Modern Math Logic and Kantianism

Platonism holds that Numbers are self-subsistent entities that inhabit the realm of Forms. Its historically primary opponent, Nominalism, denies the existence of any such realm, and, instead, treats Numbers as abstractions from empirical experience. In contrast with both, for Kant, possibly echoing Spinoza's notion of Definition, Numbers are rules of construction. The extent to which modern Mathematical Logic, originated by Frege, is a reaction to Kant, can be gleaned from the fact that its most eminent expression, Principia Mathematica, is a collaboration of a Platonist, Whitehead, and a Nominalist, Russell. Likewise, contemporary Analytic Logic, inspired by these attempts to reduce an active process such as counting to intellectual abstraction, is generally oblivious to some of its Philosophical pre-suppositions, e. g. the priority of Theory over Practice, that are common to Platonism and Nominalism. As such, they remain under-Evolved doctrines.