Switch to: References

Add citations

You must login to add citations.
  1. Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.
    Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended generality. This article (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  • The Company Kept by Cut Abstraction (and its Relatives).S. Shapiro - 2011 - Philosophia Mathematica 19 (2):107-138.
    This article concerns the ongoing neo-logicist program in the philosophy of mathematics. The enterprise began life, in something close to its present form, with Crispin Wright’s seminal [1983]. It was bolstered when Bob Hale [1987] joined the fray on Wright’s behalf and it continues through many extensions, objections, and replies to objections . The overall plan is to develop branches of established mathematics using abstraction principles in the form: Formula where a and b are variables of a given type , (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • The Breadth of the Paradox.Patricia Blanchette - 2016 - Philosophia Mathematica 24 (1):30-49.
    This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation