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Forthcoming articles
  1.  28
    Tim Button & Sean Walsh (forthcoming). Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics. Philosophia Mathematica:nkw007.
    This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent `internal' renditions of the famous categoricity arguments for arithmetic and set theory.
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  2.  24
    Santos Gon?alo (forthcoming). Numbers and Everything. Philosophia Mathematica.
    I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.
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  3.  53
    Luca Incurvati (forthcoming). Maximality Principles in Set Theory. Philosophia Mathematica:nkw011.
    In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...)
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  4.  11
    Ansten Mørch Klev (forthcoming). Dedekind's Logicism. Philosophia Mathematica:nkv027.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  5.  23
    B. Larvor (forthcoming). The Growth of Mathematical Knowledge. Philosophia Mathematica.
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  6.  10
    Dirk Schlimm (forthcoming). Metaphors for Mathematics From Pasch to Hilbert. Philosophia Mathematica:nkv039.
    How mathematicians conceive of the nature of mathematics is reflected in the metaphors they use to talk about it. In this paper I investigate a change in the use of metaphors in the late nineteenth and early twentieth centuries. In particular, I argue that the metaphor of mathematics as a tree was used systematically by Pasch and some of his contemporaries, while that of mathematics as a building was deliberately chosen by Hilbert to reflect a different view of mathematics. By (...)
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  7.  2
    Aberdein Andrew (forthcoming). Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW] Philosophia Mathematica:nkw020.
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  8.  4
    Alan Baker (forthcoming). Russell Marcus. Autonomy Platonism and the Indispensability Argument. Philosophia Mathematica:nkw017.
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  9.  16
    Neil Barton (forthcoming). Richness and Reflection. Philosophia Mathematica:nkv036.
    A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...)
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  10.  2
    Jessica Carter (forthcoming). John W. Dawson, Jr. Why Prove It Again: Alternative Proofs in Mathematical Practice. Basel: Birkhäuser, 2015. ISBN: 978-3-319-17367-2 ; 978-3-319-17368-9 . Pp. Xii + 204. [REVIEW] Philosophia Mathematica:nkw003.
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  11.  6
    Roy T. Cook (forthcoming). Abstraction and Four Kinds of Invariance. Philosophia Mathematica:nkw014.
    Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...)
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  12.  2
    José Ferreirós (forthcoming). Dedekind’s Map-Theoretic Period. Philosophia Mathematica:nkw010.
    In 1887–1894, Richard Dedekind explored a number of ideas within the project of placing mappings at the very center of pure mathematics. We review two such initiatives: the introduction in 1894 of groups into Galois theory intrinsically via field automorphisms, and a new attempt to define the continuum via maps from ℕ to ℕ in 1891. These represented the culmination of Dedekind’s efforts to reconceive pure mathematics within a theory of sets and maps and throw new light onto the nature (...)
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  13.  9
    Dagfinn Føllesdal (forthcoming). Richard Tieszen. After Gödel. Platonism and Rationalism in Mathematics and Logic. Philosophia Mathematica:nkw016.
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  14.  6
    Casper Storm Hansen (forthcoming). Brouwer's Conception of Truth. Philosophia Mathematica:nkv025.
    In this paper it is argued that the understanding of Brouwer as replacing truth conditions with assertability or proof conditions, in particular as codified in the so-called Brouwer-Heyting-Kolmogorov Interpretation, is misleading and conflates a weak and a strong notion of truth that have to be kept apart to understand Brouwer properly: truth-as-anticipation and truth- in-content. These notions are explained, exegetical documentation provided, and semi-formal recursive definitions are given.
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  15.  7
    Burt C. Hopkins (forthcoming). Claire Ortiz Hill and Jairo José da Silva. The Road Not Taken: On Husserl's Philosophy of Logic and Mathematics. Texts in Philosophy; 21. London: College Publications, 2013. ISBN 978-1-84890-099-8 . Pp. Xiv + 436. [REVIEW] Philosophia Mathematica:nkw006.
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  16.  16
    Kevin C. Klement (forthcoming). A Generic Russellian Elimination of Abstract Objects. Philosophia Mathematica:nkv031.
    In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...)
