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Philosophy
Advances in Proof-Theoretic Semantics
A short course of lectures
«Advances in Proof-Theoretic Semantics»
Prawitz's Conjecture
Self-Reference and Typing
The Need for an Intensional Notion of Harmony
Functions of Language
Further Development of Gentzen's Ideas
Extending the Mapping Proof to Arguments for A
Comments on an Opinion
Deductions in Categories
Degrees of Paradoxicality of Logical Constants
Shifting Opinions
Model-Theoretic Semantics
Definition 7
Concluding Remarks: From Semantic Dualism to Duality
Goldfarb's Account of Dummett's Approach
Defining Meanings: Specialise Then Generalise
Open Proofs and the Placeholder View
Local and Global Proof-Theoretic Semantics
The Reception of the Theory of Constructions and the Second Clause
Categorical Harmony in Comparison with Other Principles
A Proof-Theoretic Interpretation
Stratification
The Kreisel-Goodman Paradox
Neo-Verificationist Approaches
On the Relation Between Heyting's and Gentzen's Approaches to Meaning
Normal Deductions in a Fragment of N
Definition 19
Proof-Theoretic Validity for Generalized Atomic Systems
Open Problems in Proof-Theoretic Semantics
On Dummett's “Proof-Theoretic Justifications of Logical Laws”
Unknown Statements
Foundational Issues
Decidability
Meaning Conditions
Reductions of Deductions in N−=
Rules for Deductions
Diagnosing the Paradox
The Problem of Harmony
Several I-Rules
Proof-Theoretic Semantics Beyond Logic
The Functional Closure
Tarski's Definition of Logical Consequence
Weak and Strong Validity and Their Features
Deductions in Multicategories and Polycategories
Failure of Completeness for Intuitionistic Logic
Appendix
GE Harmony: A Counter-Example
Frege's Question
Model Theory
Predicativity, Decidability, and the BHK Interpretation
Logic, Paradoxes, Partial Definitions
The Mode of Presentation
Validity of Arguments
Definitional Reflection
Equality of Senses
The Nature of Hypotheses and the Format of Proofs
On the Proof-Theoretic Foundations of Set Theory
Representing the Meaning
Background on General Elimination Rules
Morning Star Versus Evening Star Revisited
Is Bullet a Logical Constant?
(21) is intuitionistically valid
Variables and Substitution
Soundness, Completeness, and Internalization
Equality
Categorical Harmony and Paradoxes in Proof-Theoretic Semantics
The GE-rule for Implication and the Type-Theoretic Dependent Product Type
Propositional Logic
Proof-Theoretic Semantics
Self-contradictory Reasoning
The No-Assumptions View
An Intuitionistic Solution
Kreisel's Theory of Constructions, the Kreisel-Goodman Paradox, and the Second Clause
Equality Versus Identity
Explicit Composition and Its Application in Proofs of Normalization
Remarks
Some Remarks on Proof-Theoretic Semantics
Strong Completeness Results
Guilt by Association?
Outlook: Applications and Extensions of Definitional Reflection
Concluding Remarks
The Axiomatization of T
Concluding Remarks and Further Applications
Self-contradictory Reasoning in N−∀∃=
Schematic Inferences
Notation for Natural Derivations
Failure of Completeness
Gentzen's Approach to Meaning
Naïve Set Theory
Analysis of the Method
Assessment
Internalization
Strong Normalization by Bar Induction
Generalized Atomic Systems
Towards a Proof-Theoretic Semantics of Equalities
The Paradox of Knowability from an Intuitionistic Standpoint
Local Logic
Proof-Theoretic Validity
Absoluteness
Self-contradictory Reasoning in N−=
Appendix
Defining Logical Consequence
Completeness Results for Classical Logic
The Principle of Categorical Harmony
Another [Counter-]Example
The Theory of Constructions and the Second Clause
Towards a Definition of Strong Harmony
On the Paths of Categories
Truth Notions
Mappings of Valid Arguments on BHK-Proofs and Vice Versa
I-Rule Has Several Premisses
How Is a Rational Discussion Possible?
Deductions Not Necessarily Based on Propositions
Arguments
Sets
Bidirectionality
A Completeness Result for Intuitionistic Logic
An Overview of the Theory of Constructions
Heyting's Approach to Meaning
A First Comparison Between Heyting's and Gentzen's Approaches
Argument Structures
The Liar Paradox
Defining Sets
The Language of T
Premiss of I-Rule Discharges Some Assumptions
Defining Meanings in General
Boundary Rules
Harmony Based on Generalised Rules
Functional Closure, Local Logic and the Notion of Absoluteness
Lemma 3
Reflection
Comparison with Kripke Semantics
Internal and Intuitive Truth
Self-contradictory Reasoning in N−∃=
Extending the Mapping Arg to BHK-Proofs of A
Formalizing the BHK Interpretation in T
A Strongly Differing Opinion on Proof-Theoretic Semantics?
GE-Rules in General
Definition 18
Harmony Based on Equivalence
Completeness in Proof-Theoretic Semantics
In Other Words
Failure of Strong Completeness
Definition 1
Author's Postscript, January 2015
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