Logic in Question: Talks from the Annual Sorbonne Logic Workshop (2011- 2019)

Preface
What's It All About?
10 Questions
List of Speakers – Logic in Question 2011 –2019
Contents
Part I Historical Questions
What Is “Ancient Chinese Logic” ?
1 Brief Introduction
2 The Emergence of “Ming-Bian Logic” ([abstract][][]section.7..1.2UTF8gbsn名辩逻辑section.7..1.2[abstract][][])
3 Difficulties to Define Ancient Chinese Logic as Classical Logic
4 Can Other Logical Theories Rebuild Ancient Chinese Logic?
References
Logical Hylomorphism in the Thirteenth Century
1 Introduction
2 The Early Distinction Between Logical Form and Logical Matter and the Puzzle of “Fallacious, Formally Defective Barbaras”
2.1 Logical Form and Logical Matter in the Sophisitici Elenchi
2.2 “Materially-Formally Defective” and “Formally-Formally Defective” Arguments in Anonymus Cantabrigiensis
2.3 A Split in the Logical Tradition: A Substitutional vs. Rich Concept of Syllogistic Form
3 Thirteenth-Century Logical Hylomorphism: A “Material Logic” in Latin
3.1 Logical Hylomorphism in the Thirteenth Century
3.2 `MacFarlanian' Logical Hylomorphism and Thirteenth-Century Logical Hylomorphism
3.3 Three Senses of “Matter” (Distinguished From “Stuff”) in Logic
3.4 Tensions and Controversies over the Degree of Independence of Form From Matter
3.5 Further Puzzles: A Material Logic in Latin
4 Arguments in a “Syllogistic Limbo”
4.1 Type A: “Not-Formally-Valid-Syllogistically-Disposed Arguments”
4.2 Type B. “Non-Syllogistic-Formally Valid Arguments (Thanks to Their Matter)”
5 A Case Study: The “Two Barbaras” Problem
5.1 The Distinction Between “As-of-Now” and “Unrestricted” Assertoric Propositions in Mixed Modal Syllogistic
5.2 The “Two Barbaras” Problem
5.3 The “As-of-Now vs. Unrestricted Syllogistic Rule”
5.4 The “Appropriation Rule” by Robert Kilwardby
References
The Representation of Negative Terms with Euler Diagrams
1 Introduction
2 Transformation of the Data
3 Amendment of the Diagrams
4 Modification of the Mode of Representation
5 On Negation in Modern Diagrammatic Systems
6 Conclusion
References
Inference in Nineteenth-Century British Logic
1 Introduction
2 Three Traditional Logicians
3 The Transitional Logicians: Augustus De Morgan and George Boole
4 George Boole
4.1 Boole's Rule of 0 and 1
5 William Ernest Johnson
6 William Stanley Jevons
7 John Venn
8 John Neville Keynes and Emily Elizabeth Constance Jones
9 Hugh MacColl
10 Implication as Inference
11 Conclusion
References
Symbolism in Boole: Its Inability to be Interpreted
1 Introduction
2 In Search of the Laws of Thought. Such a Study Is Possible and Necessary
3 Operations and Logical Calculation on Classes. On the All-powerful Symbolism
4 On Propositional Calculus. Putting Primary Propositions into Equations and Interpretation
5 Logical Equations and Systems. Equations Processing
5.1 Logical Functions and Development
5.2 The Logical Division
5.3 On ``Responsible Beings''
6 Boole and Uninterpretable Symbolism
7 The Inability to be Interpreted in Boole
References
Boole's Symbolized Laws of Thought Facing Empiricism
1 Introduction
2 Boole's Relationship with “The Analytics”
3 The Symbolical Approach of Reasoning and Its Social Stakes
3.1 The Main Features of the Symbolical Approach from Peacock to Boole
3.2 Boole's Symbolical Answer to Empiricism
4 Boole's Symbolical Writing of the Laws of Thought for Demonstrative Knowledge
5 Boole's Symbolical Writing of the Laws of Thought for Probable Knowledge
6 Conclusion
References
Boole's Untruth Tables: The Formal Conditions of Meaning Before the Emergence of Propositional Logic
