, naturalistically respectable theory of intentionality, mental contents are a form of measurement system for representing behavioral and psychological dispositions. This chapter ...
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On an attractive, naturalistically respectable theory of intentionality, mental contents are a form of measurement system for representing behavioral and psychological dispositions. This chapter argues that a consequence of this view is that the content/attitude distinction is measurement system relative. As a result, there is substantial arbitrariness in the content/attitude distinction. Whether some measurement of mental states counts as characterizing the content of mental states or the attitude is not a question of empirical discovery but of theoretical utility. If correct, this observation has ramifications in the theory of rationality. Some epistemologists and decision theorists have argued that imprecise credences are rationally impermissible, while others have argued that precise credences are rationally impermissible. If the measure theory of mental content is correct, however, then neither imprecise credences nor precise credences can be rationally impermissible.Less

On an attractive, naturalistically respectable theory of intentionality, mental contents are a form of measurement system for representing behavioral and psychological dispositions. This chapter argues that a consequence of this view is that the content/attitude distinction is measurement system relative. As a result, there is substantial arbitrariness in the content/attitude distinction. Whether some measurement of mental states counts as characterizing the content of mental states or the attitude is not a question of empirical discovery but of theoretical utility. If correct, this observation has ramifications in the theory of rationality. Some epistemologists and decision theorists have argued that imprecise credences are rationally impermissible, while others have argued that precise credences are rationally impermissible. If the measure theory of mental content is correct, however, then neither imprecise credences nor precise credences can be rationally impermissible.

*Pippa Norris and Andrea Abel van Es*

- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780190603601
- eISBN:
- 9780190603632
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190603601.003.0001
- Subject:
- Political Science, Comparative Politics, International Relations and Politics

During the last two decades, the issue of the most effective regulation of political finance, and the prevention of corrupt practices in the public sector, has risen to the top of the governance ...
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During the last two decades, the issue of the most effective regulation of political finance, and the prevention of corrupt practices in the public sector, has risen to the top of the governance agenda for the international community and for many domestic reformers. To address this challenge, this book focuses upon three questions: (1) What types of public policies are commonly employed to regulate the role of money in politics? (2) What triggers major political finance reforms? (3) “What works,” what fails, and why, when countries implement reforms? Section 1.1 of this chapter describes the evolving research agenda on money in politics, highlighting important advances during recent decades. Section 1.2 establishes the conceptual typology, which identifies four common public policies used to regulate political finance in states worldwide Section 1.3 outlines how the book explores these issues. Section 1.4 provides a roadmap of the rest of the book.Less

During the last two decades, the issue of the most effective regulation of political finance, and the prevention of corrupt practices in the public sector, has risen to the top of the governance agenda for the international community and for many domestic reformers. To address this challenge, this book focuses upon three questions: (1) What types of public policies are commonly employed to regulate the role of money in politics? (2) What triggers major political finance reforms? (3) “What works,” what fails, and why, when countries implement reforms? Section 1.1 of this chapter describes the evolving research agenda on money in politics, highlighting important advances during recent decades. Section 1.2 establishes the conceptual typology, which identifies four common public policies used to regulate political finance in states worldwide Section 1.3 outlines how the book explores these issues. Section 1.4 provides a roadmap of the rest of the book.