Deflating Existential Consequence: A Case for Nominalism

Paperback | April 13, 2006

byJody Azzouni

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If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essentialpart of scientific doctrine) true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything that our theories quantify. Escaping metaphysical straitjackets (such as the correspondence theory of truth), while retaining the insight that some truths areabout objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictionalobjects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time.

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If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essentialpart of scientific doctrine) true statements...

Jody Azzouni is at Tufts University.

other books by Jody Azzouni

Talking About Nothing: Numbers, Hallucinations and Fictions
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Kobo ebook|Sep 30 2010

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see all books by Jody Azzouni
Format:PaperbackDimensions:256 pages, 9.25 × 6.13 × 0.68 inPublished:April 13, 2006Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195308670

ISBN - 13:9780195308679

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Table of Contents

Introduction. Part I: Truth and Ontology1. Why Empirically Indispensable Mathematical Doctrine and (Some) Scientific Law Must Be Taken as True: Preliminary Considerations. 2. Circumventing Commitment to Truth Despite Empirical Indispensability. 3. Criteria for the Ontological Commitments of Discourse. 4. Criteria for What Exists. 5. Ontological Commitment and the Vernacular: Some Warnings. Part II: Applied Mathematics and Its Posits6. Posits and the Epistemic Burdens They Bear. 7. Posits and Existence. 8. Applying Mathematics: Two Models. 9. Applied Mathematics and Ontology. Conclusion. References. Index.

Editorial Reviews

"[Azzouni] supplies an informative and reasonably subtle account of how mathematics gets applied in scientific theorizing."--Notre Dame Journal of Formal Logic