Is a work proposal without the signature of the contractor a legal contract?

My electrical contractor filed in a small claim court saying I owned him $2670 for "extra work" done. I only signed a working proposal with detailed items and total price of $1800 with a fine print saying any extra work will be additional. Most of his claimed extra works were either not authorized or never done or included in the original proposal.
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I have had a varied practice that began in New Orleans in the areas of primarily environmental, employment, and bankruptcy law although I have researched other areas throughout my career.

It can be under certain circumstances, such as when work is performed in accordance with the agreement.  Only you have to sign.  He is offering the work and the price.  You accepted it and his terms.