There are no stone lions in my garden, either.

The puzzle posed by local pragmatics is how it comes to be that a word is interpreted in such a way that it departs from its literal or lexical meaning:

There are no stone lions in my garden.

Geurts argues that this must be a "local pragmatic process."

Metalinguistic negation negates an utterance, complete with its conventional and conversational implicatures in tow. It has been observed that we need recourse to a similar mechanism to explain cases where two sentences (non-finite clauses--type t, as far as I can tell by looking at Wikipedia) joined by connectives like

___ is better than ___

for example,

Drinking warm coffee is better than drinking hot coffee.

(looks like good data for the application of contrastivist semantics!...) The idea is that "drinking warm coffee," while subsentential, must be subject a scalar implicature that turns "warm" into "warm but not hot," so that it can be sensibly contrasted with "drinking hot coffee."

Hence we will have to take our implicatures at the subsentential level. Intuitively, this doesn't seem so bad. After all, metalinguistic negation, even though it is (by hypothesis) targeted at a full-blown speech act, is usually accompanied by stress on a particular part of the asserted sentence:

She didn't make *a* mistake, she made *many* mistakes.

The target of the metalinguistic negation--assuming that's what it is--is, first, an assertion of the form "she made a mistake"; but it is clear that within this sentence, the target is the lexical item "a".