It just takes some imagination. Hollow out both the Earth and the Moon to reduce their gravitational pull; support the ladder with carbon nanotube filaments; stave off collapse by pushing it around with high-efficiency ion impulse engines; etc.
I agree, though, that philosophers often make too much of the distinction between "logically impossible" and "physically impossible." There's probably no in principle possible way to hollow out the Earth significantly while retaining its structure; etc.
support the ladder with carbon nanotube filaments
So basically, build a second ladder out of some other material that's feasible (unlike steel), and then just tie the steel ladder to it so it doesn't have to bear any weight.
Another month has passed and here is a new rationality quotes thread. The usual rules are: