It looks as if with and without admit a construction that other prepositions usually do not. With or without may have a noun or pronoun object followed by a complement. The complement may be a noun, an adjective, a prepositional phrase, an infinitive or a participle, as here:

With George mayor, we'll have better city government.
With George angry now, we can hardly expect concord.
With George in Boston, whom can we put in charge?
With George to protect us, we should be safe.

With George helping us, we'll get things done..

Without George mayor, the city will be less corrupt.
Without George angry any longer, we can proceed.
Without George in Boston, there'll be some peace and quiet around here.
Without George to protect us, we're doomed.
Without George helping us, we can't achieve much.

But we would not usually say:
Despite George mayor
Because of George mayor
After George mayor
etc.

But there is also a case with a possessive and a gerund, as here:

With George's helping us being more of a bother than a blessing, I think we should ask him not to.

So in different constructions, we have both with George helping us and with George's helping us as correct phrasing.

Anyone have any thoughts on this? I'd like to have an authority to consult but I don't know how to look it up, especially since I have to do it online.
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For some reason I'd never say "With George mayor". I'd use "with George as Mayor". I can't really comment on the rest of your post because I'm not sure what exactly you're interested in. Perhaps you could be a bit more specific.
I've been unable to find any authority to support your proposition, Electrum, but I think you might be right. With and without seem to have their own unique set of constructions.
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Look up "nominative absolute", an older term for such a construction.

Look up "small clause", which is a more recent analytical term.

See Small Clauses. Note that there is one example there where the small clause is introduced by "with".

CJ
IvanhrFor some reason I'd never say "With George mayor". I'd use "with George as Mayor
I would too, but I feel that With George mayor is a valid construction, if a little odd. How about With George now mayor?
Here are Wikipedia's small clauses:
  • Robert painted the house blue.
  • We consider Mary intelligent.
  • Abby saw Patrick eat the cake.
  • Eating too much cake makes me sick.
I've always considered the second term in these constructions a factitive complement or causative complement. I've never heard this term small clause before, but I am familiar with this construction.

I don't think the nominative absolute quite fills the bill though, because it usually has no introductory preposition.
This done, Caesar sailed to Egypt.
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Here's what Bryan A. Garner has to say:

...as nominative absolutes become rarer, fewer and fewer writers understand how to handle them. Three problems arise:

First, many writers insert with at the beginning of the phrase (making it something like an "objective absolute") <With Jacobsen being absent, the party was a bore>....

He never goes on to explain why adding with is a problem.
FuturistHere's what Bryan A. Garner has to say:

...as nominative absolutes become rarer, fewer and fewer writers understand how to handle them. Three problems arise:

First, many writers insert with at the beginning of the phrase (making it something like an "objective absolute")
....

He never goes on to explain why adding with is a problem.

John dead, we would enjoy more liberty.
With John dead, we would enjoy more liberty.

Clouds in the west, we couldn't see the sunset.
With clouds in the west, we couldn't see the sunset.

It seems to me that the nominative absolutes are harder to understand.

Perhaps the nominative abolute is a clone of the ablative absolute in Latin:
His rebus factis, Caesar Aegyptum navigavit. (I think)
These things done, Caesar sailed to Egypt.
With these things done, Caesar sailed to Egypt.

With is justified IMO as a way of making the phrase ablative (from, with, by).

electrumPerhaps the nominative abolute is a clone of the ablative absolute in Latin:
I think so. Don't the Roman writers also sometimes use "with" ("c u m") in such a construction?

CJ
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