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I asked this question stating whether we should use the definite article before the noun "manipulation" in the phrase "manipulation of formal symbols" or not, and I was told that using the definite article is optional but justified.

In this post I will not repeat that question. However, the provided argument for justification of using the definite article in that example led to some controversial general point, which needs a separate thread to inspect it further.

It was explained that using the definite article in that example is justified because the noun phrase "formal symbols" specifies the kind of the noun "manipulation", so it is now specified and needs a definite article.

However, I argued that if the explanation is right, then one can always use the definite article before the first noun in the "of-phrase" [noun] + of + [noun] because one can argue that the second noun specifies the kind of the first noun.

But, in my opinion, whether we should use the definite article in such a phrase or not is independent of the fact that the nouns lie within an of-phrase; if the first noun is specified, then we need the definite article. So, in my opinion, we should not use the definite article before the noun "manipulation" because it is an abstract noun meaning the act of manipulating and does not refer to any specific manipulation.

Clarifying what I mean, let us consider the following example phrases:

  • kitchens of houses
  • the kitchens of houses.

In my opinion, the above phrases do not mean the same. If we assume that any house has just one kitchen, then we should say "the kitchens of houses." However, if we assume that a house can have many kitchens, then we should say "kitchens of houses" because "kitchens" in this case are not specified.

I wonder whether I am right in using the definite article in such phrases or not.

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    Your opinion about [the] kitchens of houses is just wrong. Here's a list of the usage the kitchens of houses in Google Books, and here's another list of instances of the same collocation without the definite article. My gut feel after leafing through a couple of pages of each is that in the vast majority of cases, it makes no difference at all whether the article is present or not for that particular sequence. Commented Oct 5, 2021 at 11:18
  • (But even where it could make a difference, I don't think that would ever be anything to do with the fact that any given house normally has only one kitchen.) Commented Oct 5, 2021 at 11:21
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    Bear in mind that, according the the Cambridge Dictionary, the word of has nineteen different meanings. It is unreasonable to expect the same rules to apply to all of them. In addition, in the particular example you provided, the first noun described an action and the second noun something that is acted upon. It is unreasonable to expect that an explanation applicable to this particular usage should be applicable to all other "noun of noun" situations, or to use the failure of your extrapolated version to discredit the explanation of the original usage.
    – JavaLatte
    Commented Oct 5, 2021 at 11:26
  • @FumbleFingers If a house has only one kitchen, we say "the kitchen of a house"; if a house may contain more than one kitchen, we say "a kitchen of a house," right? Now, the pluralization of them should be "the kitchens of houses" and "kitchens of houses", respectively. When there are houses and we know that each house has only one kitchen, we should use the definite article for the "kitchens" because in this case the specification of the "kitchens" is already determined. Does my justification contradict any established grammar rules in reliable resources?
    – Later
    Commented Oct 6, 2021 at 10:32
  • Forget about comparing usages in contexts where a house has either only one kitchen, or multiple kitchen. That's a very contrived distinction that wouldn't normally have any significance for native Anglophones. I'm pretty sure you won't learn anything useful about definite/indefinite articles in English by further reference to single-/multi-kitchen houses. Commented Oct 6, 2021 at 16:19

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