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That or Which

What's the rule?

As a relative pronoun, Merriam Webster's says that that can be used as an antecedent for persons or things; which can be used chiefly for things; and who can be used for persons. To find this form I searched [nn*] that/which [v*] in the corpora. 
There is also another difference between that and which when not referencing humans in restrictive and nonrestrictive clauses. If the referent is a person, than the rules above apply.
The rule is quite convoluted for this one. Historically, we only used that  until which entered the language in the 14th century. They were interchangeable and used for both restrictive and nonrestrictive clauses until that fell in use in the late 17th century. It returned to use in the 1800s at which time it was used primarily with restrictive clauses. While which was used with both restrictive and nonrestrictive clauses, grammarians of the 20th century recommended it fulfill a parallel role to that and be used only with nonrestrictive clauses, in which it was used the most anyway. Today Merriam-Webster's concludes that either which or that can be used to introduce a restrictive clause and which to introduce an nonrestrictive clause. 

Examples of restrictive and nonrestrictive clauses:

    restrictive: The shoe on the floor that is green belongs to my sister. (As opposed to the blue shoe also on the floor)
    nonrestrictive: An apple, which is such a delicious fruit, is great remedy to illness. (This whole phrase can be removed and not cause confusion.)

What are we actually doing?

COHA

It looks like we have gotten confused by all the rules and the flipping back and forth that we are starting to use only one form, that, and getting rid of which. On one hand, this is surprising since the rule on restrictive and nonrestrictive clauses says that you can use which in either place and that with only restrictive clauses. It would make sense that we would have started to use which in both places since it was correct to use it in either place.  However, seeing as we can use that to reference anything, while we can only use which to reference things, it does make sense we have started to use that more than which. The only rule retaining the use of which is the one saying that it is the only proper form to use with nonrestrictive clauses with a thing as the referent. However, "disobedience" of this rule makes sense since we are to include the needed information found in restrictive clauses in speech and other forms than we are to use unneeded information in nonrestrictive forms. 

COHA Token Comparison of that and which


Google Books

While I wasn't able to get a search using [nn*] that/which [v*] in the Google Books corpus, in a search of that and which alone showed similar data to COHA. However, which has not dropped as much in use. I'm not sure exactly the reason for it. One reason may be that that does not have a genitive form and can't follow prepositions (this is to the best of my knowledge). Thus, forms like "of which" and "in which" must use which rather than that. In this shallow study of that and which, I believe this is the only use that is keeping which alive at present. These forms wouldn't be eliminated in a lexical search of that and which.

Google Books Token Comparison of that and which


COCA

A look in COCA shows some separation in usage of that and which in terms of genre. Not surprisingly, academic writing is holding fast to the older rules, evolving slower than everything else and uses which more often than any other genre uses it. Less formal writing shows more uses of that. In the first graph showing the ratio of that to which, notice that even in academic writing that still accounts for about 89% of uses. We are using that overwhelmingly more often than which.

Ratio of that Compared to which


This second graph shows the percentage of total use for each term among different genres. Not surprisingly, 45% of all the uses of which were academic. This is the last stronghold for which as a relative pronoun. Note that the uses of that are more evenly spread out among genres.

Individual Percentage in Each Genre for that and which

BNC

Lastly, a search of that and which in the BNC showed a difference to the trends noted above in the British dialect. Among newspaper, non-academic, academic, and miscellaneous sources, which actually had many more uses than that. While that was used more in magazine writing, it wasn't by a large gap. The only areas where that far outnumbered which was in spoken and fiction usage. It could be that that is used only colloquially in British English and fiction mimics speech in dialogue passages. The Chicago Manual of Style suggests that British speakers are more open in the use of which with restrictive clauses than American speakers are. This may be a reason why there is a difference here. The ubiquitous usage of that in American English seems to only have a foothold in spoken speech in British English. However, the gap between the two is not excessively large in any genre, so it doesn't seem like that is in threat of being replaced by which in the same way that the opposite appears to be happening in American English.

BNC Token Comparison of that and which

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