Wittgenstein Finitism and the Foundations of Mathematics

Author: Mathieu Marion
Publisher: Oxford University Press
ISBN: 9780198235163
Format: PDF
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Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking from the 1920s through to the 1950s, in the context of themathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. He shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy,and also that it can do much to illuminate current debates about the foundations of mathematics.

Category Mistakes

Author: Ofra Magidor
Publisher: OUP Oxford
ISBN: 0191662844
Format: PDF, Mobi
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Category mistakes are sentences such as 'Green ideas sleep furiously', 'Saturday is in bed', and 'The theory of relativity is eating breakfast'. Such sentences strike most speakers as highly infelicitous but it is a challenge to explain precisely why they are so. Ofra Magidor addresses this challenge, while providing a comprehensive discussion of the various treatments of category mistakes in both philosophy of language and linguistics. The phenomenon of category mistakes is particularly interesting to both these fields because a plausible case can be (and has been) made for explaining it in terms of syntax, semantics, and pragmatics—making it a fruitful case for exploring the relations between and nature of these three fundamental realms of language. Category Mistakes follows this division. After an introduction which explains the aims and motivations for the project and provides a brief historical survey of the (modern) treatment of category mistakes in each of philosophy, linguistics, and computer science, Magidor discusses four approaches in turn: first, the syntactic approach, which maintains that category mistakes are syntactically ill-formed; then two semantic approaches, though ones that appeal to different semantic facets: the meaninglessness view, which maintains that category mistakes are meaningless, and the MBT view, according to which category mistakes are meaningful but truth-valueless; and finally the pragmatic approach, according to which category mistakes are syntactically well-formed, meaningful, truth-valued but nevertheless pragmatically inappropriate. Magidor argues that the first three approaches ought to be rejected, and in the final chapter addresses the main challenge by developing and defending a particular version of the pragmatic approach: a presuppositional account of category mistakes.

Moral Reason

Author: Julia Markovits
Publisher: Oxford University Press
ISBN: 0199567174
Format: PDF, ePub, Mobi
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What is it to have a reason to do something? is one sort of question; what is it we have reason to do? is another. These questions are often explored separately. But our answers to them may not be independent: what reasons are may have implications for what reasons there are. In Moral Reason, Julia Markovits develops and defends a version of a desire-based, internalist, account of what normative reasons are. But doesthat account entail that there are no moral reasons that apply to all of us, regardless of what we happen to desire? It may look obvious that it does--that a bullet must be bitten somewhere. But on Markovits' account, the bullet may yet be avoided. She builds on Kant's argument for his formula of humanity to provide an internalist defense ofuniversal moral reasons, and provides a more satisfying answer to the age-old question: why be moral?

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