Time and space in formal logic / Richard L. Epstein.

Format:

Book

Author/Creator:

Epstein, Richard L., author.

Series:

Logic, Language, and the World

Logic, Language, and the World ; v.2

Language:

English

Subjects (All):

Metaphysics.

Physical Description:

1 online resource (303 pages)

Edition:

First edition.

Place of Publication:

Socorro, NM : Advanced Reasoning Forum, [2022]

Summary:

Time and Space in Formal Logic begins with an analysis of assumptions about how logic and language relate. Then in the first section, times are taken to be established by true propositions, and those are related as before and after with temporal propositional connectives. In the second section, times are treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over times. In the third section, locations in space are also treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over both times and locations. Many applications of the formal systems to formalizing ordinary language propositions and inferences clarify better the assumptions we make in reasoning taking account of time and space by making those precise in the formal systems. Appendices on events, branching times, intentions, and descriptive names add to the scope of the work.

Contents:

Intro

Table of Contents

Preface

Cast of Characters

Logic and Language

1 Propositions and Inferences

2 Logic and Language

Relative Times

Temporal Propositional Connectives

3 Times and Propositions

4 Temporal Connectives

5 Time as an Ordering

6 Classical Propositional Logic with Temporal Connectives

7 Reduced Models

8 An Axiom System

9 Examples of Formalizing

10 Other Orderings of Time

11 Past, Present, and Future

Summary

Quantifying over Relative Times

12 Quantifying over Relative Times via Indices

13 Examples of Formalizing

Times and Locations as Things

Time in Predicate Logic

14 The Timelessness of Classical Predicate Logic

15 Time and Reference in Predicate Logic

16 Times as Things

17 Basic Assumptions about Times

18 Times and Predications

19 Identity and the Equality Predicate

20 When Things Exist

21 The Logic QT

22 Examples of Formalizing: The Nature of Time

23 The Internal Structure of Atomic Predicates

Formalizing with Quantifying over Times

24 Quasi-Linear Time

25 Formalizing English Tenses

26 Examples of Formalizing: Context of Utterance

27 Examples of Formalizing: Existence

28 Examples of Formalizing: Attributes

29 Relativizing Quantifiers

30 Examples of Formalizing: Meaning Axioms

31 Examples of Formalizing: How Many Times

32 Examples of Formalizing: The Internal Structure of Atomic Predicates

33 Measuring Time?

34 Other Tenses

35 The Habitual

Summary of Quantifying over Times

Space in Predicate Logic

36 Things in Time and Space

37 Locations

38 References to Things, Times, and Locations Are Independent

39 Assumptions about Locations

40 True in a Location

41 Locational Predicates

42 Existence in Space and Time

43 Where Things Are.

44 A Formal Language for Reasoning about Things in Time and Space

45 Semantics

46 An Axiom System for QTS

47 Examples of Formalizing: The Nature of Space

48 Informal Examples

49 Examples of Formalizing

50 Location-Orienting Predicates

51 Parts of Physical Things

Metaphysical Bases of Logics of Time and Space

Appendices

Appendix A Tenses as Propositional Operators

Appendix B The Tapestry of Time

Appendix C Events

Appendix D Intentions

Appendix E Are Things Needed to Pick Out Locations?

Appendix F Descriptive Names in the Logic of Quantifying over Times

Bibliography

Index of Examples

Index of Symbols

Index.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Other Format:

Print version: Epstein, Richard L. Time and Space in Formal Logic

ISBN:

9781938421693

OCLC:

1344541733