You are quite right. Stating that the definition of money is somehow socially determined has many flaws. Most importantly, the reasoning is viciously circular, meaning that it is a formal logical fallacy in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. As our reasoning must adhere to basic rules of logic, we cannot go down the slippery slope of defining something socially. What is ridiculous for all other scientists must be ridiculous for an economist. Therefore, if we want to understand the real world - in which payments are obviously made with money - we must understand what money is.

For these reasons, the idea that money is defined by its social acceptance cannot be accepted on purely scientific grounds. Therefore, go back to the last question.