Are these double negatives? "No it is not. No I don't think so."

A double negative is generally defined as two negative words in the same clause. In these examples:

"No it is not."

"No I don't think so."

is "No" considered a clause unto itself? Or is it in the same clause as the rest of the sentence, thus constituting a double negative?

Solution 1:

Yes, “no” is separate from the clause containing the verb. No, these are not double negatives.

Whether you consider “yes” and “no” clauses on their own is more contested, but it really doesn’t matter—they are not part of the clause that the double negatives would appear in. The fact that they (“yes” and “no”) are normally followed by a comma—and can perfectly well be followed by a period—indicates that they are separate entities:

No, it is not.
No. It is not.

In cases of double negations, such separations are not possible:

I ain’t got nothing against double negations.
*I ain’t got, nothing against double negations.
*I ain’t got. Nothing against double negations.

The last two of these are quite obviously not valid, since “I ain’t got” (or “I haven’t got”) is not a complete sentence.

Solution 2:

Possibly apocryphal but worth recounting:

The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive, but none in which a double positive makes a negative — to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.”

http://opinionator.blogs.nytimes.com/2010/02/14/the-enemy-of-my-enemy/, also referenced at http://msgboard.snopes.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=95;t=000006;p=0: