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  1. Who needs (to assume) Hume's principle?Andrew Boucher - manuscript
    Neo-logicism uses definitions and Hume's Principle to derive arithmetic in second-order logic. This paper investigates how much arithmetic can be derived using definitions alone, without any additional principle such as Hume's.
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  • Arithmetic without the successor axiom.Andrew Boucher -
    Second-order Peano Arithmetic minus the Successor Axiom is developed from first principles through Quadratic Reciprocity and a proof of self-consistency. This paper combines 4 other papers of the author in a self-contained exposition.
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