Switch to: Citations

References in:

Methodology and metaphysics in the development of Dedekind's theory of ideals

In José Ferreirós Domínguez & Jeremy Gray (eds.), The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford, England: Oxford University Press (2006)

Add references

You must login to add references.
  1. The genesis of ideal theory.Harold M. Edwards - 1980 - Archive for History of Exact Sciences 23 (4):321-378.
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • The nineteenth-century revolution in mathematical ontology.Jeremy Gray - 1992 - In Donald Gillies (ed.), Revolutions in mathematics. New York: Oxford University Press. pp. 226--248.
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Dedekind's structuralism: An interpretation and partial defense.Erich H. Reck - 2003 - Synthese 137 (3):369 - 419.
    Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...)
    Download  
     
    Export citation  
     
    Bookmark   53 citations  
  • (1 other version)Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
    Download  
     
    Export citation  
     
    Bookmark   255 citations  
  • Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics.José Ferreirós - 2002 - Studia Logica 72 (3):437-440.
    Download  
     
    Export citation  
     
    Bookmark   51 citations  
  • Falsification and the methodology of scientific research programme.Imre Latakos - 1970 - In Imre Lakatos & Alan Musgrave (eds.), Criticism and the growth of knowledge. Cambridge [Eng.]: Cambridge University Press. pp. 91--196.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Three Forms of Naturalism.Penelope Maddy - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press.
    This chapter compares and contrasts Quine’s naturalism with the versions of two post-Quineans on the nature of science, logic, and mathematics. The role of indispensability in the philosophy of mathematics is treated in detail.
    Download  
     
    Export citation  
     
    Bookmark   39 citations