
Published online:
01 May 2008
Published in print:
11 January 2007
Online ISBN:
9780191710445
Print ISBN:
9780199290932
Contents
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1. Additions to the Syntax of Simple English1 1. Additions to the Syntax of Simple English1
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2. A Truth Theory for Simple English2 2. A Truth Theory for Simple English2
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1. Existence axioms 1. Existence axioms
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1 Reference axioms 1 Reference axioms
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2 Satisfaction axioms 2 Satisfaction axioms
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(A) Satisfaction Axioms for Atomic Sentences (A) Satisfaction Axioms for Atomic Sentences
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(B) Satisfaction Axioms for Open Atomic Formulas (B) Satisfaction Axioms for Open Atomic Formulas
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3 Recursive axioms 3 Recursive axioms
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(A) Recursive Axioms for Logical Connectives (A) Recursive Axioms for Logical Connectives
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(B) Recursive Axioms for Quantifiers (B) Recursive Axioms for Quantifiers
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4 Truth 4 Truth
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3. Proofs of T‐Sentences 3. Proofs of T‐Sentences
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4. Convention T Revisited 4. Convention T Revisited
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Reference Axioms Reference Axioms
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Predicate Axioms Predicate Axioms
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Recursive Axioms Recursive Axioms
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Reference Axioms Reference Axioms
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Predicate Axioms Predicate Axioms
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Comments Comments
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5. Regimentation and Natural Language 5. Regimentation and Natural Language
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Appendix A. Rules Used in Proofs Appendix A. Rules Used in Proofs
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Appendix B. A Canonical Proof Procedure Appendix B. A Canonical Proof Procedure
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Chapter
3 Implementation of the Extension of the Truth Theory to Quantifiers
Get access
Pages
76–98
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Published:January 2007
Cite
Lepore, Ernest, and Kirk Ludwig, 'Implementation of the Extension of the Truth Theory to Quantifiers', Donald Davidson's Truth-Theoretic Semantics (Oxford , 2007; online edn, Oxford Academic, 1 May 2008), https://doi.org/10.1093/acprof:oso/9780199290932.003.0004, accessed 7 May 2025.
Abstract
This chapter gives a small informal theory for a language fragment including quantifiers in illustration. The discussion in subsequent chapters takes place, then, in this new framework in which the axioms of the theory are either reference axioms or satisfaction axioms. The chapter discusses also some issues having to do with how to apply these devices to natural languages, particularly with regard to the use of regimented versions of natural language sentences which aid in the presentation of a formal theory for the language.
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