The Logic of Metaphor

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Table of Contents

1. Introduction

• 1. Metaphors and Logic
• 2. Metaphor and Possible Worlds Semantics
• 2.1 Logical Truth-Conditions for Metaphors
• 2.2 Analogical Access and Counterparts
• 3. Analogical Counterparts
• 3.1 Hobbes's Analogy A STATE IS AN ORGANISM
• 3.2 Swanson's Analogy THE CELL IS A FACTORY
• 4. Theory-Constitutive Metaphors
• 4.1 Some Different Kinds of Metaphors
• 4.2 Explication of Theory-Constitutive Metaphors
• 4.3 Examples of Theory-Constitutive Metaphors
• 4.4 Analogical Inferences to Existence
• 5. Analyzing Metaphors
• 5.1 Literal and Metaphorical Meanings
• 5.2 Meanings and Contexts
• 5.3 Stories as Contexts for Metaphors
• 5.4 Descriptions as Contexts for Metaphors
• 5.5 Shared Syntactical Patterns of Descriptions
• 5.6 Shared Objective Patterns of Situations
• 5.7 Analogical Truth-Conditions for Metaphors
• 5.7.1 "Juliet is the sun"
• 5.7.2 "Her lips are cherries"
• 5.7.3 "Sally is a block of ice"
• 6. Philosophical Application of the Computer
• Appendix 1.1: Sample Metaphorical Texts
• 1. Augustine: Memory as Stomach
• 2. Newton: Sound and Light
• 3. Kant: Human Action
• 4. Kant: The State
• 5. Schopenhauer: Experience
• Appendix 1.2: Analogical Inferences to Existence
• 1. Argument by Analogy for Other Minds
• 2. Argument by Analogy for the Existence of God
• 3. Argument by Analogy for Imaginary Boolean Values
• 4. Argument by Analogy for the Null Individual
• 5. Argument by Analogy for Luminiferous Ether

2. Language

• 1. Introduction
• 2. Languages
• 2.1 The Internal and External Languages
• 2.2 Surface Structures and Deep Structures
• 2.3 Literal and Metaphorical Meanings
• 2.4 Context and Interpretation
• 3. The Grammar of Metaphor
• 3.1 Rewrite Rules
• 3.2 Grammatical Classes of Metaphors
• 3.3 Metaphorical Word-Combinations
• 3.4 Marking Word-Combinations as Literal or Metaphorical
• 3.5 Rewrite Rules for Making Metaphors
• 4. Propositions
• 4.1 The Predicate Calculus
• 4.2 Aliing Thematic Roles to Propositions
• 4.3 Aliing Indexes to Propositions
• 4.4 Logical Space and Situations
• 4.5 Analogous Situations in Logical Space
• 5. Propositions as Networks
• 5.1 Atomic Propositions as Networks
• 5.2 Reference and Truth for Atomic Propositions
• 5.3 Molecular Propositions as Networks
• 5.4 Descriptions of Situations
• 6. Conclusion
• Appendix 2.1: Semantics
• 1. The Extended Predicate Calculus
• 1.1 Events and Occurrences
• 1.2 Arguments for Occurrences
• 1.3 Symbols in the Extended Predicate Calculus
• 1.4 Relations in the Extended Predicate Calculus
• 1.5 Models for the Extended Predicate Calculus
• 1.6 Sample Simple Logical Space
• 2. Situations
• 2.1 Situations are Collections of Occurrences
• 2.2 Sample Logical Space and Situation
• 2.3 Graphs of Situations
• 3. Semantics for the Extended Predicate Calculus
• 3.1 Meaning Functions and Variable Assignments
• 3.2 Truth-Values for Atomic Propositions
• 3.3 Atomic Proposition Correspond to States-of-Affairs
• 3.4 Truth-Values for Molecular Propositions
• 3.5 Truth-Values for Quantified Propositions
• 3.6 Truth-Values for Modal Propositions

3. Conceptual Structures

• 1. Introduction
• 2. The Network of Concepts
• 3. The Taxonomic Hierarchy of Types
• 4. The Mereological Hierarchy of Types
• 5. Taxonomic Hierarchy of Processes
• 6. Contrastive Structures
• 7. Symmetries in Networks
• 8. Rules and Lexical Entailments
• 9. Conceptual Fields
• 9.1 Fields are Clusters of Concepts
• 9.2 The Utility of Conceptual Fields
• 9.3 Similarity Fields and Topical Fields
• 9.4 How Metaphors Depend on Conceptual Fields
• 10. Conclusion
• Appendix 3.1: Sample Descriptions
• 1. Descriptions as Input to NETMET
• 2. Methods for Making Input for NETMET
• 3. NETMET's Conceptual Network
• 4. Descriptions and their Textual Origins
• 5. Sample Descriptions
• 5.1 The Description of Human Reproduction
• 5.2 The Description of Intellectual Creativity
• 5.3 The Description of Memory
• 5.4 The Description of the Wax Tablet
• 5.5 The Description of the Aviary
• 5.6 The Description of the Atom
• 5.7 The Description of the Solar System