1 Introduction
2 The Place of Boole in the History of Truth Tables
3 Boole's Singular System
3.1 Boole's Logic of Propositions Is Not Propositional Logic: the Logical Meaning of Expressions
3.2 The Method of Development and the Compositional Form of Expressions
3.3 Brief Archeology of 1 and 0: Dual Algebra as Foundations of the Expressive System
4 Boole's Untruth Tables: The Formal Conditions of Expressive Meaning
5 Concluding Remarks
References
Lewis Carroll's Almost Diagrammatic Logic Notation
1 Introduction
2 It All Started with Aristotle
3 Seeing Reason
4 A Simpler Notation Than Boole's?
5 What Makes a Good Notation?
6 Anatomy of a Notation
7 Composition and Suggestiveness
8 There Is Always Better
9 A Diagrammatic Variation
10 Conclusion
References
What Is the Relation Between Peirce's Logic and His Philosophy of Logic?
1 Introduction
2 An Overview of Peirce's Contributions to Logic
2.1 The Logic of Relatives
2.2 Propositional Logic and Quantification
2.3 Existential Graphs
3 An Overview of Peirce's Philosophy of Logic
3.1 Antipsychologism
3.2 Logic and Semiotics
3.3 Normativity
3.4 The Functions of Logic
4 An Outline of Some Connections Between Peirce's Logic and His Philosophy of Logic
References
Husserlian Pure Logic from the Standpoint of Intentionality
1 Introduction: Looking for Grounds (1887–1901)
2 The System of Pure Logic
2.1 The Structuring of Pure Logic
2.1.1 The Sub-theoretical Level
2.1.2 The Theoretical Level
2.1.3 The Meta-Theoretical Level
2.2 The articulation of pure logic
2.2.1 The Connection of the Two Sides of Pure Logic
2.2.2 The Problem of the Imaginary in Mathematics
2.2.3 The Notion(s) of ``Definiteness''
2.3 The Grounding of Pure Logic
2.3.1 The Mereologicality of Morphologies
2.3.2 The Morphosyntactic Subdivision
2.3.3 The Grounding Relationships
3 The Semiotic Standpoint of Intentionality
3.1 The Concrete Intentionality
3.1.1 Expressions as Physical Phenomena
3.1.2 Meaning-Giving Acts (a.k.a. Meaning-Intention)
3.1.3 Meaning-Fulfilling Acts (a.k.a. Meaning-Fulfillment)
3.2 The Abstract Intentionality
3.2.1 Expressions in specie
3.2.2 The Intending-Sense or Meaning Simpliciter
3.2.3 The Fulfilling-Sense (and the Object's Ideal Correlate)
3.3 The Phenomenological Categorialities
3.3.1 The Apophantic Categoriality
3.3.2 The Ontological Categoriality
3.3.3 The Categorial Intentionality
4 Conclusion: Toward a Phenomenological Epistemology of Mathematical Logic?
References
Frege's Silence About Bolzano
1 Introduction
2 Resemblances
3 Bolzano's Irrungen
4 What About Bolzano's Oddities?
5 Conclusion
Appendix
References
The Place and Value of Logic in Louis Couturat's PhilosophicalThinking
1 Introduction: Engagement and Paradoxes of Louis Couturat, Philosopher and Logician
2 The Rationalism of Couturat
3 Principles for Choosing a Good Philosophy and Its Exclusions
4 First Approach of Logic, Between Philosophy and Science
5 Position of the Logic, Couturat Reading Leibniz
6 Position of the Logic, Couturat Reading Russell
7 The Meaning of “Logicism,” Between Logic and Mathematics
8 The Struggle Between Logic and Algebra of Logic
9 Conclusion: The Heart of the Problem—The Lack of Degrees of Liberty in the Relationship Between Philosophy and Science
References
Definition and Inference in Leśniewski's Logic
1 Introduction
2 The Eliminability of Definitions
3 Łukasiewicz's Solution
4 Leśniewski's Solution
5 Two Discoveries
6 Leśniewski's Evolutive Systems
7 Conclusion
References
Part II Philosophical Questions
Is Logic Exceptional?
