The Common Foundation of Neo-Logicism and the Frege-Hilbert Controversy

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Dissertation Hilbert's Principle An introduction to Hilbert's Principle The misguided reading of Hilbert's Principle What is misguided about the misguided reading? In defence of the misguided reading Critiquing the defence of the misguided reading A new reading of Hilbert's Principle Hilbert's Principle as a response to Frege The priority reading Reflections on the priority reading The Frege-Hilbert Controversy The axioms and aims of Hilbert's Grundlagen der Geometrie The aims of the Festschrift The axioms of Foundations of Geometry The methodology of Hilbert's Festschrift The dispute of the Frege-Hilbert controversy Hilbert's muddle The substance of Frege's terminological objection Hilbert's reply to the terminology objection Frege's diagnosis of Hilbert's axioms Hilbert's reaction to diagnosis Hilbert's Principle in the context of the Frege-Hilbert controversy The misguided reading in context The priority reading in context Textual support for the four priority conditions Frege's 1906 independence test The two priority claims The Deeper Disagreement and Hilbert's Ontology Blanchette on Frege and Hilbert on consistency Frege-consistency Hilbert-consistency Frege-consistency and Hilbert's proofs Another threat of a merely verbal disagreement The priority reading on the deeper disagreement The purpose of the axiomatic method for Frege The purpose of the axiomatic method for Hilbert The final priority reading Hilbert's early structuralism Non-eliminativist structuralism Existence and uniqueness worry An objection to Neo-Fregean Logicism Rehearsing Frege's diagnosis The basic tenet of neo-Fregean logicism Frege's dilemma for the neo-Fregean logicists Two commitments of neo-Fregean logicism Two criticisms Applying Frege's dilemma for implicit definition Anticipating a counter-objection An objection to Hale and Wright's Plan B Hale and Wright's Plan B: conditional forms of Hume's Principle Conditional introduction of numbers Impredicativity The strategy for a conditional introduction of numbers Generalising the strategy Frege's critique of Plan B The first application The second application Way out for Hale and Wright, ontological revision Hale and Wright's ontological concession An independent means of specification Sortal inclusion principle Sortals and categories: Exposition of the distinctions appealed to by Hale and Wright What is the Sortal Inclusion Principle and how does it circumvent the Caesar problem? The need for a criterion for criteria of identity The sortal ontology and Frege's ontology MP Problem Minimalism The need for a meta-ontology Lockeanism Hale and Wright's preferred theory of reference Bibliography