4. Analogy

• 1. Introduction
• 2. Towards a Formal Theory of Analogy
• 2.1 Formal Definition of Analogy
• 2.2 Subsymbolic Analogies
• 2.3 Synesthetic Analogies
• 3. The Stages of Analogical Inference
• 4. Analogical Access
• 4.1 The Purpose of the Access Phase
• 4.2 Analogical Access as a Kind of Plausible Inference
• 5. Analog Retrieval by Constraint Satisfaction
• 5.1 Plausible Inference via Constraint-Satisfaction in ARCS
• 5.2 The Network in ARCS
• 5.3 Arguments Used to Build an ARCS Network
• 5.4 Running an ARCS Network
• 5.5 Evaluation of ARCS
• 6. The Access Phase in NETMET
• 6.1 Generating the Target Field
• 6.2 Finding the Indexes in the Target
• 6.3 Collecting Target Predicates
• 6.4 Finding Candidate Source Indexes
• 6.5 Finding Candidate Source Fields
• 7. Analogical Mapping
• 7.1 The Analogical Mapping Function
• 7.2 Analogical Mapping as a Kind of Plausible Inference
• 7.3 Computing the Analogical Mapping Function
• 8. Analogical Mapping by Constraint Satisfaction
• 8.1 Generating Match Hypotheses
• 8.2 Relations between Match Hypotheses
• 8.3 Finding the Analogical Mapping Relation
• 8.4 Running the Hypotheses Network
• 9. Difficulties with Proportional Analogy
• 10. A Structural Model of Analogical Mapping
• 10.1 Structural Principles for Analogical Mapping
• 10.2 Principles for Generating a Hypothesis Network
• 10.2.1 The Principle of Proportional Analogy
• 10.2.2 The Principle of Extension to Contrast Sets
• 10.2.3 The Principle of Mereological Analogy
• 10.2.4 The Principle of Extension to Properties
• 10.2.5 The Principle of Extension to Covering Sets
• 10.2.6 The Principle of Mutual Inconsistency
• 10.3 Supplying External Activation to NETMET Hypothesis Nets
• 10.4 Running NETMET Hypothesis Nets to Convergence
• 10.5 Extracting a One-to-One Map
• 11. Conclusion

5. Analogical Transference

• 1. Introduction
• 2. Analogical Transference
• 2.1 The Mechanism of Analogical Transference
• 2.2 The Analogical Transference Operator
• 2.3 Aliing Novel Propositions to the Target
• 3. Subsymbolic Analogical Transference
• 4. An Extended Example of Analogical Transference
• 5. Rules for Analogical Transference
• 5.1 The Process of Analogical Transference
• 5.2 Transference of Source Properties
• 5.3 Transference of Source Features
• 5.4 Transference of Source Relations and Processes
• 5.5 Transference of Source Rules
• 6. Analogical Transference and Induction
• 6.1 Inductive Arguments
• 6.2 Syntactic Form of Inductive Arguments by Similarity
• 6.3 Syntactic Form of Inductive Arguments by Analogy
• 6.4 The Problem of Inductive Support
• 6.5 Determination in Inductive Arguments by Similarity
• 6.6 Determination in Inductive Arguments by Analogy
• 6.7 Inductive Support for Analogically Transferred Propositions
• 7. Perfect Analogies
• 8. Self-Mirroring Universes
• 8.1 Analogous Situations within Possible Worlds
• 8.2 Black's Dual Universe
• 8.3 Infinite Two-Way Recurrence
• 8.4 Royce's Perfect Map of England
• 9. Conclusion
• Appendix 5.1: Examples of Analogical Transference
• 1. Transference in the SOCRATES IS A MIDWIFE Analogy
• 2. Transference in the MEMORY IS A WAX TABLET Analogy
• 3. Transference in the MEMORY IS AN AVIARY Analogy

