Switch to: References

Add citations

You must login to add citations.
  1. Our Knowledge of Numbers as Self‐Subsistent Objects.William Demopoulos - 2005 - Dialectica 59 (2):141-159.
    A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Our Knowledge of Numbers as Self-Subsistent Objects.William Demopoulos - 2005 - Dialectica 59 (2):141–159.
    A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • The Consistency of Predicative Fragments of Frege’s Grundgesetze der Arithmetik.Richard G. Heck - 1996 - History and Philosophy of Logic 17 (1):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   54 citations