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Consider this sentence, please:

They need permission to help you.

In the above sentence, is to help you modifying permission Or the verb need?

a) They need [permission to help you]. OR

b) They need permission (in order) to help you.

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With no more context or information, (b) is the interpretation that comes to my mind. However, it depends on context. For example:

Interpretation (a):
What kind of permission do they need?
They need permission to help you.

Interpretation (b):
Why aren't they helping me?
They need permission to help you.

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The infinitival "to help you" can't be modifying "permission", since that would mean it was a relative clause, which is clearly not the case here.

The salient interpretation is that it is a purpose adjunct, an optional item in clause structure, i.e. it modifies the verb phrase "need permission".

Most often the preposition "in order" can be optionally added, in which case the subordinate clause is governed by the preposition rather than functioning as purpose adjunct itself. In this case the adjunct is the PP "in order to help you".

Both constructions are purpose adjuncts and have the same meaning.



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Comments  
BillJThe infinitival "to help you" can't be modifying "permission"

In some contexts it can.

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GPY
BillJThe infinitival "to help you" can't be modifying "permission"

In some contexts it can.

That's true, but as I said it's not the case here.

BillJThat's true, but as I said it's not the case here.

I don't know whether you saw my examples, but in my view it is apparent that "to help you" in the first context is not describing purpose of / reason for "need permission". This is confirmed by the fact that the following does not make (much) sense:

What kind of permission do they need?
In order to help you, they need permission.

Compare this, which is OK:

Why aren't they helping me?
In order to help you, they need permission.

In the OP's examples, the salient interpretation of the infinitivals is that of purpose adjunct, especially as the second example contains the preposition "in order", a sure sign of a purpose adjunct.

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BillJ

In the OP's examples, the salient interpretation of the infinitivals is that of purpose adjunct, especially as the second example contains the preposition "in order", a sure sign of a purpose adjunct.

The OP's presentation of examples is intended to contrast the "in order to" interpretation with the other interpretation. I agree that the "salient" interpretation is (b), as I intimated in my original reply. However, in my opinion the (a) interpretation is also possible in some contexts, such as the one that I provided.