The only alternative to what? If there is only one it's no a alternative.

Annotation:

It is an idiom meaning it's the only logical choice, or there is no question that this is the best choice.

Then you use it an ellipsis of "There is no alternative to this.", and I would prefer to see the complete form here, because tatoeba pretends to give examples. Otherwise foreign language learner can gain the impression this is the complete expression.

http://www.thefreedictionary.com/alternative

Usage Note: Some traditionalists hold that alternative should be used only in situations where the number of choices involved is exactly two, because of the word's historical relation to Latin alter, "the other of two." Despite the word's longstanding use to mean "one of a number of things from which only one can be chosen" and the acceptance of this usage by many language critics, a substantial portion of the Usage Panel adheres to the traditional view, with only 49 percent accepting the sentence Of the three alternatives, the first is the least distasteful. · Alternative is also sometimes used to refer to a variant or substitute in cases where there is no element of choice involved, as in We will do our best to secure alternative employment for employees displaced by the closing of the factory. This sentence is unacceptable to 60 percent of the Usage Panel. · Alternative should not be confused with alternate. Correct usage requires The class will meet on alternate (not alternative) Tuesdays.

My personal comments:

It's no use trying to infer any logic from English. It has absolutely none and here is the reason:
http://tatoeba.org/fre/sentences/show/1258105