The Internal Structure of Predicates and Names
1st Edition
Published on 31. October 2018
298 pages
978-1-938421-34-1 (ISBN)
Description
This series of volumes is meant to extend the scope of what we can formalize in classical predicate logic, and in doing so see the limitations of what can be done. The first section of this volume presents classical predicate logic with equality. In the second section, that logic is extended to formalize reasoning that involves adverbs and relative adjectives by viewing those as modifiers of simpler predicates. What is normally taken to be an atomic predicate, such as "barking loudly", can then have internal structure. Reasoning that involves conjunctions of terms, as in "Tom and Dick lifted the table", conjunctions of modifiers, conjunctions of predicates, and disjunctions of predicates can also be formalized by viewing them as part of the internal structure of atomic predicates. Many questions about the nature of formalizing arise in doing this. The internal structure of names is the topic of the third and last section. Names for functions are used in classical predicate logic to form complex names. In our ordinary reasoning we also use descriptions to form functions, such as "the wife of", and descriptions to form names, such as "the cat that scratched Zoe". To reason with those we can take account of their internal structure by dropping the assumption that every name must refer to a specific thing. The formal systems that are developed here are meant to help us understand how to reason well. Many worked examples show how to use them. Those examples also uncover limitations of the formal work. Throughout this series of volumes, the work proceeds by abstracting and creating formal models to formalize reasoning. By paying attention to the process of abstracting we gain insight into why we consider some reasoning to be good and some reasoning bad, and insight also into the deeper assumptions we make about the world on which our judgments rely.
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Richard L. Epstein
The Internal Structure of Predicates and Names
Book
12/2016
Advanced Reasoning Forum
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Person
Richard L Epstein received his B.A. summa cum laude from the University of Pennsylvania, and his Ph.D. from the University of California, Berkeley. He held a post-doctoral fellowship in mathematics and philosophy at Victoria University of Wellington, New Zealand, and was a Fulbright Fellow to Brazil and a National Academy of Sciences Scholar to Poland. He is the author of "Propositional Logics" and, with Walter Carnielli, "Computability". He is now the Head of the Advanced Reasoning Forum.
Content
1 Formal Logic
2 Classical Propositional Logic
3 Formal Theories of Reasoning Well and Limitations of Propositional Logic
4 The Language of Predicate Logic
5 Semantics for Classical Predicate Logic
6 An Axioimatization of Classical Predicate Logic
7 Classical Predicate Logic with Equality
8 Formalizing in Classical Predicate Logic
9 Adverbs as Predicate Restrictors
10 Adjectives as Predicate Restrictors
11 A Formal Logic of Simple Predicate Restrictors for Unary Predicates
12 Examples of Formalizing
13 Are Predicate Restrictors Extensional?
14 Multiple Predicate Restrictors
15 Variable Predicate Restrictors
16 A Formal Theory of Classical Predicate Logic with Predicate Restrictors
17 Examples of Formalizing
18 Predicate Negators
19 Other Kinds of Predicate Modifiers?
20 Modifiers of Modifiers
21 The Pure Negator "Not"
22 Examples of Formalizing
23 "And" Joining Terms
24 "And" Joining Predicates
25 "And" Joining Modifiers
26 "Or" Joining Modifiers
27 Examples of Formalizing
28 Modifiers of Relations
29 Internal Conjunctions and Disjunctions with Relations
30 Examples of Formalizing
31 A Formal Theory
32 Predicates Restricting Predicates
33 Examples of Formalizing
Summary
34 Functions
35 Classical Predicate Logic with Function Names
36 Functions as Descriptive Names
37 The Syntax of Descriptive Names and Descriptive Functions
38 Semantics for Classical Predicate Logic with Descriptive Names and Descriptive Functions
39 An Axiomatization of Classical Predicate Logic with Descriptive Names and Descriptive Functions
40 Examples of Formalizing
41 Names that Don't Refer
42 Classical Predicate Logic with Non-Referring Simple Names
43 Examples of Formalizing
44 Non-Referring Names in Mathematics
45 Classical Predicate Logic with Non-Referring Simple Names and Names for Partial Functions
46 Examples of Formalizing Mathematics
47 Classical Predicate Logic with Non-Referring Simple Names, Descriptive Names, and Descriptive Functions
Summary
Appendices
1 Minimal Metaphysics
2 Events in the Metaphysics of Predicate Logic
3 The Dynamic and the Static
4 Propositional Operators
5 A Mathematical Abstraction of the Semantics
6 Parts of Things
7 Completeness Proofs
Bibliography
Index of Notation
Index of Examples
Index
2 Classical Propositional Logic
3 Formal Theories of Reasoning Well and Limitations of Propositional Logic
4 The Language of Predicate Logic
5 Semantics for Classical Predicate Logic
6 An Axioimatization of Classical Predicate Logic
7 Classical Predicate Logic with Equality
8 Formalizing in Classical Predicate Logic
9 Adverbs as Predicate Restrictors
10 Adjectives as Predicate Restrictors
11 A Formal Logic of Simple Predicate Restrictors for Unary Predicates
12 Examples of Formalizing
13 Are Predicate Restrictors Extensional?
14 Multiple Predicate Restrictors
15 Variable Predicate Restrictors
16 A Formal Theory of Classical Predicate Logic with Predicate Restrictors
17 Examples of Formalizing
18 Predicate Negators
19 Other Kinds of Predicate Modifiers?
20 Modifiers of Modifiers
21 The Pure Negator "Not"
22 Examples of Formalizing
23 "And" Joining Terms
24 "And" Joining Predicates
25 "And" Joining Modifiers
26 "Or" Joining Modifiers
27 Examples of Formalizing
28 Modifiers of Relations
29 Internal Conjunctions and Disjunctions with Relations
30 Examples of Formalizing
31 A Formal Theory
32 Predicates Restricting Predicates
33 Examples of Formalizing
Summary
34 Functions
35 Classical Predicate Logic with Function Names
36 Functions as Descriptive Names
37 The Syntax of Descriptive Names and Descriptive Functions
38 Semantics for Classical Predicate Logic with Descriptive Names and Descriptive Functions
39 An Axiomatization of Classical Predicate Logic with Descriptive Names and Descriptive Functions
40 Examples of Formalizing
41 Names that Don't Refer
42 Classical Predicate Logic with Non-Referring Simple Names
43 Examples of Formalizing
44 Non-Referring Names in Mathematics
45 Classical Predicate Logic with Non-Referring Simple Names and Names for Partial Functions
46 Examples of Formalizing Mathematics
47 Classical Predicate Logic with Non-Referring Simple Names, Descriptive Names, and Descriptive Functions
Summary
Appendices
1 Minimal Metaphysics
2 Events in the Metaphysics of Predicate Logic
3 The Dynamic and the Static
4 Propositional Operators
5 A Mathematical Abstraction of the Semantics
6 Parts of Things
7 Completeness Proofs
Bibliography
Index of Notation
Index of Examples
Index
