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The following is a line from a famous movie -- 2001: A Space Odyssey.

"Dave, although you took very thorough precautions in the pod against my hearing you, I could see your lips move."

I understand the meaning: Dave did lots of preparation to prevent HAL noticing him, that's why "against" is used.

What I don't understand is the grammar of "my hearing you". If it was "against/prevent I hearing you", I would be in tune with the meaning.

Could someone please tell me what is the grammar rule of "against my hearing you"?

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Let us start by simplifying the sentence as much as possible:

You took precautions against my hearing.

The word "hearing" is a participle. By adding the suffix -ing HAL has turned the verb "hear" into a noun. This noun is the name of the action indicated by the verb "here".

HAL needs to turn "hear" into a noun because he wants to use it as the object of the preposition "against", like this:

You took precautions against hearing.

But this is not the correct meaning. Dave did not try to prevent himself from hearing. He did not want HAL to hear. So:

You took precautions against my hearing.

Since "hearing" functions as a noun, HAL can attach an adjective to it to indicate that he is the (potential) hearer. But this is not precise enough for HAL. Dave did not try to prevent HAL from hearing any sound at all, just what Dave was saying. So:

You took precautions against my hearing you.

This is good and something a native speaker would say, but it does start to strain the logic of grammar. The participle "hearing" is now both modified by an adjective "my" and followed by a direct object "you" as if it were still a verb.

You propose to resolve this tension by having HAL say "I" instead of "my". In theory this is better because it is more consistent. You construct a valid verb phrase "I hear you" and turn the whole thing into the participle "I hearing you".

And in theory this is grammatical. Native speakers would have no problem with this sentence:

Dave took precautions against HAL hearing him.

But they will tell you that your proposal is ungrammatical:

You took precautions against I hearing you.

Why? Because you have run afoul of the last vestiges of the English case system. Some pronouns still have cases! You seem to be aware of this because you have correctly chosen the nominative case form "I" for the subject of your participle phrase. But the result is incredibly jarring to a native speaker. He will likely offer the following mistaken correction:

You took precautions against me hearing you.

English speakers get little practice in using cases in difficult situations. All they have to work with is a hazy impression that after a preposition one should say "me", not "I".

This correction, which I have described as "mistaken", is actually widely accepted in conversational English. But in science fiction computers are almost always depicted as speaking formal literary English. HAL, being a computer, cannot make grammatical mistakes and he cannot use your suggestion since native speakers will see it as ungrammatical. So he says it the way he did. And a human speaking literary English would likely say it the same way.

P.S. HAL did have one more option:

You took precautions to prevent me from hearing you.

Now I/me is no longer part of a participle phrase. It is the simple object of the verb "prevent" which will now govern its case. Whether it is accusative or dative or whatever does not matter. All of the oblique cases have the form "me" and that is what we put.

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"Against" is a preposition and must be followed by an object, which can be only a noun, pronoun, or gerund. If it is a pronoun, it must either be in the objective case, "me," "you," "him," "her," "it," "us," or "them," or else be a possessive pronoun, "mine," "yours," "his," "hers," "its," "ours," or "theirs." Furthermore, pronouns in the objective case be modified by a progressive participle acting as an adjective. A gerund, which is a progressive participle acting as a noun denoting the generic activity associated with the root verb of the participle, may be restricted by the use of a possessive adjective such as "my," "your," "his," "her," "its," "our," or "their."

Thus both

precaution against my hearing

and

precaution against me hearing

are grammatical and mean much the same thing. Some may say that the first slightly emphasizes that the precaution is against being heard and that the second slightly emphasizes that the precaution is against me personally. For people who think that difference in emphasis is conveyed by the difference between possessive adjective and plain objective pronoun, "my hearing" would clearly be preferred in this case although, frankly, few would pick up that nuance.

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  • Interesting argument for the grammatical logic of "against me hearing you". So Dave took precautions against HAL who was [potentially] hearing him. This would make "me" the object of the preposition. The alternative explanation is that "me hearing you" is a gerund phrase which has been incorrectly declined. The gerund itself should be in the object case, not its grammatical subject. The correct form then would be "against I hearing you" as the question poser suggested! Ouch! One source I consulted indicates that in formal English gerund phrases do not have subjects. I think now we know why. – David42 Mar 15 '20 at 1:30
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    @David42 Interesting.. Yes, I would interpret the "me" as being the object of the preposition in "against me hearing you." The "hearing you" would then be a participial phease used adjectivally as in "I, hearing your knock, hurried to let you in." If you grew up translating ablative absolutes from Latin as I did, participial phrases modifying pronouns seem grammatical though very stilted. Needless to say, I find "my" better in the specific context of this question, and I am sure HAL was programmed with impeccable grammar. – Jeff Morrow Mar 15 '20 at 16:51
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An oncoming gerund is often signalled by a possessive - my, your, his etc. - and that is the case here.

A gerund with a possessive is . . .

variously describable as an -ing noun, or a verbal noun, or a verb equipped for noun-work, or the name of an action. Being the name of an action it involves the notion of an agent, just as the verb itself does. He went is equipped for noun-work by being changed to his going. "His" specifies the agent in "his going", just as "he" did in "he went".

[H.W.Fowler, Modern English Usage, 1937.]

There are other uses for gerunds without possessives: Fowler has two pages on them.

Simple Wikipedia's page on gerunds is a less complicated introduction to the subject than Wikipedia's, but the latter has many excellent examples.

BTW, I only reached for Fowler when I couldn't find a clearer definition online. (I simplified the last two sentences of the quotation.)

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