The question of whether a contract is binding does not depend on the parties' subjective intent. Instead, in determining whether the parties entered into a contractual
agreement and on what terms, a court must look to the objective manifestations of the parties' intent as expressed in their words and deeds. Put simply, the manifestation of the parties' intention is controlling, not their actual or real intention.
Gator Hillside Vil., LLC v. Schuckman Realty, Inc., NY Slip Op 01178 (2d Dep't February 22, 2018)
Here is the decision.