It's always worth recalling <i>why</i> we bother with set theory. Philosophical objections like Leśneivski's are extremely valuable and good insights which we cannot discard trivially. Maybe sets are not good things to study. The main reason that we study sets today is because they are a place where we could study ordinals and the rest of number theory. We know about two bananas, two apples, two trees, etc. but what is two itself? Set theory provides a capable if unsatisfying answer: Two is anything which is uniquely isomorphic to the second ordinal number, which happens to be a particular finite set, and since sets formally contain nothing but other sets, we can manipulate two as a set without having to know about bananas, apples, trees, etc.<p>The modern way to talk about this stuff is via categorification; [0] is a good high-level introduction.<p>[0] <a href="https://math.ucr.edu/home/baez/quantization_and_categorification.html" rel="nofollow">https://math.ucr.edu/home/baez/quantization_and_categorifica...</a>