Full Reserve Fallacy

There is a theory that fractional reserve banking is a fraud, allowing banks to create money "out of thin air". The theory implies that legitimate banking must be full reserve.

This theory hinges on the definition of the word "bank". Rothbard makes the above argument, but explicitly limits his definition of a bank to that of a "warehouse" for money:

When a man deposits goods at a warehouse, he is given a receipt and pays the owner of the warehouse a certain sum for the service of storage. He still retains ownership of the property; the owner of the warehouse is simply guarding it for him. When the warehouse receipt is presented, the owner is obligated to restore the good deposited. A warehouse specializing in money is known as a "bank."

Banks do offer this warehousing service, in the name of safe deposit. But banks are not so narrowly defined. They also generally offer interest-bearing accounts such as savings deposit and certificates of deposit respectively. Rothbard uses the expectation of interest to differentiate warehouse banking from borrowing and lending generally:

Someone else's property is taken by the warehouse and used for its own money-making purposes. It is not borrowed, since no interest is paid for the use of the money.