This is based on a comment I made here.
One of the alleged paradoxes of fiat money is that any given fiat money will, eventually, end. So how can it retain any value now, given there will come a time when it is no longer accepted in transactions? That is, the range of transactions for which it will be accepted will shrink to zero, eliminating its transaction value. (David Glasner explains the reasoning nicely.)
On this indeterminacy issue, I suggest that there is much less there than there seems. Think of it in terms of transaction horizons. If you buy a good you are going to use up, so there is no future transaction involved, then its transaction horizon finishes once you have bought it. You have no concern with its future price. If you buy a good that you are not going to use up--an asset, or something that you might possibly sell (albeit it at a depreciated value) to the second-hand market--then it has an open transaction horizon (for you). Until you sell it, when its transaction horizon closes.
The transaction horizon of the person you sell it to matters for the expected price but, once you have sold it, they take on the risks (positive or negative). Your concern is merely their expectations at the time of sale. Future information after that point no longer matters to you. Any such information is on the other side of the (now closed) transaction horizon.
Such transaction horizons are how assets can surge in price even though we may have reason to believe a turning point will occur (sometime). A theoretical turning point does not matter for the price until it becomes part of the information within current transaction horizons.
The utility of fiat money as a transaction good is similarly a matter of transaction horizons. Any putative loss of utility by some fiat money as a transaction good does not matter until it becomes part of the information within current transaction horizons. Even then, there is the possibility of unloading before the game of "musical transaction chairs" stops. So, for example, as the prospect of the collapse of the Confederacy loomed, the value of the C$ dropped dramatically, but people kept transacting with it up until the bitter end.
So, the theoretical end of a fiat money does not matter if no specific information (beyond its theoretical possibility) has entered folk's transaction horizons. Arguing backwards from "it will end" does not work because it imports information into the sequence of transactions that does not yet exist.
ADDENDA: A very similar, but much more mathematically literate, argument is made by Josh Hendrickson here.
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