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  1. The metaphysics and mathematics of arbitrary objects
    Author: Horsten, Leon
    Published: 2019
    Publisher:  Cambridge University Press, Cambridge ; New York ; Port Melbourne ;New Delhi ; Singapore

    "Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the... more

    Location:
    Bayerische Staatsbibliothek
    Inter-library loan:
    Unlimited inter-library loan, copies and loan

     

    "Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day"--Back cover

     
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    Content information
    Source: Union catalogues
    Language: English
    Media type: Book
    ISBN: 9781107039414
    Subjects: Objekt <Philosophie>; Variable; Strukturalismus; Mathematik
    Other subjects: Mathematics / Philosophy; Variables (Mathematics); Random variables; Continuity; Fine, Kit; Logic, Symbolic and mathematical
    Scope: xvii, 231 Seiten, Illustrationen
    Notes:

    Introduction. Arbitrary objects and the philosophy of mathematics -- Metaphysics of mathematics -- Arbitrary objects -- Mathematical objects as arbitrary objects -- Structure in mathematics -- Mathematical structures -- Kit Fine -- Generic systems and mathematical structuralism -- Reasoning about generic sequences -- Probability and random variables -- Directions for future research