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I was reading the Tobira textbook recently and I became a little confused when
reading the following passage.

> "日本語では、会話をスムーズに進めるために「あいづちをうつ」ということをします。「はい/ええ」「うん」「そうですか」など色々ありますが、これらは
> ″Yes, I'm following you; please continue.″という意味で、″Yes, I
> agree.″という意味ではありません。"

More specifically this particular sentence

> "これらは ″Yes, I'm following you; please continue.″という意味 **で** 、″Yes, I
> agree.″という意味ではありません。"

From my understanding this sentence means

->"This means "Yes, I'm following you; please continue" and **NOT** "Yes I agree"."

Is this correct?

The reason I'm confused over this is because despite the clauses being
opposite polarity they are using the て/で form.

Normally wouldn't a sentence with opposing polarities be better suited/more
natural to using the が particle such that

> これらは ″Yes, I'm following you; please continue.″という意味 **ですが** 、″Yes, I
> agree.″という意味ではありません。

Is using the で in the first example the same as using the が in the second
example?

Theoretically speaking, if I wanted to negate both clauses would it make sense
to use じゃなくて？

> これらは ″Yes, I'm following you; please continue.″という意味 **じゃなくて** 、″Yes, I
> agree.″という意味ではありません。

Would it make sense to interpret this sentence as "These do **NOT** mean "Yes,
I'm following you; please continue" and **NOT** "Yes I agree".

I.E both clauses are negative.

Basically what's troubling me is: is the polarity determined from the ending
of each individual relative clause or is the polarity of the entire sentence
determined by the ending of the sentence. Because tense IS determined by the
sentence final ending, correct?

Thanks
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syntax て-form clause-pattern
Sentence Polarity when connecting sentences/clauses with て/で
> これはAで、Bではありません。

means 'This is A, not B.' This is similar to

> これはBではなく、Aです。(This is not B, but A).  
>  これはAですが、Bではありません。(This is A, but not B.)

So

> これらは "Yes, I'm following you; please continue."という意味で、"Yes, I agree."
> という意味ではありません。

means 'This means "Yes, I'm following you; please continue" and NOT "Yes I
agree".'

You would say

> これはAでもBでもありません。  
>  これはAでもなくBでもありません。  
>  これはAでもないしBでもありません。  
>  これはAでもなければBでもありません。  
>  これはAではなく、またBでもありません。 etc.

to mean 'This is not A or B.'

So, 'These do NOT mean "Yes, I'm following you; please continue" and NOT "Yes
I agree".' would be written

> これらは "Yes, I'm following you; please continue."という意味でも(なく/ないし)、"Yes, I
> agree."という意味でもありません。
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> _The reason I'm confused over this is because despite the clauses being
> opposite polarity they are using the て/で form._

The で you mentioned is used to **join two sentences** here, and it **isn't a
counterpart of て/で form** in verbs, though their... they're very confusing. As
it's... its true identity is somewhat debatable and I don't know how your
textbook explains, I go theory-neutral here.

Functionally, it serves as:

> これらはAという意味だ。 + これらはBという意味ではない。  
>  → これらはAという意味 **で** 、Bという意味ではない。

...and is parallel with:

> 私は日本人ではない。 + 私はアメリカ人だ。  
>  → 私は日本人では **なく** 、アメリカ人だ。
>
> 彼女は朝走る。 + 彼女は午後に散歩する。  
>  → 彼女は朝走 **り** 、午後に散歩する。

In summary, this particle is found in the following grammatical paradigm:

```

    Dictionary Form      This equivalent      TE-Form
    走る                 走り                 走って
    美しい               美しく               美しくて
    ない                 なく                 なくて
    である               であり               であって
    だ                   で    <- HERE!       ×
    きれいだ             きれいで             ×
    
```

You can see we don't have te-form of copula だ because of some grammatical
restriction, and we use this form in situations other words would have te-
form, too. It ultimately comes from case particle で, so we have to borrow であって
when we need to differentiate it from other possible meanings で could have.
(The same applies to _na-adjectives_ like きれいだ, because they're basically
diverting だ to their conjugation except before nouns.)

> _Basically what's troubling me is: is the polarity determined from the
> ending of each individual relative clause or is the polarity of the entire
> sentence determined by the ending of the sentence._

Yes, polarity is independent. Only tense and politeness are carried over. (The
reason why, I guess, belongs to another lengthy answer.)

> **これらは ″Yes, I'm following you; please continue.″という意味ですが、″Yes, I
> agree.″という意味ではありません。**

It's grammatically correct but semantically weird. The latter half is
supporting the former, so it shouldn't be connected with が "though".

> **これらは ″Yes, I'm following you; please continue.″という意味じゃなくて、″Yes, I
> agree.″という意味ではありません。**

So is this. At least it needs "either"; you should say: ～という意味で **も** ありません.
And ideally, "nor ~ neither ~" pattern is more preferable:

> これらは ″Yes, I'm following you; please continue.″という意味 **でも** 、″Yes, I
> agree.″という意味 **でも** ありません。
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