Abstraction and Infinity


Abstraction and Infinity
Bog, hardback
  • Beskrivelse
  • Yderligere info
  • Anmeldelser

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.

Andre udgaver:

Bog, paperback
E-bog, PDF

Vis mereVis mindre

494 g
18 mm
166 mm
234 mm
  • 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.

Vis mereVis mindre

Vis mereVis mindre

Abstraction and Infinity


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

på lager

Fandt du ikke hvad du søgte?

Hvis denne bog ikke er noget for dig, kan du benytte kategorierne nedenfor til at finde andre titler. Klik på en kategori for at se lignende bøger.

Velkommen til Saxo

Du har nu adgang til din konto hos Saxo, og kan se alle oplysninger om dit medlemskab, dine
ordrer og din digitale boghylde under "Mit Saxo".

Som tak for, at du har aktiveret dit medlemskab, har vi valgt at give dig fri læsning hele
sommeren. Dvs. at du frit kan tilgå de mere en 50.000 bøger i Saxos app, samt købe bøger til
vores altid lave medlemspris og fri fragt her på Saxo.com hele juli. Din næste medlemsbetaling
vil først falde i august.

Vi glæder os meget til at byde dig velkommen i vores univers, og håber at du kommer godt i
gang med Saxo Premium.

God sommer og god læselyst!

Med venlig hilsen Saxo

Kom i gang nu!