The Caesar-problem Problem Francesca Boccuni, Luca Zanetti Philosophia Mathematica, 2025 Hume’s Principle (HP) does not determine the truth values of ‘mixed’ identity statements like ‘$ \\#F $ = Caesar’. This is the Caesar Problem (CP). Still, neologicists such as Hale and Wright argue that (1) HP is a priori, and (2) HP introduces the pure sortal concept Number. We argue that Neologicism faces a Caesar-problem Problem (CPP): if neologicists solve CP by establishing that ‘$ \\#F\\neq $ Caesar’ is true, (1) and (2) cannot be retained simultaneously. We examine various responses neologicists might provide and show that they do not address CPP. We conclude that CP uncovers a fatal tension in Neologicism.
FREGE'S THEORY of REAL NUMBERS: A CONSISTENT RENDERING FRANCESCA BOCCUNI, MARCO PANZA Review of Symbolic Logic, 2022 Frege’s definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege’s ill-fated Basic Law V. We restate Frege’s definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege’s own indications is possible at all.
Structuralist neologicism Francesca Boccuni, Jack Woods Philosophia Mathematica, 2020 Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all (known) properties of the numbers, achieving a key neofregean advantage, while preserving the key structuralist advantage, which objects play the number role does not matter.
Reference in formal semantics and natural language: A methodological route F. Boccuni Phenomenology and Mind, 2018 In this paper, I will tackle the notion of reference of singular terms in the light of a classic analytic divide, i.e. whether its analysis, like the analysis of other basic notions, should be carried out in natural language or in the semantics of formal frameworks. I will incline toward the latter strategy, and consider reference in classical first-order logic as the simplest framework in which to investigate reference.