1 Challenging the Exceptionality of Logic
2 Logic, logic, and ogic
3 Is Logic Exceptional?
4 Is logic Exceptional?
5 Is ogic Relative?
6 The Exceptional Interplay between Logic and Metalogic
7 The Exceptional Interdisciplinarity of Logic
8 The Transdisciplinarity of logic: From Mathesis Universalis to Logica Universalis
9 The Universe, the Universal, and the Universality of Logic
Bibliography
Philosophical Logic == Philosophy + Logic?
1 Introduction
2 In What Sense Can Logic be Taken as Philosophical?
3 In What Sense Has Logic Been Taken as Philosophical?
4 In What Sense Should Logic Not be Taken as Philosophical?
5 In What Sense Should Logic be Taken as Philosophical?
6 Conclusion
References
Revising Logics
1 Introduction
2 Arguments Against Logical Revision
2.1 Logic and the Structure of the Word
2.2 Logic, Meaning Change, and Logical Revision
3 Laws of Nature and Logical Laws: Universal, Unchangeable, Necessary
4 Are There Logical Laws?
5 Revising Logical Laws: An Empiricist View
6 Conclusion
References
Images and Their Ability to Negate
1 Introduction
2 Negation as a Conflict of Forces According to a Semiotic Approach
2.1 Negation from an Enunciative Perspective
2.2 Susanna and the Elders by Tintoretto: A Case of Negation in an Image
3 Conclusion
References
What Does a Concept Entail?
1 Introduction
2 Concepts, Features, and Categorial Membership
2.1 Concepts and Features
2.2 Categorial Membership
2.2.1 Categorial Membership for Compound Concepts
2.2.2 The Determination Connective
2.2.3 Membership Orders for Compound Concepts
3 Typicality
3.1 Typical Instances of an Elementary Concept
3.2 The Characteristic Set
3.3 Typicality for Compound Concepts
4 Concept Inference
5 Concept Induction
5.1 Within-Category Induction
5.1.1 Smooth Subconcepts and Non-exceptional Modifiers
5.1.2 The Case of Exceptional Modifiers
5.2 Over-Category Induction
5.2.1 The Case of Compound Concepts
5.2.2 Typical Subconcepts
5.3 Induction Through Resemblance
5.3.1 Resemblance Between Objects and Concepts
6 Conclusion
References
A Carnapian Logic of Conceivability
1 Introduction
2 Conceivability
3 C Logics
4 C for Conceivability
5 Decidability Issues
6 Conceivability and Possibility
7 Conclusion
References
About All and Nothing: Meinongian Views of All and Nothing as Maximal and Minimal Objects of Thought
1 Exceptions to the Principle of Inverse Proportionality of Intension and Extension
2 Nothingness Characterized Extensionally or Intensionally
3 The Property of Being Nothing and the Only (Abstract) Object Which Satisfies It
4 The Mereologically Null Object
References
The Analytic and the Synthetic from Homology to Heterology
1 Another Look at the Problem
2 From Special Logic to General Logic
2.1 The Limits to Special Logic
2.2 The Shift to General Logic
3 The Analytic and the Synthetic: Main Criticisms
3.1 The Criteria of the Distinction
3.2 The Criticisms to the Distinction
3.2.1 Type I: Synthetic/A Priori
3.2.2 Type II: Analytic/A Posteriori
3.2.3 Type III: Analytic, A Priori/Synthetic, A Posteriori
3.2.4 Type IV: A Priori, Necessity/A Posteriori, Contingency
3.3 The Problem with Criteria
3.4 The Debates on the Analytic and the Synthetic
4 The Analytic and the Synthetic: New Criticisms
4.1 From Homology to Heterology
4.2 Another Logical Framework
4.3 An Extension of Criteria
4.4 Another Definition of the Analytic and the Synthetic
5 Problems with Logicism and Empiricism
6 Ways Out of the Problems
6.1 Ways for the Analysis and the Synthesis
6.2 Ways for the Analyticity and the Syntheticity
References
Bibliography
Analogical Proportions and Binary Trees
1 Introduction
2 A Logical View of Analogy
2.1 Formalizing Analogical Proportion
2.1.1 Postulates
2.1.2 Function-Based View
2.1.3 Boolean Definition
