Conservativeness, Stability, and Abstraction

Abstract
One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable abstraction principles be strictly logically symmetrically class conservative . The article concludes with an examination of which classes of abstraction principles meet this criteria
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DOI 10.1093/bjps/axr047
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Relative Categoricity and Abstraction Principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
Higher‐Order Abstraction Principles.Beau Madison Mount - 2015 - Thought: A Journal of Philosophy 4 (4):228-236.
Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.
Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.

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