Rethinking Identity and Metaphysics

Rethinking Identity and Metaphysics: On the Foundations of Analytic Philosophy

Claire Ortiz Hill
Copyright Date: 1997
Published by: Yale University Press
Pages: 200
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  • Book Info
    Rethinking Identity and Metaphysics
    Book Description:

    In this elegant book, Claire Ortiz Hill offers a sophisticated rethinking of the foundations of twentieth-century analytic philosophy. She carefully uncovers the flaws of the central analytic tenet that philosophical discourse is reducible to identities. Closely examining the writings of the analytic philosophers Gottlob Frege, Bertrand Russell, and Willard Quine, she shows that the extensionalistic treatment of identity initiated by Frege and followed by the others has served as a hidden constraint on subsequent work in the mainstream of analytic philosophy. The result has been a flawed treatment of a range of philosophical problems, including necessity, objecthood, meaning, the ontology of mathematics, and Russell's paradox. Hill shows that heroic attempts by philosophers to free philosophical discourse from "intensions"-meanings, concepts, attributes-must fail.

    Hill's conclusions have implications not only for logicians but for all those inquiring into the "ultimate furniture of the universe." She illustrates her arguments with well-chosen examples from a variety of sources-astronomy, the Kennedy assassination, organ transplantation-and shows how lack of clarity in regard to the abstract issue of identity has consequences in such concrete areas as medical ethics and the abortion debate, and how clarity in this issue can bring a better understanding to other problems of analytic philosophy.

    eISBN: 978-0-300-14645-5
    Subjects: Philosophy

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Acknowledgments
    (pp. xi-xvi)
  4. Abbreviations
    (pp. xvii-xviii)
  5. Part One The Twilight Zone
    • 1 Unfettering Reasoning
      (pp. 3-4)

      Gottlob Frege wanted to break the domination of the word over the human mind by laying bare the misconceptions that arise through the use of ordinary language. As an essential part of this project he developed a symbolic language that he hoped would free thought from the fetters language imposed on it.¹

      In Frege’s new symbolic language, nothing would be allowed to slip in unperceived into reasoning. All the principles appealed to would be set out in explicit terms, and precise transformation rules would show exactly what each step in the reasoning depended on. Frege even once confidently proclaimed that...

    • 2 The Equals Sign
      (pp. 5-7)

      Even as Frege began to develop a formal language that he hoped could remove the ambiguity and imprecision imposed on reasoning by ordinary language, he was aware that the equals sign possessed an unusual property. Whereas in other contexts signs merely designate their content, he observed, “names at once appearin propria personaas soon as they are joined together by the symbol for equality of content.” This, Frege reasoned in §8 of his 1879Begriffsschrift, was because this particular sign expresses that two names have the same content, and “thus along with the introduction of the symbol for equality...

    • 3 Confusing Sign and Object in Identity Statements
      (pp. 8-19)

      “Identity,” Willard Van Orman Quine wrote in his influential workWord and Object,“invites confusion between sign and object in men who would not make the confusion in other contexts” (WO, §24). And confusions brought on by the misleading bifurcation in meaning produced by the presence of the equals sign in canonical notation have indeed been a source of confusion and controversy for those who have sought to further the work Frege began. Moreover, it is clear that logicians cannot afford to overlook such difficulties because the preeminent role identity statements have been assigned in symbolic logic means that deeper...

    • 4 Confusing Names and Descriptions in Identity Statements
      (pp. 20-30)

      “One feature of language that threatens to undermine the reliability of thinking,” Gottlob Frege wrote in the last year of his life, “is its tendency to form proper names to which no objects correspond” (PW, 269). The presence of the definite article in a phrase, he explained, can create the impression that the phrase designates an object, and so the phrase may come to be in a place for which it is unsuited. “The difficulties which this idiosyncrasy of language entangles us in are incalculable,” he warned, and he came to rue that he had let himself be tricked by...

    • 5 Confusing Concepts and Objects in Identity Statements
      (pp. 31-42)

      Confusion and controversy have also resulted from failure to distinguish between objects and intensional phenomena such as concepts, senses, attributes, properties, and essences that often find their way into identity statements. And here the problems are much more subtle and harder to uncover and correct than are confusions of mention and use in identity statements. In this chapter I present some initial arguments as to why concepts are not to be identified with objects; in later chapters I discuss some special problems arising from confusing concepts and other intensional phenomena with objects or signs. By showing how, from a logical...

