Madness, n.
Etymology: [From Mad, a.]
1. The condition of being mad; insanity; lunacy.
2. Frenzy; ungovernable rage; extreme folly.
Syn. -- Insanity; distraction; derangement; craziness; lunacy; mania; frenzy; franticness; rage; aberration; alienation; monomania. See Insanity.
Shades of meaning
Fernald has no entry of its own for madness; he lists it under insanity.
Where he writes about it:
Madness is the old popular term, now less common, for insanity in its widest sense, but with suggestion of excitement, akin to mania. — from insanity
In the derived sense, lunacy denotes what is insanely foolish, madness what is insanely desperate. — from insanity