Abstract

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character ‐ permutation invariance ‐ has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each.

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