2.2 Why Analogical Proportions Are Pervasive
2.3 Analogical Proportion-Based Inference and Classification
2.4 Toward an Analogical Proportion Reading of Mill's Methods of Induction in Causal Reasoning
3 From the Analogical Cube of Opposition to Binary Trees
3.1 Oppositions Underlying an Analogical Proportion Organized into a Square
3.2 Analogical Cube of Opposition
3.3 Super Analogical Proportion
3.4 A Linkage with Formal Concept Analysis
3.5 Back to Binary Trees
3.6 Analogical Proportion in Binary Trees
3.6.1 Brief Review About Decision Trees
3.7 Analogical Decision Trees
3.7.1 Principle
3.7.2 Illustrative Example
4 Conclusion
References
On Dichotomy and Analogy: A Question on the Next “Unbloody” Revolution in Logic
1 On Bloody and Unbloody Revolutions: Introductory Remarks
2 Łukasiewicz: Logic as Ethics of Thinking
3 Mercy Calls for Wisdom or the Bocheński's Concept of Wisdom as Heuristic Theory
4 Analogy: Toward New Paradigm against the Rules
5 The Joy and Happiness of Noncontradictions
6 Revolutions in Style
References
The Role of Explanatory Virtues in Abduction and IBE
1 Introduction
2 Peircean Abduction vs IBE
2.1 Peircean Abduction
2.2 IBE and How It Relates to Peircean Abduction
2.3 Refining the Definition of IBE
3 The Role of Explanatory Virtues
3.1 Explanatory Power and Explanatory Virtues
3.2 Cataloguing Explanatory Virtues
3.3 Connecting Explanatory Power and Explanatory Virtues
3.4 Towards a Contextual Approach to IBE
4 Conclusion
References
No, No, and No
1 Introduction
2 Pragmatics and Logic
2.1 Affirmations and Negations
2.2 Self-contradiction as a Pragmatic Contradiction
3 A Formal Semantics of Questions–Answers
3.1 Meaning as Predication
3.2 An Algebraic Logic of Term-Oppositions
3.3 A Three-Dimensional View of Logical Values
4 Applications
4.1 Self-contradiction as an Antilogy-Forming Negation
4.2 Neg-raising as a Contrary-Forming Negation
4.3 Litote as a Superalternation-Forming Operator
4.4 Implicature as a Subcontrariety-Forming Operator
4.5 Two Metalinguistic Negations: Presupposition and Category Mistake
5 Affixal Negations
5.1 Definition
5.2 Affixal Oppositions
6 Conclusion: The Three Dimensions of Meaning
References
Grammar Is Not a Mechanism (Wittgenstein): What Could an Anthropology of Mathematics Do?
1 Introduction
2 Le parricide de Frege
3 When Anthropology Takes the Place of Ontology
4 A Look at the Prose of Homo Mathematicus
5 Life Forms
6 An ``applicative'' Engineering Practice
References
Existential Presupposition and Logical Square
1 Dialogical Approach to the Assertive Presupposition
2 The Postulate of Existence in Traditional Syllogistic Logic
3 Modern Logical Approach and Condition of Existence
4 The Pragmatic Approach to the Presupposition of Existence
5 Toward a Presuppositional Logic
6 Conclusion
References
Tabular Notations
1 Truth-Operations Versus Truth-Functions
2 Propositional Signs
3 Tabular Versus Operational Logical Notations
4 Conclusion: A Note on Diagrammatic Typology
References
Part III Mathematical Questions
Contributions of Logical Analysis for Mathematics Education
1 Motivations
2 Syntax, Semantics and Pragmatics in Mathematics Education
3 What Does “Pairwise” Means in Mathematics
4 True/False/Neither True nor False/Both True and False
5 Conclusion
References
The Unification of Mathematics via Topos Theory
1 Introduction
2 Geometric Theories and Their Classifying Toposes
2.1 Geometric Theories
2.2 Classifying Toposes
3 The Logic Underlying Grothendieck Toposes
4 One Topos, Many Sites
5 Morita Equivalences
6 Toposes as ``Bridges''
7 Topos-Theoretic Invariants
7.1 The Logical Meaning of Invariants
8 A Duality Theorem
9 Examples
9.1 Theories of Presheaf Type
9.2 Fraïssé's Construction from a Topos-Theoretic Perspective
9.3 Other Examples
