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I Pagliacci (in English)

Participial relative clauses
Language Log noticed this kind of sentence, and Languagehat has got a large number of comments, most of which regarding them as ungrammatical.

Here are four ways of saying the same thing:

(1) At present, personal injury cases are heard by many different judges, some having no experience in this field.
(2) At present, personal injury cases are heard by many different judges, some of them having no experience in this field.
(3) At present, personal injury cases are heard by many different judges, some of whom have no experience in this field.
(4) * At present, personal injury cases are heard by many different judges, some of whom having no experience in this field.

Now to me, (4) is plainly ungrammatical; but why, when it's so close to all of (1)-(3)? My reaction to it is that it's a confusion, a blend of (2) and (3), and in writing you don't notice these errors, but if you read it aloud you'd pick up that you can't say it. But enough examples were found that perhaps some people do say it. So let's look at some toy examples and try to work out what's going on.

The problem sentences have some partitive element 'some of', 'both of', 'one of', 'most of', etc. governing a relative pronoun. In English we have exceptionally free choice about relative clause formation, and can do these by taking only the pronoun, or Pied-Piping the PP it's in, or Pied-Piping the whole DP that's in:

these books, which Mary has read some of
these books, of which Mary has read some
these books, some of which Mary has read

That's extracting the relative from objects; when we extract from subjects we find one of the possibilities is ungrammatical or severely degraded:

?* these books, which some of have torn covers
these books, of which some have torn covers
these books, some of which have torn covers

Now a relative clause is necessarily finite. Compare these with simple relative pronouns:

these books, which have torn covers
* these books, which having torn covers
these books, which Mary has read
* these books, which Mary having read

'Which having' is obviously impossible. For the same reason so to me are those that just differ from it by degrees of Pied-Piping:

* these books, which Mary having read some of
* these books, of which Mary having read some
* these books, some of which Mary having read

And the reason is straightforward in Case theory: there's no Case assigner in a non-finite inflection, so 'having' can't mark its subject as nominative, whether the subject is 'which' or 'Mary'.

You can get this sequence of words however if there's a relative pronoun followed by a parenthetical absolute clause:

these books, having torn covers, are used goods
these books, which, having torn covers, are used goods, should be thrown out
these books, Mary having read them, are used goods
these books, which, Mary having read them, are used goods, should be thrown out

I've put in all the commas to indicate intonations and grammar, but you could leave them out and it'd read quite all right. You could also have partitives in this construction:

these books, which having torn covers are used goods, should be thrown out
these books, which Mary having read them are used goods, should be thrown out
these books, both of which having torn covers are used goods, should be thrown out
these books, both of which Mary having read them are used goods, should be thrown out

The 'both' versions sound bad with that intonation, but the point is that they're unquestionably grammatical, and the participial relative clauses that started this discussion are hypothesized to arise by confusion or reanalysis of closely similar grammatical formations, or (my first reaction) just anacoluthon. Losing track of the intonation could do that.

Now here's something odd:

these books, having torn covers, are used goods
?# these books, having torn covers
these books, which have torn covers
these books with torn covers

The 'having' clause is fine as part of a sentence, but you can't say it as a modifier of the DP in isolation, unlike a relative clause or PP, as an answering fragment. (Can you? I don't think I can.) So what on earth is its relation to the rest of the sentence? It feels like a clause-level adjunct with PRO subject. Whatever it is, it can take a partitive subject with a pronoun, and it can take the partitive pronoun alone, as -- well, I don't know what, specifier of PRO? But if so, what is the status of the explicit 'them'?

these books, both having torn covers, are used goods
these books, both of them having torn covers, are used goods

I think I'm getting lost and will wind it up now. These absolute subjects with no Case-assigner are the ones my syntax lecturer had no answer for, so I don't want to lean on the edifice too much. Clearly the last sentence above is very close to the one of interest, but for all that, some strong intuition still makes this ungrammatical for me:

* these books, both of which having torn covers, are used goods

So I still have no real idea why.