I'm a linguist however I correct mistakes

I teach, among other things, first-year syntax seminars. I've found that this year's cohort are pretty good at knowing the basic parts of speech but one of the things we do at degree level is learn how to identify nouns, verbs and so on based on their behaviour and question mis-classifications. The other day, I said English really only has three conjunctions: and, or and but. (Actually this isn't totally accurate but those are the common ones, I think. Note that I'm only referring to what are sometimes called 'coordinating conjunctions' - subordinating ones are another thing.) One of my students asked whether however isn't a conjunction as well.

This is an excellent question. And as with most excellent questions, the answer is 'yes and no'. I was suddenly, in a 9am seminar, suffering from severe tiredness, faced with the descriptivist academician's paradox.

This is one of the things that is mentioned time and again when lecturers compare notes on common writing mistakes in student essays: however used as a conjunction. Here's an example:

This argument is very persuasive, however I believe the premise is false. 

This sentence could be written perfectly grammatically with but instead of however as follows:

This argument is very persuasive, but I believe the premise is false. 

With however, it's a comma splice and at best, clumsy, and at worst confusing. If you're desperate to use the word however, because you're keen to use polysyllabic words wherever you can, the following is acceptable:

 This argument is very persuasive; however, I believe the premise is false.

 So far, this is not linguistics so much as standard essay-marker's griping. The linguistics comes now. As linguists, we are descriptive, no matter how prescriptive we are as essay-markers. For that reason, we apply writing rules in what I think is a more sensible manner than many other subjects do (in my former life as a writing tutor I heard of history lecturers with flat-out bans on completely innocuous things for no discernible reason). We allow things that others might outlaw as long as it's done well. Lately, for instance, I've noticed that I no longer care about contracted forms in essays, as long as the apostrophes are correct and the style is otherwise formal and reads well - correcting this might lead to stilted, lumpy writing. We allow first-person pronouns (why on earth not?) as long as students don't use them to say things like 'I believe' (cf. my example above). Passive voice is perfectly fine as long as it's not used to pad out the essay with extra words.

So what of however? It all depends. Is the error in my example above a punctuation error, in which case it most definitely is an error and deserves the red pen, or is it a reflection of a change in language which will be permitted before long? The only way we could check would be to listen to the intonation. Is there a semicolon break preceding it and a comma break following it in speech? If so, it's wrongly punctuated. If not, perhaps I'll have to learn to live with it. Unfortunately, this isn't really a feature of everyday speech: it's formal style, and formal style is highly influenced by written style. If that written style is wrong to start with, we have a chicken and egg problem on our hands.