Have you ever wondered just what exactly is language? What exactly are words? What exactly do we mean by the word ‘exactly’?
In fact, what is the meaning of ‘What is?’ ?
The vision of infinite regress is very palpable when we phrase questions in such a manner. The terror of an epistemic black hole with no escape. Perhaps a metaphysical terror is implied too, since even to read these words implies participation in some kind of knowledge formation that cannot be ‘exactly’ understood, and meta-metaphysical too? Are there infinitely many infinite regresses?
And if we ‘know’ the answer to any of the above, the meta question still persists,
How do we know we know?
Interestingly, from this perspective Godel’s theorems of incompleteness seem almost trivially obvious. There is no escape from infinite regress and/or circular reasoning if we actually attempt a complete definition of anything!
Although axiomatic reasoning might be a plausible alternative, there is no way to actually define anything, including axioms, without using some sort of language, i.e. using something itself based on axioms. And so then you need meta-axioms, which implies meta-meta-axioms, and so on all the way to infinity. Axiomatic reasoning is therefore another type of infinite regress in disguise!
The implications are of course profound given that this leads to the conclusion that no ‘exact’, or complete, knowledge of anything is attainable.
I got thinking along these lines by an unlikely source, the idea popularized by Donald Rumsfeld’s of known known’s, unknown unknown’s, and so on. Some reflection will provide the key realization that second order knowledge (or ignorance) implies the existence of third order knowledge (or ignorance) which implies the fourth order, and so on to infinity.