Abstraction and Modest Reflection

In “Neo-fregeanism: An Embarrassment of Riches” (Notre Dame J Formal Logic 44(1):13–48, 2003) Alan Weir introduces a number of formal constraints on abstraction principles that have become central to subsequent discussions of the Bad Company Problem, including stability and (Field and Caesar-neutral) conservativeness. In this essay we return to another notion introduced in that paper that has received much less attention—modest reflection—and we demonstrate that a natural version of this criterion is (i) a plausible constraint that acceptable abstraction principles must meet, (ii) distinct from all other such constraints proposed in the subsequent literature, yet (iii) intimately connected to a recent puzzle raised by Heck (and intimately connected to Heck’s own preferred solution to this puzzle).