Someone PM'ed me today and used this word: eruditeness. Though it is perfectly correct, it somehow struck me as awkward; dunno why. For a second, I thought it should be erudity, but that's not right! So, I looked it up, and thought you-all might find this interesting, as I did:
er'u·dite'ness n.
WORD HISTORY One might like to be erudite but hesitate to be rude. This preference is supported by the etymological relationship between erudite and rude. Erudite comes from the Latin adjective çrudîtus, “well-instructed, learned,” from the past participle of the verb çrudîre, “to educate, train.” The verb is in turn formed from the prefix ex–, “out, out of,” and the adjective rudis, “untaught, untrained,” the source of our word rude. The English word erudite is first recorded in a work possibly written before 1425 with the senses “instructed, learned.” Erudite meaning “learned” is supposed to have become rare except in sarcastic use during the latter part of the 19th century, but the word now seems to have been restored to favor.

From Atomica (AHD 2000).