The trouble with a comma splice, of course, is that it pretends to be one sentence when in fact it's two; the comma should have been a full stop (or even a semi-colon - we'll come back to that later). On the other hand, that comma is a great deal better than nothing at all - at least it signals a boundary. The wrong kind of boundary, maybe, but recognising the boundary is the first hurdle.
The strange thing about comma-splicers is that they're often pretty good punctuators in other respects; you find plenty of them among university students and some well-known novelists, and there may even be a few teachers who comma-splice under pressure. So why do they do it?
We guess that the problem is that they have a theory of punctuation in which comma splices are not a problem. That shows a lack of clarity about the purposes of the two punctuation marks. So what is the difference between a comma and a full-stop? According to the standard theory, commas signal boundaries inside a sentence, and full-stops boundaries between sentences. Comma splices are wrong because the comma is at a boundary between two sentences. (What is a sentence? Good question - see below.) But suppose we change the theory so that commas and full-stops are on a scale of "strength". According to this theory, a comma signals a weaker boundary than a full-stop, and neither has anything special to do with sentences (or grammar). If you look again at our first paragraph, you'll see that the commas and full-stops are just right: they group the sentences into two pairs which are bound together by their related meanings.
But this theory ignores grammar and makes everything rest on meaning. Our guess is that comma-splicers espouse the semantic-scale theory of strong and weak boundaries. However much red ink or kindness you lavish on them, they'll persist in their errors until you confront their basic theory. They think they're right, and can't understand the fuss.
If you want to help a comma-splicer, you'll need a clear view of the standard theory; so you need to be able to explain what a sentence is.
That's tough, we know, but it's worth trying because it's essential to clear and accurate expression. We'll dedicate another column to sentence-hood, but the main point will be that it's grammar, not just meaning, that holds a sentence together.
Once a comma-splicer has been weaned off the comma, what can they use instead to show that some sentences are more closely linked in meaning than others? Why not try a semi-colon? They are sophisticated and impressive; exactly what's needed, in fact.
Richard Hudson is professor of linguistics at University College, London Geoff Barton is headteacher of King Edward VI School, Bury St Edmunds, Suffolk