Year:

Forthcoming articles
  1. 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.
    Direct download  
     
    My bibliography  
     
    Export citation  
  2. Charles McCarty (forthcoming). Structuralism and Isomorphism. Philosophia Mathematica:nkt024.
    If structuralism is a true view of mathematics on which the statements of mathematicians are taken ‘at face value’, then there are both structures on which (1) classical second-order arithmetic is a correct report, and structures on which (2) intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures (1) and structures (2) are isomorphic. Consequently, first- and second-order statements true in structures (1) must hold in (2), and conversely. Since instances of the general law of (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  3. Andrea Sereni (forthcoming). Frege, Indispensability, and the Compatibilist Heresy. Philosophia Mathematica:nkt046.
    In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument (ia) later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of ia, it facilitates acceptance of suitable formulations of ia. The prospects for making the empiricist ia compatible with a rationalist Fregean framework (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  4. Shigeyuki Atarashi (forthcoming). Alison Walsh. Relations Between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce. Boston: Docent Press, 2012. ISBN 978-098370046-3 (Pbk). Pp. X + 314. [REVIEW] Philosophia Mathematica:nku028.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  5. Thomas Forster (forthcoming). Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF. Philosophia Mathematica:nku005.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories (e.g., NF and Church's CUS) which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for “low” sets, and thus, for example, a set of all (low) ordinals. However, that set has an ordinal in turn which is not a member (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  6. Emily R. Grosholz (forthcoming). Carlo Cellucci. Rethinking Logic: Logic in Relation to Mathematics, Evolution and Method. Dordrecht: Springer, 2013. ISBN: 978-94-007-6090-5 (Hbk); 978-94-007-6091-2 (E-Book). Pp. Xv + 389. [REVIEW] Philosophia Mathematica:nku023.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  7. Matthew Inglis & Andrew Aberdein (forthcoming). Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals. Philosophia Mathematica:nku014.
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  8. Marc Lange (forthcoming). Depth and Explanation in Mathematics. Philosophia Mathematica:nku022.
    This paper argues that in at least some cases, one proof of a given theorem is deeper than another by virtue of supplying a deeper explanation of the theorem — that is, a deeper account of why the theorem holds. There are cases of scientific depth that also involve a common abstract structure explaining a similarity between two otherwise unrelated phenomena, making their similarity no coincidence and purchasing depth by answering why questions that separate, dissimilar explanations of the two phenomena (...)
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  9. B. Larvor (forthcoming). The Growth of Mathematical Knowledge. Philosophia Mathematica.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  10. 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.
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  11. Wilfried Sieg & Dirk Schlimm (forthcoming). Dedekind's Abstract Concepts: Models and Mappings. Philosophia Mathematica:nku021.
    Dedekind's mathematical work is integral to the transformation of mathematics in the nineteenth century and crucial for the emergence of structuralist mathematics in the twentieth century. We investigate the essential components of what Emmy Noether called, his ‘axiomatic standpoint’: abstract concepts (for systems of mathematical objects), models (systems satisfying such concepts), and mappings (connecting models in a structure-preserving way).
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  12. 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.
    Direct download  
     
    My bibliography  
     
    Export citation  
  13. Audrey Yap (forthcoming). Dedekind and Cassirer on Mathematical Concept Formation. Philosophia Mathematica:nku029.
    Dedekind's major work on the foundations of arithmetic employs several techniques that have left him open to charges of psychologism, and through this, to worries about the objectivity of the natural-number concept he defines. While I accept that Dedekind takes the foundation for arithmetic to lie in certain mental powers, I will also argue that, given an appropriate philosophical background, this need not make numbers into subjective mental objects. Even though Dedekind himself did not provide that background, one can nevertheless (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
 Previous issues
  
Next issues