10 Toposes for the Working Mathematician
10.1 A Comparison with Genetics
References
Back and Forth in Positive Logic
References
Quasi-Topological Structure of Extensions Within Logic of Typicals and Atypicals (LTA)
1 A Preliminary Example: The Case of the Ostrich
2 A Distinction Between Property and Concept
2.1 Exemplaries of a Property: Instances of a Concept
2.2 A Concept, a Property, Its Intension, and Its Extension
2.3 Some Definitions and Notations
2.4 Some Examples of Exemplaries of a Concept
2.4.1 A Case of Exception: A Homeless Person Among the Inhabitants of a Community
2.4.2 A Mathematical Example of an Exception
3 Logic of the Determination of Objects (LDO) and Logic of Typical and Atypical Instances (LTA)
4 Quasi-Topological Structuration of a Place
4.1 Examples of Quasi-Typological Structurations
4.1.1 Spatial Course from the Contiguous Interior of a Place to the Interior of a Contiguous Place
4.1.2 Course Between Contiguous Cognitive Places
4.2 Quasi-Topological Structure of a Part of a Set
5 Quasi-Topological Structuration of the Extension of a Concept in LTA
6 Relations of Proximity Between Instances (and Exemplaries) in LTA
6.1 Relations of Proximity Between Instances of a Concept
6.2 Quasi-topological Structure Generated by a Topology Defined Based on the Extension
6.3 Relations of Proximity Between Exemplaries and Instances
6.4 Distancing relationship between Instances and Exemplaries
6.5 Quasi-Topological Structure Generated by a Topology Defined on the Extension
7 Concluding Remarks
8 Annexe: Brief Historical Note on Intension and Extension
References
Bibliography
On the Logical Expressive Power of Natural Languages
1 Introduction
2 Formal Preliminaries
3 Some Invariance Principles
4 Non-reducible Quantifiers
5 Non-homomorphic Predicates
6 Conclusive Remarks
References
A Categorical Aspect of the Analogy Between Quantifiersand Modalities
1 Analogy Between Quantifiers and Modalities
2 Dynamic Logic
3 Cylindric Algebras
4 Categorical Representation
5 Completing the Circle
References
Algebraic and Logical Operations on Operators One Application to Semantic Computation
1 Introduction
2 Combinatory Logic
3 Types, Sorts
4 Functions, Operators
5 ``Trees'' and ``Treille''
5.1 Graph Theory
5.2 Computer Science
6 S-Coprojectifs
6.1 T-Operation of Intrication ``'' on S-Coprojectifs
6.2 T-Operation of Greffe ``o'' on S-Coprojectifs
7 Multioperators from T[Σ]
7.1 T-Operation of Intrication ``'' on Multioperators
7.2 T-Operation of Greffe ``o'' on Multioperators
8 Elements of Comparison with Combinatory Logic
8.1 Combinator W
8.2 Combinator
9 Application to the Representation of Meanings
10 Conclusion
References
The Relevance Logic Programme: Failed or Just Stalled?
1 State of Play
2 Classical Decomposition Trees
3 Decomposing Arrows: Examples
4 Decomposing Arrows: Rules
5 Direct Acceptability
6 Recursion to Acceptability
Is Logic Relevant to Classifications?
1 Introduction
2 An Informal View of the Question
3 A Quotation of Poincaré
4 The Correspondence Between Logic and Classification
4.1 Logical Objections
5 Classifications: Formal Basic Definitions
6 A Generalization of the Correspondence
7 Construction of Classifications
8 Categories, Models, and Classification Theory
9 Conclusion
References
Logic and Theory of Representation
1 Introduction
2 A (Brief) Theory of Representation
2.1 Representational Systems
2.2 Symbolic Systems and Analogical Extensions
2.3 From Situations to Representational Space
3 Some Logical Properties of a Representational System
3.1 Completeness
3.2 Faithfulness
3.3 Coherence
4 Inferences and Theory of Representation
4.1 Elementary Mechanisms of Analogical Extensions
4.2 General Implications and Laws
4.3 Inferences as Laws of Representation
5 Conclusion
References