Some Mathematical Thoughts Dangerously Close to Being Epistemological Rhetoric (Probably Are) by Justin

These ideas are not new to my mind, but the sophistication and intellectual weight recently attained under academic influence has deepened their muse, although I do not assert that either their sophistication or their weight are entirely correct, as I have some uncertainty over my own conceptual mastery of them.

It seems that the rigorous evaluations and logical strictures imposed on mathematics as a whole beginning with Hilbert et al leading to fields of "metamathematics" and modal logic which concluded for higher level mathematical practitioners and discoverers a mathematical foundation comprising ZFC and its equivalents can be construed as a confinement. The confinement of ZFC. Gödel's theorems impose and define philosophical scope of ZFC.

It is true that from Gödel's incompleteness theorems we learn that mathematics is an unbounded pursuit and discovery of novel facts, but they also signify a very significant bound. Gödel's result is perhaps the highest achievement of thought society has produced, but its elegant veracity suggests, or to my mind, demands, a question whose answer would be still greater an achievement.

Do Gödel's theorems formalize an emphatic epistemological compass on cognition itself? At the same time they both prohibit finite entire (recursive?) novelty and draw elegant closure on the whole of mathematics. Are we humans bound by Gödel to the bounded, yet infinitely novel regime defined by ZFC? Or does evolution allow, if not ultimately favor, the chance infusions of such inspirational endowments of selective brilliance beyond the range of contemporary human cognition?

Is every system of thought whose genesis is capable of human intellect commesurate with ZFC? If so, then Gödel's theorems offer the most profound implications for thought itself. It is perhaps the most general statement of truth possible. Perhaps the search for logical and mathematical truth will ultimately surpass the domain of logos. Or perhaps a system of thought constructed from postulates which violate or surpass ZFC and whose methods are not beholden to its traditions may be worthy of scientific investigation.