and similarly low confidence in the negation of the latter [“Deep in their hearts, all men desire to torture women. Some of them are just too afraid of legal consequences.”]

On the off chance that you're speaking personally rather than hypothetically (I hope not)... What??? FWIW, I am a man and, while I can't see arbitrarily deep into my heart, I have no desire to torture women (or anyone else, actually) so far as I can see, and I seldom think about possible legal consequences of my actions. Now I might be lying about that (so you have to take my word for it), or maybe I do have such a desire but it's so deep in my heart that I can't see it (but how would you make that belief pay rent?), but still... I'd find it appalling that anyone would give a non-negligible probability that “Deep in their hearts, all men [emphasis as in the original] desire to torture women”, for any value of deep that wouldn't make that statement useless-whether-true-or-false. (BTW, Gandhi was also a man, wasn't he?)