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  17.  5
    Brendan Larvor (forthcoming). Why the Naï Ve Derivation Recipe Model Cannot Explain How Mathematicians’ Proofs Secure Mathematical Knowledge. Philosophia Mathematica:nkw012.
    The view that a mathematical proof is a sketch of or recipe for a formal derivation requires the proof to function as an argument that there is a suitable derivation. This is a mathematical conclusion, and to avoid a regress we require some other account of how the proof can establish it.
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  18.  24
    Graham Leach-Krouse (forthcoming). Structural-Abstraction Principles. Philosophia Mathematica:nkv033.
    In this paper, I present a class of ‘structural’ abstraction principles, and describe how they are suggested by some features of Cantor's and Dedekind's approach to abstraction. Structural abstraction is a promising source of mathematically tractable new axioms for the neo-logicist. I illustrate this by showing, first, how a theorem of Shelah gives a sufficient condition for consistency in the structural setting, solving what neo-logicists call the ‘bad company’ problem for structural abstraction. Second, I show how, in the structural setting, (...)
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  19.  7
    Shay Allen Logan (forthcoming). Categories for the Neologicist. Philosophia Mathematica:nkw013.
    ion principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.
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  20. Gianluigi Oliveri (forthcoming). Book Review.'I Fondamenti della Matematica nel Logicismo di Bertrand Russell'. Stefano Donati. Firenze (Firenze Atheneum). 2003. ISBN: 88-7255-204-4. 988 pages.€ 39.00. [REVIEW] Philosophia Mathematica.
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  21.  2
    Manya Raman-Sundström & Lars-Daniel Öhman (forthcoming). Mathematical Fit: A Case Study. Philosophia Mathematica:nkw015.
    Mathematicians routinely pass judgements on mathematical proofs. A proof might be elegant, cumbersome, beautiful, or awkward. Perhaps the highest praise is that a proof is right, that is, that the proof fits the theorem in an optimal way. It is also common to judge that one proof fits better than another, or that a proof does not fit a theorem at all. This paper attempts to clarify the notion of mathematical fit. We suggest six criteria that distinguish proofs as being (...)
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  22.  7
    Peter Roeper (forthcoming). A Vindication of Logicism. Philosophia Mathematica:nkv026.
    Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the (...)
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  23.  3
    Dirk Schlimm (forthcoming). José Ferreirós. Mathematical Knowledge and the Interplay of Practices. Philosophia Mathematica:nkw018.
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  24.  55
    Stewart Shapiro & Geoffrey Hellman (forthcoming). Frege Meets Aristotle: Points as Abstracts. Philosophia Mathematica:nkv021.
    There are a number of regions-based accounts of space/time, due to Whitehead, Roeper, Menger, Tarski, the present authors, and others. They all follow the Aristotelian theme that continua are not composed of points: each region has a proper part. The purpose of this note is to show how to recapture ‘points’ in such frameworks via Scottish neo-logicist abstraction principles. The results recapitulate some Aristotelian themes. A second agenda is to provide a new arena to help decide what is at stake (...)
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  25.  20
    Daniël F. M. Strauss (forthcoming). The On to Log I Cal Sta Tus of the Prin Ci Ple of the Ex Cluded Mid Dle. Philosophia Mathematica.
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  26.  6
    R. S. D. Thomas (forthcoming). Beauty Is Not All There Is to Aesthetics in Mathematics. Philosophia Mathematica:nkw019.
    Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...)
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  27.  4
    Nigel Vinckier & Jean Paul Van Bendegem (forthcoming). Feng Ye. Strict Finitism and the Logic of Mathematical Applications. Synthese Library; 355. Springer, 2011. ISBN: 978-94-007-1346-8 ; 978-94-007-1347-5 . Pp. Xii + 272. [REVIEW] Philosophia Mathematica:nkw005.
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  28.  6
    Audrey Yap (forthcoming). Stephen Pollard. A Mathematical Prelude to the Philosophy of Mathematics. Springer, 2014. ISBN: 978-3-319-05815-3 ; 978-3-319-05816-0 . Pp. Xi + 202. [REVIEW] Philosophia Mathematica:nkw001.
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