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Francesca Boccuni
University Vita-Salute San Raffaele
  1.  75
    Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
    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 properties of the numbers, achieving a key (...)
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  2.  87
    Plural Logicism.Francesca Boccuni - 2013 - Erkenntnis 78 (5):1051-1067.
    PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of logicism which is radically (...)
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  3.  35
    Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-44.
    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.
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  4.  97
    On the Consistency of a Plural Theory of Frege’s Grundgesetze.Francesca Boccuni - 2011 - Studia Logica 97 (3):329-345.
    PG (Plural Grundgesetze) is a predicative monadic second-order system which is aimed to derive second-order Peano arithmetic. It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.
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  5.  87
    Plural Grundgesetze.Francesca Boccuni - 2010 - Studia Logica 96 (2):315-330.
    PG (Plural Grundgesetze) is a predicative monadic second-order system which exploits the notion of plural quantification and a few Fregean devices, among which a formulation of the infamous Basic Law V. It is shown that second-order Peano arithmetic can be derived in PG. I also investigate the philosophical issue of predicativism connected to PG. In particular, as predicativism about concepts seems rather un-Fregean, I analyse whether there is a way to make predicativism compatible with Frege’s logicism.
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  6.  13
    Salvatore Florio and Øystein Linnebo. The Many and the One. A Philosophical Study of Plural Logic.Francesca Boccuni - forthcoming - Philosophia Mathematica.
  7.  4
    Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientae 26:189-206.
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  8. Book Review. [REVIEW]Francesca Boccuni - 2011 - Epistemologia 34:166-168.
     
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  9. Mathematics and Cognition: Some Objections to a Cognitive Foundation for Mathematics.Francesca Boccuni - 2006 - The Baltic International Yearbook of Cognition, Logic and Communication 2.
  10.  13
    Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Logicism.Francesca Boccuni & Andrea Sereni (eds.) - 2021 - Routledge.
    This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. The first section focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in (...)
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  11. Origins and Varieties of Logicism. A Foundational Journey in the Philosophy of Mathematics.Andrea Sereni & Francesca Boccuni (eds.) - 2021
     
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  12.  13
    Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics.Francesca Boccuni & Andrea Sereni (eds.) - 2016 - Cham, Switzerland: Springer International Publishing.
    This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of (...)
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  13.  27
    Minimal Logicism.Francesca Boccuni - 2014 - Philosophia Scientae 18:81-94.
    PLV (Plural Basic Law V) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a first-order formulation of Frege's infamous Basic Law V. George Boolos' plural semantics is replaced with Enrico Martino's Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. ACS provides a form of logicism which is radically alternative to Frege's and which is grounded on the existence of (...)
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  14.  2
    Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientiae 26:189-206.
    In [Boccuni 2010], a predicative fragment of Frege’s blv augmented with Boolos’ unrestricted plural quantification is shown to interpret pa2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic fa because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret fa and consequently pa2 in a way that parallels Frege’s. In that way, the presented system will be (...)
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