This is a great question! it's represented in various ways in different philosophical viewpoints, statements and the like, perhaps most notably in Skolem's paradox. Skolems paradox is actually a much stronger statement relating to the size of "models" (essentially, models are actual sets in set theory that satisfy the axioms of some axiomatic system) and what things we can describe using those models.

Despite the name, most people agree there's no paradox at all here! Simply put: What is uncountable is defined

Intuitively with a little thinking this starts to make sense, after all how do we say anything at all about the infinite with statements of only finite length? We can define infinite objects very simply! The peano axioms mentioned in the video perfectly define natural number arithmetic, yet number in only a few hundred characters. It's clear from this that the size of our definitions and logic aren't tied to the size of the things they define.