Abstraction and Infinity

af


Abstraction and Infinity
Format:
Bog, hardback
Udgivelsesdato:
29-12-2016
Sprog:
Engelsk
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Sexting. Cyberbullying. Narcissism. Social media has become the dominant force in young people's lives, and each day seems to bring another shocking tale of private pictures getting into the wrong hands, or a lament that young people feel compelled to share their each and every thought with the entire world. Have smartphones and social media created a generation of self-obsessed egomaniacs?Absolutely not, Donna Freitas argues in this provocative book. And, she says, these alarmist fears are drawing attention away from the real issues that young adults are facing. Drawing on a large-scale survey and interviews with students on thirteen college campuses, Freitas finds that what young people are overwhelmingly concerned with-what they really want to talk about-is happiness. They face enormous pressure to look perfect online-not just happy, but blissful, ecstatic, and fabulously successful. Unable to achieve this impossible standard, they are anxious about letting the less-than-perfect parts of themselves become public. Far from wanting to shareeverything, they are brutally selective when it comes to curating their personal profiles, and worry obsessively that they might unwittingly post something that could come back to haunt them later in life. Through candid conversations with young people from diverse backgrounds, Freitas reveals how even themost well-adjusted individuals can be stricken by self-doubt when they compare their experiences with the vast collective utopia that they see online. And sometimes, as on anonymous platforms like Yik Yak, what they see instead is a depressing cesspool of racism and misogyny. Yet young people are also extremely attached to their smartphones and apps, which sometimes bring them great pleasure. It is very much a love-hate relationship.While much of the public's attention has been focused on headline-grabbing stories, the everyday struggles and joys of young people have remained under the radar. Freitas brings their feelings to the fore, in the words of young people themselves. The Happiness Effect is an eye-opening window into their first-hand experiences of social media and its impact on them.Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-onecorrespondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part ofthe book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can beexploited to provide surprisingly novel perspectives on neo-logicism.

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Udgivelsesdato:
29-12-2016
ISBN13:
9780198746829
Vægt:
494 g
Dybde:
18 mm
Bredde:
166 mm
Højde:
234 mm
Format:
Hardback
  • Forfattere

  • Bibliotekernes beskrivelse

    Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.

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Abstraction and Infinity

af

  • Leveringstid 4-6 hverdage
  • Forventet levering 23-09-2019

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