Non-defining “that” and defining “which” are often to be found in older formal and informal writing.
Although non-defining “that” is still common in spoken English, there is a tendency nowadays among copy editors to replace non-defining “that” with “which” (and less often, to replace defining “which” with “that”).
The choice is stylistic, rather than grammatical. I suspect the tendency has its origins in the first edition of Fowler’s Modern English Usage, where, after a long article in which the author argues for a strict division of duties between “that” and “which”, he nonetheless engagingly confesses that “it would be idle to pretend that it is the practice either of most or of the best writers”.
Thank you for your advice that the choice is stylistic. I have never heard about the Fowler. I have just known it is very famous as an English usage book. The following question occurs to me.
What on earth makes the copy editors choose the non-restrictive that?
Generally, non-restrictive “that” is changed to “which” by copy editors, in books and magazines. This makes it fairly unusual, in modern edited English. However, in unedited English (e.g. emails, memos, self-published texts, etc.) you will still encounter it. Some people simply seem to tend towards using it.
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I think there is probably also a bit of a difference in usage between BE and AmE. It seems to me you’re more likely to hear a defining usage of ‘which’ in BE than in AmE. And the example that Molly gave of the non-defining use of ‘that’ sounds odd to my American ears.
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I feel very sorry that you should change commas to dashes in the quotation. You look too pedantic. The non-restrictive that in the quotaition would sound odd for you, native speakers, since it is ungrammatical. But your oddness against non-restrictive that might make you feel something except “strange”.
I did not say one cannot choose, but questioned how one does indeed choose. You questioned the choice made in the Cambridge Grammar of English and offered an alternative. What was you alternative choice based on?
As daily we are supposed to be in touch with the spoken language more than the written, why would “that” used in non-defing clauses, seem “odd” when spoken?