Dedekind's problem is about enumerating antichains in the Boolean lattice. Is there an explicit reference where Dedekind stated this problem? Is there a good motivation to study this problem except that it is an old open problem stated by a famous mathematician?

Speaking as a nonexpert, the enumeration and classification of monotone Boolean functions can give insight into optimization problems in logic, for instance by considering how far off an arbitrary function is from a monotone one. Doing a web search should reveal other motivations for studying Dedekind's problem.

Gerhard "Who Doesn't Like Enumeration Problems?" Paseman, 2020.02.12.

regrettably behind a paywall$\endgroup$ – Carlo Beenakker Feb 12 at 14:18