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The old joke says that I cannot define art, but I know it when I see it. So it is with coins. No definition of the word includes all the the cases. The question is not merely academic. People have been prosecuted by the federal government for claiming that objects are coins.
In 1994, the Principality of Hutt River Province was prevented from using the word "coin" in its advertising. According to the US Federal Trade Commission, only a government with authority can issue coins. And the United States had no diplomatic relations with Hutt River and in fact sides with Australia in denying the validity of HRP independence.
Speaking for the entire numismatic community, Alan Herbert claimed in Numismatic News for July 5, 1994, that the US Mint holds legal title to the word "coin." He said:
The term "coin" has been legally and professionally banned for use in the hobby to prevent applying it to medals, tokens and other similar pieces. A coin is defined as a piece that has been issued and is assigned a specific value by a legal body entitled to issue money.
By this definition, the British gold sovereign is not a coin. It has no specific value. Its weight and fineness are not stated in the coin.
Herbert's definition and most others commonly offered include some reference to a government. Herbert calls it "a legal body entitled to issue money." These words are also meaningless. who "entitles" a "legal body"? On the British gold sovereign, the name of the issuer is hidden within the abbreviated Latin legend, but you can find the names "Victoria" "Eduardus" "Georgius" and "Elizabeth." Who entitled them to issue money and what makes them a legal body?
What about the Confederate States of America or South Vietnam? For many years, the United Nations refused to admit the two Germanies and the two Koreas on the grounds that they were not separate countries but different occupied areas of the same country. Did Israel not issue "coins" for 40 years simply because its neighbors refused to recognize it? And now that they have, do its "tokens" or "medals" suddenly acquire the patina of coinness?
In the context of American history, Pine Tree Shillings were struck without the authority of the King of England. (In a brilliant essay on the subject Michael J. Hodder shows that the government of Massachusetts issued coins and invaded Maine in 1652 because they viewed themselves as an independent nation.) The coins of the Mormons, Oregon, and California would also fail the Herbert Test.
The American colonies began as corporations. In our day, most cities and other local governments are also incorporated entities. Obviously, then a corporation can issue "coins." If an incorporated city can issue a coin, why cannot an incorporated automobile manufacturer? And if so, then, why must the company be organized as a corporation instead of a partnership or proprietorship? Why must a person be a partner or a proprietor in order to issue coins? Why not strike coins in your own name as a sovereign individual and call them coins.
I offer the following workable definition:
A coin is a durable and ponderable medium of indirect barter.
Coins are differentiated from banknotes, flooz, bonds, etc., which are paper, or fabric, or immaterial. It also differentiates coins from "tokens" which are a medium of direct exchange. It also separates coins from medals which are not a medium of exchange.
This definition allows a coin to be metal, plastic, or wood, round or square or triangular, a disk or an annulus. Coins can come from from kings with families going back 1000 years or from constitutional republics or from outlaws and rebels hiding in the mountains or from businenesses or from you.
This definition is a workable definition for numismatics. It is not intended to be a legal definition. If I choose to call a plucked chicken a coin and you come to me because you want to make soup from it (clearly, a rich diet, high in bullion) and we agree on a price, that is our business and no business of any third party.