Informal notes on improving The First Order Predicate Calculus

The limitations of First Order Predicate Calculus have been explored and extensions thereof suggested and incorporated to varying degrees and with varying success, for the purposes of defining if-then-else functions, the definition of categories/types, and other new functions proposed within the constraints of first order operations to limit the necessity of second order logic, especially as pertains to the needs of logic automation. My extensive research has revealed an overlooked condition which need be applied to the entire body of FOPC theory. For illustration, I will apply this condition to the commonly recognized Zermelo–Fraenkel set theory.

ZFC consists of "a single primitive ontological notion, that of set, and a single ontological assumption, namely that all individuals in the universe of discourse (i.e., all mathematical objects) are sets. There is a single primitive binary relation, set membership; that set a is a member of set b is written a \in b (usually read "a is an element of b" or "a is in b")."*

These axioms are proposed to govern how sets behave and interact. What has been until today overlooked is the qualitative nature of existence (the universe) in which said elements/sets are assembled. The a priori concept of a set in general practice does fulfill the needs of predicting general behavior. However, I propose that we need to assess the obvious effect of wide-scale mental retardation as a universal condition before proceeding with any quantitative analysis or utilization of this or any FOPC theorem. The problem lies in considering accepted metaverse theory. It follows, (within the logical confines of our non-retarded universe), that there must also exists a universe wholly comprised of mental retards. The problem with the a priori concepts of individuals and sets is self-evident in such a universe. It will be argued that the application of the First Order Predicate Calculus has no application in other universes, and that current physical theory has no bearing on the utility or purpose of FOPC. Here I will simply propose to such critics that they present me with any retard who has mastered Zermelo–Fraenkel set theory in its current form.

*Jean van Heijenoort, 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press.