Can Two Words that Mean the Exact Opposite also Mean the Same Thing?

The answer is, well, yes. At least in the following quirky example:

Can.

Can't.

Opposites.

But not so fast. How about here:

"See if you can get a better quote from that source," the editor said to Bill.

"See if you can't get a better quote from that source," the editor said to Bill.

Uh-oh. Now "can" and "can't" really serve the same purpose and mean the same thing. And either one -- can or can't -- would be acceptable in this context.

What a crazy, crazy language English is.