How does the formula “X counts as Y in context C” explain social institutions in John Searle’s theory?

In the philosophy of John Searle, the formula "X counts as Y in context C" is the fundamental mechanism by which objective social reality is created through collective intentionality, or "we-intentions".1

According to Searle, individuals create social institutions by collectively agreeing to treat a certain phenomenon (X) as having a new status or function (Y) within a specific social setting (C). For example, the institution of money is established when a society collectively intends that certain pieces of paper or metal serve as currency.1

A critical feature of this process is iteration: the status Y assigned in one instance can serve as the X in a higher-level intention. This allows for the construction of complex social structures from simpler ones. For instance, an utterance (X) may count as a sentence (Y), which in turn counts as a promise (X) that functions as a marriage vow (Y) within a ceremony (C). Through this recursive application of the formula, Searle explains how diverse institutions—such as property, governments, and language—are built and maintained as objective facts of our social world.1