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Forthcoming articles
  1.  25
    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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  2.  58
    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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  3.  12
    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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  4.  23
    B. Larvor (forthcoming). The Growth of Mathematical Knowledge. Philosophia Mathematica.
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  5.  6
    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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  6.  15
    Alan Baker (forthcoming). Mathematics and Explanatory Generality. Philosophia Mathematica:nkw021.
    According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...)
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  7.  4
    Don Berry (forthcoming). Proof and the Virtues of Shared Enquiry. Philosophia Mathematica:nkw022.
    This paper investigates an important aspect of mathematical practice: that proof is required for a finished piece of mathematics. If follows that non-deductive arguments — however convincing — are never sufficient. I explore four aspects of mathematical research that have facilitated the impressive success of the discipline. These I call the Practical Virtues: Permanence, Reliability, Autonomy, and Consensus. I then argue that permitting results to become established on the basis of non-deductive evidence alone would lead to their deterioration. This furnishes (...)
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  8.  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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  9.  10
    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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  10.  4
    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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  11.  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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  12.  18
    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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  13.  25
    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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  14.  8
    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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  15. 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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  16.  3
    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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  17.  5
    Dirk Schlimm (forthcoming). José Ferreirós. Mathematical Knowledge and the Interplay of Practices. Philosophia Mathematica:nkw018.
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  18.  61
    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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  19.  21
    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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  20.  8
    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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  21.  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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  22.  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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