    • 6 Equating Equality and Identity
      (pp. 43-54)

      According to dictionaries, two things are identical when they are the same in every way. They are equal when they are the same under a specific description, as given in a particular way. According to the dictionary definition, the difference between equality and identity would then be the difference between sharing any given property or properties, or having all properties in common. This is the ordinary, non-mathematical, use of the words ‘equality’ and ‘identity’. For example, we commonly say that the United States of America was dedicated to the proposition that all men are created equal with respect to their...

  6. Part Two The Quest for a Clear Extensional Ontology
    • 7 Identity and Frege’s Foundations for Arithmetic
      (pp. 57-72)

      Arithmetic, Frege told his readers in his preface to theBegriffsschrift, had been the point of departure for his work to develop a symbolic language whose first purpose it would be “to provide us with the most reliable test of the validity of a chain of inference and to point out every proposition that tries to sneak in unnoticed, so that its origin might be investigated.” “That is why,” he wrote of the new symbolic language unveiled in his book, “I intend to apply it first of all to that science to provide a more detailed analysis of the concepts...

    • 8 Russell on the Origins of the Set-theoretical Paradoxes
      (pp. 73-90)

      Intellectual sorrow descended upon Bertrand Russell in full measure early in 1901. The cause: a contradiction about classes that are not members of themselves which had managed to slip into Frege’s foundations for arithmetic.28A year later, Russell wrote of his finding to Frege, who immediately wrote back to him that the discovery had surprised him beyond words and left him thunderstruck because it rocked the very ground on which he had hoped to build arithmetic (PMC, 130–32).

      Russell’s discovery eventually led Frege to give up all his efforts to provide secure logical foundations for arithmetic and to conclude...

    • 9 Russell’s Paradoxes and His Theory of Definite Descriptions
      (pp. 91-110)

      Bertrand Russell always said that his theory of definite descriptions represented his first breakthrough in his efforts to find a solution to the paradoxes associated with set theory.36The theory, he considered, had “swept away a host of otherwise insoluble problems.”37

      Like Frege, Russell connected certain problems encountered in trying to translate descriptions into the logical idiom their theories required with the set-theoretical paradoxes. Frege originally thought that descriptions like ‘the discoverer of America’ or ‘the extension of the word ‘star’’ denoted objects, and his Basic Law V would have made such descriptions subject to the same formal rules of...

    • 10 Prepositional Attitudes
      (pp. 111-123)

      The logical landscape ofPrincipia Mathematicaand related systems was predetermined never to be able to deal adequately with intensions. However, some phenomena that defied translation into an extensional idiom right from the beginning are still found lurking about today to blur the clean shaven, austere picture of reality Russell was so eager to bequeath posterity. Notorious among these are what Russell called prepositional attitudes. He considered the problems raised by them to be crucial (PM, 401–02).

      Propositional attitudes are expressions involving notions—like believing, supposing, asserting, and denying—which govern whole clauses or statements. They often figure in...

    • 11 Modalities
      (pp. 124-135)

      Modal logicians vexed Quine by undertaking to expand classical logic to embrace areas of discourse other than those that can be accommodated in the sterile environment secured by the stringent rules of strong extensional calculi. Much to Quine’s dismay, these logicians set out to increase the depth and utility of the standard symbolic languages by developing intensional languages capable of investigating epistemic and deontic contexts and of analyzing the many non-extensional statements that figure significantly in the empirical sciences, law, medicine, ethics, politics, and ordinary philosophy, but that have not been adequately studied within the analytic tradition because they complicate...

  7. 12 Conclusion
    (pp. 136-152)

    In his 1968Leçons sur la première philosophic de Russell, Jules Vuillemin wrote that Russell had often been considered an iconoclast but that the royal road of metaphysics goes by way of such forms of destruction.52

    Twentieth century thought has been thoroughly iconoclastic. The icons it earmarked for destruction were variously judged to be fake, outmoded, irrelevant, worn out, meaningless, repulsive, inhibiting, repressive, pernicious, destructive, dangerous, misleading, unproductive, and so on. And in many cases they were. There was a rage to break them, and along with them, the civilization and traditions many people felt they would rather do without....

  8. Notes
    (pp. 153-158)
  9. Bibliography
    (pp. 159-174)
  10. Index
    (pp. 175-180)