some historical context: the proof came as a direct response to the culmination of high modernist mathematics, in the form of Russell & Whitehead's Principia Mathematica, which was an attempt to codify the ultimate axiomatic system, capable of consistent universal expression

Gödel showed, to their great chagrin, that this was fundamentally impossible, using methods from {language, number} theory, due to consequences of recursive expressions and infinite spaces

this effectively spelled the end for high modernism and spurred the development of PM

w/o the ability to create complete & consistent semantic systems, it becomes crucial to learn how to reason usefully within these constraints

PM-based analyses function by making some tradeoff between the two; constructing complete theories by composing domain-consistent parts

or, by negating the assumption that completeness is even desirable; this is where the critical-theory denial of objectivity stems from

if you relax this constraint, you find yourself being able to make many useful statements, without them needing to agree. this helps one publish

cynicism aside, the collapse of high modernism into PM has many parallels, such as the negation of the "end of science" by blackbody radiation & relativity

the splintering of urban architectural styles and approaches

and the "post-truth" epistemic landscape we find ourselves in

its important to understand the insights which PM offers us, & the theoretical foundations on which they're based

but its equally important to understand the bounds of these theories' utility, & not over-eagerly apply them to everything, a la CRT

bc that creates inconsistencies