Prescriptive grammar has gotten so much, so wrong, for so long that, as Professor Bailey says, "... what is available on the shelves has fallen into sufficient discredit for grammar to have forfeited its place in the curriculum, unrespected and little heeded by the brighter students".Be careful of overgeneralisations. Many native speakers would have difficulty unravelling such a sentence (and you can count me in that group), although most would eventually arrive at the intended meaning -- this is, however, despite the unorthodox grammar.
I can't imagine anyone with a NaE background would have any trouble with that sentence, Rewboss. There are cross pond differences where both sides do have difficulties.
I think your definition of "grammatical" is unhelpful, because actually it's very rare that anyone utters complete gibberish, unless they are suffering from certain forms of aphasia. The problem is that there are many, many different dialects of English (as there are of any language), and these dialects all have different grammar rules. Many sentences may be ungrammatical in some dialects but not in others.
I'd say that Mike's definition has been the first helpful definition we've seen here at UsingEng in a good long time. His definition is precisely what The Grammar Book, a respected ESL grammar uses. His definition is remarkably close to the definition adopted by language science. Not surprisingly, it isn't how prescription deals with it.
Paradoxically, while grammar rules are (or should be) arrived at by observation and describe how native speakers actually use the language, we do need standards and conventions so that we can communicate meaningfully -- just as we find it convenient to have a "lingua franca" we can use to communicate to people on an international level.
Consider this: In some dialects of English, a double negative is used to emphasise the "negativity" of a sentence (as in: "I ain't got none"), while in others, a the second negative cancels out the first to make a positive (as in: "He can't not come", to mean that it would be impossible for him to stay away).
In all dialects of English there are certain circumstances and instances where a double negative can be interpreted as a positive. But that is a function of emphasis and intonation.
I'm not aware of any dialect of English that actually has a rule, a real rule that is, where double negatives cancel each other out to form a positive. Perhaps you could point one out for us?
Now, suppose you came across this sentence in a technical manual:
You shouldn't never supply hydrogen gas to this inlet.
Is the author saying that under no circumstances should hydrogen be supplied to this inlet, or that supplying hydrogen to this inlet is not completely inadvisable? Considering that hydrogen is a highly explosive gas when mixed with oxygen, this type of confusion could cost lives.
So here we have an example of a sentence which is grammatically correct in many dialects of English, but can be interpreted in two completely opposite ways.
This is a red herring, Rewboss. If this was to appear in a technical manual, every native speaker of English would know that it was a typo and I can't imagine any person, even the most prescriptive, thinking that the two negatives mean that a person should supply hydrogen gas to the outlet.
These unhelpful statements have been repeated for so lomg by prescriptivists that they have, for some, taken on the qualities of a mantra.
"A tin ear for stress and melody, and an obliviousness to the principles of discourse and rhetoric, are important tools of the trade for the language maven." Steven Pinker - Grammar Puss
To facilitate communication, then, we use an agreed standard, and as part of that standard we agree not to use double negatives at all. This is an artificial grammar, of course, arrived at pretty arbitrarily, but serves a purpose; and so this is what we normally teach in schools.
Of course, many native speakers who have had this standard grammar drummed into them are then inclined to view other dialects as somehow inferior or "incorrect", which, of course, simply isn't true. They're incorrect according to the prescriptive grammar rules agreed upon for the purposes of communication, but those prescriptive grammar rules don't apply to any variation of English except the artificial standards we've created ourselves.
That Standard English better facilitates communication is a complete falsehood, Rewboss. People communicate perfectly well in their dialects, at least as well, if not better using nonstandard forms.
People who have not been raised on prescriptions still use Standard English for writing and for formal speech. They use it not to communicate any more effectively but simply because that is what we use.
The conflict is usually characterised as an intellectual war between "prescriptivists" and "descriptivists", which over-simplifies the whole issue greatly. Prescriptive grammar has its uses, but those uses do not include a Yorkshireman speaking to his mother, or a Kentucky farmer speaking to his sister. We prefer to teach students standard dialects on the grounds that standard dialects are pretty much universally understood and used in the mass media.
Again, there is no need for prescriptive grammar; there actually isn't any need for prescriptive grammar for descriptive grammar accurately describes how language is used in all registers.
Prescriptive grammar, in the past and still to this day, has dismally failed to make these important distinctions as to register use. How can, why would anyone trust such dismal failure?