>The consequence of what it means is that we can't have any justified claims or knowledge at all.
Just that we can’t claim all of our knowledge are equally close to the absolute truth we suppose to exist. The belief that the current attention exist is among the closest thing we can have to an absolute truth. That something like "I" exists is a step further away. That an external world exists is yet an other step further. That 1+1=2, it depends if we take the road of Principia Mathematica à la Whitehead&Russel or if we take more faith in intuition on sensory/memory inputs + reward/penalty from what teachers asked us to integrate at primary school.
>If you can't even count on the law of identity you've lost all intelligibility.
Change as sole stable permanent foundation is harder to play with, at least by the most spread education systems in western civilization (outside it I don’t have first hand experience), and the concept of identity can be derived from it as a transitional side effect. Not that identity must be dropped entirely, but then considered under different perspectives. Somehow like we can build our math under ZFC or category theory (or without anything so firmly and meticulously founded really), and at high level notions it doesn’t prevent us to reemploy familiar patterns.
Identity as a foundational block is not only an issue for humanity at epistemological level, but also at psychological and societal level. Used as inscrutable fundamental black box, it can actually prevent intelligibility and sound reasoning in all the contexts it’s broadly employed.
>To my mind, where we've gone wrong is that we began by assuming transcendentals, holding certain axiomatic, a priori metaphysical assumptions that make the scientific method possible, and then turned around and denied that transcendentals exist in the first place- undercutting the foundation rather than really questioning our tooling or our capacity to understand the data.
That’s probably smoothing "we" very broadly here. "We" also have a very firm tendency to easily build disagreement on every matters and the rest. Nonetheless I would be interested to know more about what leads to this perspective.