What is source of:"Ignorance is not so much a lack of knowledge as
knowing so many things that ain't so"?

dunbar --

The author you are looking for is almost certainly Josh Billings.  I
say "almost" because although various versions of the quotation you
cite have been attributed to Billings, I have not found an example
with precisely the wording you quoted.  However, all the versions I
have found are very similarly worded and all carry exactly the same
meaning and tone as the words you cite.
	
Josh Billings, whose real name was Henry Wheeler Shaw, was a
19th-century American folk humorist and a contemporary of Mark Twain. 
Some information on Billings can be found at the following link:
http://64.226.98.143/bio-page-JBillings.htm

Some of the various versions of the quotation attributed to Billings
can be found at these links:

Why the Far Right is Unamerican
http://www.concentric.net/~Tycho4/UnAmer.htm
"Ignorance ain't so much what you don't know, as what you know that
ain't so."

Quotations with an Attitude
http://royhalliday.home.mindspring.com/Itopics.htm
"The trouble with most folks isn't so much their ignorance, as knowing
so many things that ain't so."

Ignorance and Stupidity Quotes
http://www.quotegarden.com/ignorance.html
"The trouble with people is not that they don't know but that they
know so much that ain't so."

The quote is generally cited without being attributed to a specific
work of Billings. That may be because he often wrote in dialect and he
and others later "translated" and paraphrased his witticisms.  For
example, the source linked below attributes a grammatically
incongruous version of the quotation in question to "The Complete
Works of Josh Billings" (1919):

Misattributed Quotes - What Mark Twain Didn't Say
http://www.boondocksnet.com/twaintexts/quotes_not_twain.html
"I honestly beleave it iz better tew know nothing than two know what
ain't so."

One supposedly comprehensive collection of Josh Billings's quotations
that is still in print is:  Everybody's Friend: Josh Billings's
Encyclopedia and Proverbial Philosophy of Wit and Humor, AMS Press
(January 1978).  Other collections can be found from sellers of used
books.

Search Terms Used

ignorance "ain't so"
"josh billings"
"josh billings" ignorance

I hope this helps.  If any of the above needs clarification, I would
be happy to provide it.

markj-ga