6. Metaphorical Communication

• 1. Introduction
• 2. Generating Metaphorical Utterances
• 2.1 From Analogies to Metaphors
• 2.2 Rules for Generating Metaphors
• 2.2.1 Noun-Identification Metaphors
• 2.2.2 Noun-Predication Metaphors
• 2.2.3 Noun-Identification Metaphors with Contrary Adjectives
• 2.2.4 Noun-Identification Metaphors with Literally Predicated Adjectives
• 2.2.5 Noun-Identification Metaphors with Functional Genitives
• 2.2.6 Noun-Identification Metaphors with Mereological Genitives
• 2.2.7 Simple Adjective-Predication Metaphors
• 2.2.8 Complex Adjective-Predication Metaphors
• 2.2.9 Verb-Predication Metaphors
• 2.2.10 Verb-Predication Metaphors with Genitives
• 3. From Metaphors to Analogies
• 3.1 Literal and Metaphorical Interpretations
• 3.2 Using the Core Schema to Interpret Metaphors
• 3.3 Sample Algorithms for Filling the Core Schema
• 3.3.1 Verb-Predication Metaphors
• 3.3.2 Noun-Identification Metaphors with Genitive Phrases
• 3.3.3 Noun-Identification Metaphors
• 3.3.4 Noun-Predication Metaphors
• 3.4 From the Core Schema to its Analogy
• 3.5 An Extended Application of the Core Schema
• 3.6 Finding the Analogies in Larger Texts
• 4. Conclusion

7. Analogy and Truth

• 1. Introduction
• 2. Truth-Conditions for Analogies
• 2.1 Truthful Metaphors based on Truthful Analogies
• 2.2 Analogy Completion: The Miller Analogies Test
• 2.3 Truth-Conditions for Analogies
• 3. Logical Paraphrases for Metaphors
• 3.1 Literal and Metaphorical Meanings
• 3.2 Simple Analogical Truth-Conditions
• 3.2.1 Noun-Identifications
• 3.2.2 Noun-Identifications with Prepositional Phrases
• 3.2.3 Verb-Predications
• 3.3 Trivial Satisfactions of Analogical Truth-Conditions
• 4. Rules for Assigning Truth-Values to Metaphors
• 4.1 Metaphor and Modality
• 4.2 Truth-Conditions based on Analogical Counterparts
• 4.2.1 Individual-Individual Identification
• 4.2.2 Sortal-Sortal Identification
• 4.2.3 Individual-Sortal Predication
• 4.2.4 Individual-Property Predication
• 4.2.5 Property-Property Predication
• 4.2.6 Source Relation with Target Arguments
• 4.2.7 Source Relation with Target and Source Arguments
• 4.3 Metaphorical Existence Problems
• 5. Metaphorical Identity is Relative Indiscernibility
• 5.1 Relative Indiscernibility
• 5.2 Analogy Metaphors as Relative Indiscernibilities
• 5.3 Similarity Metaphors as Relative Indiscernibilities
• 6. Conclusion
• Appendix 7.1: Intensional Semantics for Metaphors
• 1. Introduction
• 2. Logical Space
• 3. Permutations of Particulars
• 4. Equivalence of Situations
• 5. Isomorphism of Situations
• 6. Analogy of Situations
• 7. Intensional Semantics for Analogies
• 8. Analogical Truth-Conditions for Metaphors
• 9. Functions from Situation-Pairs to Truth-Values

8. Metaphor and Inference

• 1. Introduction
• 2. Metaphor and Inference
• 2.1 Forward and Backward Inference
• 2.2 Inference in Metaphor Interpretation
• 2.3 Inference to the Best Literal Paraphrase
• 2.4 Inference in Metaphor Justification
• 3. Metaphor Justification
• 3.1 Metaphors as Hypotheses
• 3.2 Abductive Logics for (Dis)confirmation of Hypotheses
• 3.3 Syntactic and Semantic Constraints on Abductive Arguments
• 3.4 Abductive Arguments for Metaphorical Propositions
• 3.5 The Transference of Source (In)Coherence Relations
• 3.6 Cognitive Meaningfulness for Metaphors
• 4. Metaphor Interpretation
• 4.1 The Black-Tourangeau Metaphor Interpretation Method
• 4.2 Computation of Implication Complexes
• 4.3 Transference by Deduction & Abduction
• 4.4 A Historical Example of Black's Procedure
• 4.5 Entailments of Verb-Predication Metaphors
• 4.6 Common Abstract Entailments and Logical Paraphrases
• 5. Conclusion

9. Lexical Meanings

• 1. Introduction
• 2. Definitions for Metaphorical Predicates
• 2.1 Operational Definitions
• 2.2 Open Lists of Partial Definitions
• 2.3 Definitions for Concepts in Natural Lexicons
• 2.4 From Approximate Meanings to New Definitions
• 3. Metaphors Based on Perfect Analogies
• 4. Inference to the Best Definition
• 4.1 Metaphor Interpretation via Common Abstract Entailments
• 4.2 Metaphor Interpretation via Implication and Explanation
• 5. Informative Truth-Conditions
• 5.1 From Counterparts to Meaning Postulates
• 5.2 Truth-Conditions and Confirmation-Conditions for Metaphors
• 6. Metaphors Based on Imperfect Analogies
• 6.1 First Application of the Deduction-Abduction Technique
• 6.2 Second Application of the Deduction-Abduction Technique
• 7. Conclusion

10. Conclusion

11. References