what is the function of the conjunction "that"?

"That" can be used to introduce a consequence or result. "I hit the ball so hard that it broke the window." In the case of the Gettysburg Address, Lincoln used "that" in a manner that is probably hard for foreign speakers to understand, because it is used in a multiple parenthetical construction. You can read it this way:

"It is rather for us to be here dedicated to the great task remaining before us -- so that from these honored dead we take increased devotion -- and as a result we here highly resolve that these dead shall not have died in vain -- in order that this nation, under God, shall have a new birth of freedom -- and so that government of the people, by the people, for the people, shall not perish from the earth.

Since "is" in "It is rather..." is a linking verb, those clauses are not modifying the verb, so they are not adverbial. An argument might be made that the clauses are adjective clauses, describing the subject "It," but I would say instead that it is a list of clauses which are serving as predicate nominatives.

All those clauses are adjective and they tell (modify) the word "task'

the "that" is a relative pronoun in the clause.

Now that I look at this, I think it is open to different interpretations:

I can see sullyfish6's interpretation of "task" being modified, but I also think you can see three predicate nominative clauses (a list of what "It" is for them):

1) "for us to be here dedicated to the great task remaining before us",
2) "that from these honored dead we take increassing devotion"

and

3) the rest starting with "that we here highly resolve..."

AND, within that last clause, where "we here highly resolve that", I think "these dead shall not have died in vain" is an objective subclause acting as a direct object.

Then, I think there are two ways to see the following two subclauses:

"that this nation, under God, shall have a new birth of freedom"
"that government of the people, by the people, for the people, shall not perish from the earth."

I think you can view both those subclauses as also being direct objects in a list with the first subclause (all three being things "we here highly resolve").

Or, you can view both of those last subclauses as modifying "not" in "shall not have died in vain" which would make those last two adverbial clauses after all.

Here's a similar sentence:

Here are all the tasks we should do - that we get along, that we share, and that we love one another.

You can see that the 3 clauses refer back to the "tasks we should do."

The 'thats' can't be relative pronouns, Sully. If they were, we could replace them with task.

Another sentence, also similar, with a different interpretation:

The reason for this thread is for us to be dedicated to the task of analyzing the sentence, that we gain devotion for our work from sullyfish6's posts, that we resolve that Lincoln's words shall not go undiagrammed!

Conjuction Junction

For the first two "that", I agree with joefromchicago.
It is rather for us to be here dedicated to the great task remaining before us -- that from these honored dead we take increased devotion
that we here highly resolve
"that" introduce adverbial clause of result, equal to " so that"

For the last three "that",I agree with rg123. I think the last three "that" should be analyzed as follows:
we here highly resolve that these dead shall not have died in vain --
(resolve) that this nation, under God, shall have a new birth of freedom --
and (resolve) that the government of the people, by the people, for the people, shall not perish from the earth.
"resolve that" intruduce objective clauses.

Do u agree with me? Please share your ideas with us.

I believe you are correct. "That" is often used as a relative pronoun. "This is the speech that Lincoln wrote." In the case of the quoted passage, however, "that" is used as a conjunction. To confirm this, you can replace each occurrence of "that" in the passage with "and so."

"It is rather for us to be here dedicated to the great task remaining before us -- and so from these honored dead we take increased devotion -- and so we here highly resolve that these dead shall not have died in vain -- and so this nation, under God, shall have a new birth of freedom -- and so government of the people, by the people, for the people, shall not perish from the earth."

Not nearly as good, but it works grammatically.

Not nearly as good/fitting, Joe, because the register screams for more than casual.

So what is the function of that.

Lincoln could have said/written:

It is rather for us to be here dedicated to the great task remaining before us: from these honored dead we take increased devotion; we here highly resolve that these dead shall not have died in vain; this nation, under God, shall have a new birth of freedom; [finally], government of the people, by the people, for the people, shall not perish from the earth.