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    The infinite in early modern philosophy

    Quinn, Nicola Bridget (2019) The infinite in early modern philosophy. Masters thesis, Birkbeck, University of London.

    The Infinite in Early Modern Philosophy NQuinn MPhilStud Thesis.pdf - Full Version

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    The calculus was developed in the seventeenth and eighteenth centuries in order to solve certain mathematical problems. In ‘The Analyst’ Berkeley gave his objections to the calculus. In particular, he objected to its dependence upon infinitesimals. He argued that these infinitely small distances were contradictory. Further he objected that the calculus, despite leading to true conclusions was not genuine science. So, although the calculus worked, it raised philosophical problems. I will look at Berkeley’s objections, both logical and metaphysical and explore how philosophically problematic they are. I will then consider what consequences arise from these objections. Specifically, I will look at the consequences for mathematical realism, and aim to answer the following questions: If Berkeley’s philosophical arguments are valid how can we explain that the calculus enables us to derive useful results? If we rely on non-entities such as infinitesimals in our mathematical proofs, does this mean that platonism cannot be the true metaphysical framework? If we reject platonism, does the dependence upon nonentities in the proofs of the calculus mean that all forms of mathematical realism are off the table? Or, is this methodology consistent with non-platonic forms of mathematical realism such as truth-value realism. Or, must we look to an alternative picture, such as fictionalism?


    Item Type: Thesis
    Additional Information: Date of MPhil award confirmed as 2019 by registry
    Copyright Holders: The copyright of this thesis rests with the author, who asserts his/her right to be known as such according to the Copyright Designs and Patents Act 1988. No dealing with the thesis contrary to the copyright or moral rights of the author is permitted.
    Depositing User: Acquisitions And Metadata
    Date Deposited: 23 May 2019 11:23
    Last Modified: 10 Jun 2021 17:01


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