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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
C Anthony Anderson; Michael Zelëny |

ISBN: | 9789401005265 9401005265 |

OCLC Number: | 851387431 |

Description: | 1 online resource (xiii, 627 pages). |

Contents: | Preface; C.A. Anderson, M. Zeleny. Remembering Alonzo Church; D. Kaplan, T. Burge.Part I: Logic. Logic, truth and number: The elementary genesis of arithmetic; P. Apostoli. Second-order logic; J. Corcoran. A representation of relation algebras using Routley-Meyer frames; J.M. Dunn. Church's set theory with a universal set; Th. Forster. Axioms of infinity in Church's type theory; R.O. Gandy. Logical objects; E.L. Keenan. The lambda calculus and adjoint functors; S.M. Lane. Atomic Boolean algebras and classical propositional logic; G.J. Massey. Improved decision procedures for pure relevant logic; R.K. Meyer. The `triumph' of first-order languages; S. Shapiro. Equivalence relations and groups; R. Smullyan. Part II: Computation. Discriminating coded lambda terms; H. Barendregt. lambda-calculus as a foundation for mathematics; K. Grue. Peano's lambda calculus: The functional abstraction implicit in arithmetic; D. Leivant. The undecidability of lambda-definability; R. Loader. A construction of the provable wellorderings of the theory of species; P. Martin-Loef. Semantics for first and higher order realizability; C. Mclarty. Language and equality theory in logic programming; J.C. Shepherdson. Part III: Philosophy, Meaning, and Intensional Logic. Alternative (1*): A criterion of identity for intensional entities; C.A. Anderson. Nominalist paraphrase and ontological commitment; J.P. Burgess. Peace, justice and computation: Leibniz' program and the moral and political significance of Church's theorem; M. Detlefsen. Tarski's theorem and NFU; M.R. Holmes. Church's theorem and randomness; G. Mar. Russellian type theory andsemantical paradoxes; E. Martino. The logic of sense and denotation: Extensions and applications; T. Parsons. Analysis, synonymy and sense; M. Richard. The very possibility of language; N. Salmon. Index. |

Series Title: | Synthese library, 305. |

Responsibility: | edited by C. Anthony Anderson, Michael Zelëny. |

### Abstract:

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

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