What is the difference between formal and polite verb forms?


In the answer to this question I asked ([When to use である vs
であります?](https://japanese.stackexchange.com/q/36305/10795)), sazarando
responded by saying that "である" is formal but not polite, and "です" is polite
but not formal. I sort of understand the distinction he was making, but from
my English perspective, I suppose I don't understand why you would want to be
formal and not polite at the same time.

The example he gave for である was

> A politician giving a speech on TV:
>
> 我々は日本国民である - We are Japanese citizens

In this example, why would the politician not want to be polite to the people
to whom he is speaking? I understand why you would not use である when talking
to, say, a superior at work, because that's simply a private conversation
where you need to be respectful to your superior. But in the above case where
you're speaking in public or writing in a newspaper or something, I don't
understand why you wouldn't be polite as well as formal.

Also as a side question, in some academic presentations I've witnessed, the
presenter simply uses 謙譲語, rather than using formal speech, so they would end
sentences with でございます rather than であります or である. What would be the explanation
for this?




By "formal" [they](https://japanese.stackexchange.com/a/36306/7810) seem to
have meant "literary", "solemn", "lofty" and such things, while "polite" seems
more about social courtesy. In this sense:

  * **"Formal" or not** : _get_ vs _obtain_ ; _job_ vs _profession_ ; _cold_ vs _rhinopharyngitis_ etc.
  * **"Polite" or not** : _Can I..._ vs _May I..._ ; _want_ vs _would like_ ; _Can you..._ vs _Would you mind..._ etc.

Thus, the style in academic papers is typically "formal but not polite", and
the way a hotel clerk speaks to customers is "polite but not formal". Japanese
honorifics denote "politeness" and we don't have grammar represents the degree
of "formality" they said.

> だ -- plain (not formal nor polite)  
>  です -- polite  
>  でございます -- double-plus-polite  
>  である -- formal  
>  であります -- formal and polite




By "formal" [they](https://japanese.stackexchange.com/a/36306/7810) seem to
have meant "literary", "solemn", "lofty" and such things, while "polite" seems
more about social courtesy. In this sense:

  * **"Formal" or not** : _get_ vs _obtain_ ; _job_ vs _profession_ ; _cold_ vs _rhinopharyngitis_ etc.
  * **"Polite" or not** : _Can I..._ vs _May I..._ ; _want_ vs _would like_ ; _Can you..._ vs _Would you mind..._ etc.

Thus, the style in academic papers is typically "formal but not polite", and
the way a hotel clerk speaks to customers is "polite but not formal". Japanese
honorifics denote "politeness" and we don't have grammar represents the degree
of "formality" they said.

> だ -- plain (not formal nor polite)  
>  です -- polite  
>  でございます -- double-plus-polite  
>  である -- formal  
>  であります -- formal and polite

