On p. 62 of the 2nd edition of Practical English Usage, M. Swan writes:

68 articles (8): special rules and exceptions

4 the ... of a ...

In classifying expressions of this kind, the first article is definite even if the meaning of the whole expression is idnefinite:

Lying by the side of the road we saw the wheel of a car. (NOT ...a wheel of a car.)

However, this entry is missing from the 3rd and the 4th editions. Moreover, dictionaries give these examples:

She got a glimpse of a very different way of life.

the management and disposition of the property of a deceased person, debtor, or insolvent company, by a legally appointed administrator

The phones are considered to be the property of the company.

Why is this rule not included in the modern editions? If the rule is not valid anymore, does it mean than the choice of a/the obeys general rules say:

We choose a property of a system... (random property of some system)

We investigate the property of a system... (some very interesting property mentioned earlier of some random system) ?

  • 1
    Could you state the whole rule from the second edition? Anyway, The Cambridge Grammar of the English Language by Huddleston & Pullum (2002, pp.368–9) tells us the can be used when it's not necessary clear which one we mean when we don't really care which one. While you could ask Which one (wheel)?, the speaker assumes you won't because it's not really important. Likewise, Open the window can be said when there are multiple closed windows in a room. Secondly, the is used with wheel(s) because we know exactly which wheels we're talking about – those on a car. – userr2684291 Jun 17 '18 at 14:30
  • I've updated the question. Well, Swan's version obliges to use the, not permits it (if can has this meaning in CGEL). – homocomputeris Jun 17 '18 at 15:08
  • Thanks for editing that in. Well, Swan doesn't really give you a rule there, just an example of usage. I think you'll find it much easier to follow the rule and example I gave you in my previous comment. Note that it's not ungrammatical to use the indefinite article with wheel there, just perhaps less natural in normal conversation. Some other context might even warrant it. – userr2684291 Jun 17 '18 at 15:12
  • OK, I understand the book is called English Usage, but to me this example seems quite prescriptive. Cambridge's version seems a bit more elaborated. – homocomputeris Jun 17 '18 at 15:23
  • Haha. You're conflating prescriptivism with bad prescriptivism. Also, you're overgeneralizing a single example (which really is a bit of an exception). Swan's simply telling you that in that context the version with a definite article sounds more natural. – userr2684291 Jun 17 '18 at 15:45

I think the best way to understand this usage is to forget the grammar rules for a while and look at some actual examples to illustrate what grammar books say.

  • We saw the wheel of a car.

the X of a Y: Basically this functions as explained below.

If you say: |I saw the wheel of a car| the implication is, in a conversation or if you are telling story, that you did not see the wheel of some other thing: the wheel of a cart, the wheel of a ship, etc.

It is not that the whole thing is indefinite. The car is random, the wheel belonging to it is not. Or the wheel is closely associated with it. Here are some more examples:

  • We read the introduction of a book. Compare: We read the introduction of an essay.

  • We broke off the handle of a coffeepot. Compare: We broke off the handle of a door.

The idea here is that the determiner the goes with a noun that is closely associated with the second noun in the prepositional phrase in a given context.

  • The professor explained the idea of a philosopher, not the ravings of a madman.

  • Schrödinger explained the idea of a cat as both alive and dead at the same time.

When both are indefinite and not necessarily associated with each other in a context, you can get two a's.

  • She got a glimpse of a very different kind of life.

  • He mentioned a work of art of a kind we had not heard of before.

Similarly, both can be definite [that's just a short-hand word].

  • The boats in the harbor are the boats of the men on the dock.
  • Those classroom methods were the ideas of the teachers of the primary school. [not the high school, for example.]
  • Thanks. That what I meant by writing 'general rule': If something is 'unique' (obviously, a book has only one introduction), it's the. If it's one of many (a work of art) it's a. – homocomputeris Jun 17 '18 at 15:20
  • the introduction of a book is not the introduction of something else. There is an implied exclusion. the X of a Y excludes all variables that are not a Y. – Lambie Jun 17 '18 at 15:27

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