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Predicate Logic The Semantic Foundations of Logic

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ISBN-10: 0534558461

ISBN-13: 9780534558468

Edition: 2001

Authors: Richard L. Epstein

List price: $110.95
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A presentation of the fundamental ideas that generate the formal systems of predicate logic. This text clearly relates predicate logic to reasoning in ordinary language, with hundreds of examples of formalization, with a clear theory of how to formalize ordinary arguments. The writing is exceptionally clear and easy to read.
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Book details

List price: $110.95
Copyright year: 2001
Publisher: Wadsworth
Publication date: 7/25/2000
Binding: Paperback
Pages: 480
Size: 7.25" wide x 9.00" long x 1.00" tall
Weight: 1.584
Language: English

Propositions and Propositional Logic
Propositions and agreements
Other views of propositions
Words and Propositions as Types
Propositions in English
Exercises for Sections A-D
The Basic Connectives of Propositional Logic
A Formal Language for Propositional Logic
Defining the formal language
Realizations: semi-formal English
Exercises for Sections E and F
Classical Propositional Logic
The Classical Abstraction and truth-functions
Validity and semantic consequence
Determining whether a wff is a tautology
Examples of Formalization
Exercises for Sections G and H
Relatedness Logic
The subject matter of a proposition
Relatedness relations
Subject matter as the content of a proposition
An Overview of Semantics for Propositional Logics
Exercises for Sections J and K
The Internal Structure of Propositions
Things, the World, and Propositions
Names and Predicates
Propositional Connectives
Variables and Quantifiers
Compound Predicates and Quantifiers
The Grammar of Predicate Logic
A Formal Language for Predicate Logic
A Formal Language
The Unique Readability of Wffs
The Complexity of Wffs
Free and Bound Variables
The Formal Language and Propositions
Syntax vs. Semantics as a Basis for Logic
Atomic Propositions
A name picks out at most one thing
A name picks out at least one thing
A predicate applies to an object
Predications involving relations
Other conceptions of predicates and predications
How many predicates are there?
Naming, Pointing, and What There Is
Naming, pointing, and descriptions
Avoiding names completely?
Forms of pointing: what there is
Exercises for Sections A-E
The Universe of a Realization
The Self-Reference Exclusion Principle
The assumptions of the realization: Form and Meaningfulness
Interpretations: assignments of references and valuations
The Fregean Assumption and The Division of Form and Content
The truth-value of a complex proposition
Truth in a model
Logics, Validity, Semantic Consequence
Exercises for Sections F-J
Summary Chapters II-IV.J
Tarski's Definition of Truth
Eliminating semantic terms: Convention T
Other logics, other views of truth
Intensional predicates
The Extensionality Restriction
Quantification and intensional predicates
Languages without names
Models in which every object is named
Inconsistent predications and quantification
Other Interpretations of the Quantifiers and the Use of Variables
A current variation on Tarski's definition
The substitutional interpretation
Naming all elements of the universe at once
Surveying all interpretations of the name symbols
Exercises for Sections K-M
The Logical Form of a Proposition
Rewriting English Sentences
Common Nouns as Subject and Object
Relative quantification: [for all]
Relative quantification: [exist]
Nouns into Predicates
Collections and Qualities
Mass Terms
Aristotelian Logic
Formalizations Relative to Formal Assumptions
Analysis vs. formalization
Extending the scope of predicate logic
Formalizing a notion
Criteria of Formalization
Examples of Formalization
The Equality Predicate
The Interpretation of '=' in a Model
The Identity of Indiscernibles
The Predicate Logic Criterion of Identity (p.l.c.i.)
The p.l.c.i. vs. the implicit identity of the universe
The p.l.c.i. and names
Is the Equality Predicate Syncategorematic?
The Order of Quantifiers
[for all]x[exist]y and [exist]y[for all]x
[for all]x[exist]y and [exist]x[exist]y
Superfluous quantifiers
The Scope of Quantifiers: Substituting One Variable for Another
Names, Quantifiers, and Existence
Is '--exists' a Predicate?
Quantifying Over a Finite Universe: [for all] as Conjunction, [exist] as Disjunction
Modeling Other Quantifiers
Positive quantifiers: 'there are at least n'
Negative quantifiers: 'there are at most n', 'no', 'nothing'
Exact quantifiers: 'there are exactly n'
Quantifications we can't model
Relative Quantification
Nouns into Predicates revisited
Formalizations involving the same quantifier
Formalizations involving mixtures of quantifiers
Examples of Formalization
Descriptive Names
Descriptive Names: A Problem in Formalization
Descriptive Names Relative to Formal Assumptions
Russell's Method of Eliminating Descriptive Names from Atomic Propositions
Eliminating All Names?
Examples of Formalization
A definition
The value of a function
Functions compared to predicates
A Formal Language with Function Symbols and Equality
Realizations and Truth in a Model
Partial Name-Makers
Russell's abstraction operator
The [varepsilon]-operator
Examples of Formalization
Quantifying Over Predicates: Second-Order Logic
Quantifying over Predicates?
Predicates and Things
Predicate Variables and their Interpretation: Avoiding Self-Reference
Predicate variables
The interpretation of predicate variables
Note: Higher-order logics
A Formal Language for Second-Order Logic: L[subscript 2]
Identifying Predicates with Collections of n-tuples of the Universe
Exercises for Sections A-F
Examples of Formalization
Exercises for Sections G and H
Predicates as Things: Reducing General Second-Order Logic to First-Order Logic
One universe for predicates and individuals
The translation
Proof that the mapping preserves consequences
Does the reduction preserve meaning?
Quantifying over Functions
Why quantify over functions?
A formal language: L[subscript 2F]
Realizations and models
The difficulty of reducing quantification over functions to first-order logic
Many-Sorted Languages
Exercises for Sections J-L
Language, the World, and Predicate Logic
The World
The Template Analogy
Eliminating Natural Languages?
Predicate Logic as a Model of or Guide to Reasoning
The Notion of Thing in Predicate Logic
What There Is: Restrictions on the Universe of a Realization
Primitives and Assumptions of Predicate Logic
Formalization: Criteria and Agreements
Index of Examples
Index of Notation