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A Structuralist Theory of Logic

$76.00 ( ) USD

  • Date Published: April 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511879845

$ 76.00 USD ( )
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About the Authors
  • Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics.

    Reviews & endorsements

    "...a novel and comprehensive logical theory....The beauty of this book is that it develops a mathematically rigorous and intuitively appealing vision using only the most elementary technical tools....[an] extraordinary book. Given the coherence, conceptual power, and novelty of the theory it presents, it ought to become a classic." GLH--Philosophy Review

    "In short, this volume has the makings of a classic. I have rarely found myself so enthusiastic about a recent book in logic. I recommend it in the strongest terms." Isaac Levi, Columbia University

    "Koslow's theory permits us to identify logical operators independent of their form in both logical systems and in natural languages. For linguists, his theory opens up the possibility of an entirely new approach to the study of natural-language semantics, one which does not require the postulation of a level of logical form." D. Terence Langendoen, University of Arizona

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    Product details

    • Date Published: April 2011
    • format: Adobe eBook Reader
    • isbn: 9780511879845
    • contains: 15 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Part I. Background:
    1. Introduciton
    2. The program and its roots
    3. Introduction and elimination conditions in a general setting
    4. The Belnap program
    Part II. Implication Relations:
    5. The theory of implication relations
    6. Implications: variations and emendations
    7. Familiar implication relations: deducibility and logical consequence
    8. Implication relations: direct and derived
    9. Implications from implications
    10. Implication relations and the a priori: a further condition?
    Part III. The Logical Operators:
    11. Hypotheticals
    12. Negations
    13. Conjunctions
    14. The disjunction operator
    15. The logical operators parameterized
    16. Further features of the operators
    17. The dual of negation: classical and nonclassical implication structures
    18. The distinctness and relative power of the logical operators
    19. Extensionality
    20. Quantification
    21. Identity
    22. Special structures I. logical operators on individuals: mereology reconstituted
    23. Special structures II. interrogatives and implication relations
    24. Completeness
    Part IV. The Modal Operators:
    25. Introduction
    26. Modality
    27. Modals: existence and nonextensionality
    28. Special modals
    29. The possibility of necessity-style modals
    30. Modals revisited I
    31. Quantification and modality
    32. Modals revisited II
    33. Knowledge, truth, and modality
    34. The comparative strength of modals
    35. Kripke-style systematization of the modals without possible worlds
    36. Model functions, accessibility relations, and theories
    37. Migrant modals

  • Author

    Arnold Koslow

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