Abstraction and Epistemic Economy

Plural Frege Arithmetic

“…For instance, we might consider adding further consistent formulations of BLV to V imp , in order to recover real analysis starting from the extension of all natural numbers -see, e.g., [Hale 2005] or [Panza 2016]. But see also [Boccuni & Panza 2021] for a critical view of this strategy, and an alternative.…”

Frege's Theory of Real Numbers: A consistent Rendering

“…Since, if this distinction were admitted, this argument should allow to conclude also that our definition of real numbers is no more analytic in the same sense in which neologicists take their definition of natural numbers to be so.53 We leave here apart the question of whether the neologicist definition of natural numbers or our definition of the E ⊘ -abstracta are actually logical or analytical. InPanza (2016), pp. 420-423, the point is made that the former definition might be deemed so in a quite peculiar sense, quite different than those that are current in the discussion on logicism and neologism, and because of a completely different argument than the neologicist's.…”