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People sometimes refer to the CGEL on this site. Conveniently, some
sample chapters from this publication are now online at [url="http://uk.cambridge.org/linguistics/cgel/sample.htm "]CGEL sample chapters[/url]

The preliminary chapter includes the odd lapse of logic. This is one of the first.
Apologies for the fairly lengthy quotation:
Another kind of illegitimate argument is based on analogy between
one area of grammar and another. Consider yet another construction where
there is variation between nominative and accusative forms of pronouns:

[3] a. They invited me to lunch.
[3] b.% They invited my partner and I to lunch.

The ‘%’ symbol is again used to mark the B example as typically used by some
speakers of Standard English but not others, though this time it is not a matter of
regional variation. The status of the construction in B differs from that of
It’s me, which is undisputedly normal in informal use, and from that
of !Me and Kim saw her leave, which is unquestionably non-standard.

What is different is that examples like B are regularly used by a significant
proportion of speakers of Standard English, and not generally thought by
ordinary speakers to be non-standard; they pass unnoticed in broadcast
speech all the time.

Prescriptivists, however, condemn the use illustrated by 3b, insisting
that the ‘correct’ form is They invited my partner and me to lunch.

And here again they seek to justify their claim that 3b is ungrammatical
by an implicit analogy, this time with other situations found in English, such
as the example seen in A. In A the pronoun functions by itself as direct
object of the verb and invariably appears in accusative case. What is
different in B is that the direct object of the verb has the form of a
coordination, not a single pronoun. Prescriptivists commonly take it for
granted that this difference is irrelevant to case assignment. They argue
that because we have an accusative in A we should also have an
accusative in B, so the nominative I is ungrammatical.

But why should we simply assume that the grammatical rules for case
assignment cannot differentiate between a coordinated and a non-coordinated
pronoun? As it happens, there is another place in English grammar where
the rules are sensitive to this distinction – for virtually all speakers, not
just some of them:

4 a. I don’t know if you’re eligible.
4 b. I don’t know if she and you’re eligible.

The sequence you are can be reduced to you’re in A, where
you is subject, but not in B, where the subject has the form of a
coordination of pronouns.

This shows us not only that a rule of English could apply differently to
pronouns and coordinated pronouns, but that one rule actually does. If that
is so, then a rule could likewise distinguish between 3a and 3b. The
argument from analogy is illegitimate. Whether 3b is treated as correct
Standard English or not (a matter that we take up in Ch. 5, §16.2.2), it
cannot be successfully argued to be incorrect simply by virtue of the
analogy with 3a.

This passage appears to contain two weakness. First, it uses analogy to
argue against analogy. Second, it mistakes the nature of the 'rule' in
4a and 4b.

Analogy
According to the passage above, prescriptivists say:

1. 'Apply {direct object pronoun rule 3a} to {co-ordinated direct object pronoun pair 3b}'.

The CGEL says in reply that this 'illegitimate argument is based on analogy
between one area of grammar and another'; that in fact,

2. 'We don't apply {subject pronoun rule 4a} to {co-ordinated subject pronoun pair 4b};

therefore

3. We needn't apply {direct object pronoun rule 3a} to {co-ordinated direct object pronoun pair 3b}'.

Which is to argue against the use of analogy by using an analogy.

Even more strangely, the CGEL's analogy is between uses of subject and
object pronouns; whereas the so-called prescriptivists' analogy is at least
between uses of object pronouns in both cases.

Mistaking the nature of the rule in 4a
The CGEL states that the change in form in 4b is a question of case assignment.

In fact, it's a question of contraction. In 4a, contraction is used; whereas 4b
should be corrected to 'I don't know if she and you are eligible'.

(This is independently explicable: the 'you' requires separate stress not because
of case, but because it's one of a pair. Moreover, native speakers would indeed
often slightly contract the 'are':

4. c. I don't know if she and you'er eligible.)

MrP
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http://uk.cambridge.org/linguistics/cgel/faqs.htm

How does this grammar relate to traditional grammar?

While The Cambridge Grammar does not depart from traditional grammar capriciously when it would be confusing, neither does it cling to traditional grammar when it would be incorrect. Much about the older tradition of description in English grammar is misguided or outright false. Where necessary, The Cambridge Grammar breaks with tradition, sometimes marginally and sometimes radically.

{emphasis added by JTT}
Comments  
Thanks for that, JT.

The quote isn't strictly relevant, though. My comments above relate to the line of argument, not the subject matter.

MrP