Logicism, Intuitionism, and Formalism

Introduction: The Three Foundational Programmes.- Introduction: The Three Foundational Programmes.- Logicism and Neo-Logicism.- Protocol Sentences for Lite Logicism.- Frege’s Context Principle and Reference to Natural Numbers.- The Measure of Scottish Neo-Logicism.- Natural Logicism via the Logic of Orderly Pairing.- Intuitionism and Constructive Mathematics.- A Constructive Version of the Lusin Separation Theorem.- Dini’s Theorem in the Light of Reverse Mathematics.- Journey into Apartness Space.- Relativization of Real Numbers to a Universe.- 100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?.- Intuitionism and the Anti-Justification of Bivalence.- From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory.- Program Extraction in Constructive Analysis.- Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem.- Formalism.- “Gödel’s Modernism: On Set-Theoretic Incompleteness,” Revisited.- Tarski’s Practice and Philosophy: Between Formalism and Pragmatism.- The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory.- Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics.- Beyond Hilbert’s Reach?.- Hilbert and the Problem of Clarifying the Infinite.