Yes all monetary value is ephemeral, intangible and based on the belief and good will of the market
That's an overly simplistic view of the value of money. If the value of money were only based on belief, then one would except sudden collapses of monetary value without any connection to the real economy quite regularly. In a sense, money would be like the cartoon character who defies gravity until he looks down.
In reality, the value of money is based on people's demand for money. This demand is largely circular (the store wants money in exchange for goods because that's what the suppliers demand, and the suppliers demand money because that's what their employees demand, who demand it because that's what the stores want, and so on).
However, there are two decidedly non-circular sources of the demand for money. One of these sources is taxation: If the government decides that you have to pay your taxes in currency X, then there will always be demand for that currency. Even if your employer pays you in Bitcoin, you will still have to pay your income tax in whatever the local fiat currency happens to be.
The other source is debt payment: If you are in debt, you have to make certain payments (under threat of losing your house etc.).
These two belief-free sources of demand for fiat currency are the "base case of induction" for why fiat currency has value. They ensure that the viability of fiat currency does not depend on belief.
A decent point but the government accepting payment in a certain currency requires that they are sure/believe that they will be able to use that currency to pay their debts. Same thing applies to the debt argument both rely on a communal acceptance that a dollar/euro/ruby/piece of eight/bitcoin/kongbuck will be accepted as payment.
I suppose it'd be clearer if I said it's exchange value is ephemeral, ie completely determined by the faith that currency X is worth/will be accepted in exchange for some amount of currency or product Y.
A decent point but the government accepting payment in a certain currency requires that they are sure/believe that they will be able to use that currency to pay their debts.
There are all sorts of ways to answer to this, but all of them amount to pointing out the bleedingly obvious: Most[0] governments issue debt in the same currency that they demand tax payments in, so your condition is not really a condition at all.
If somebody holds a government bond denominated in currency X, then they will be paid in currency X. If they suddenly decide that they would prefer to be paid in currency Y, well, take it to the foreign exchange: said government does not, and does not need to, care.
[0] The governments that don't do that almost invariably end up in trouble at some point because of precisely this. On a related note, almost all stories of hyperinflation are in fact stories about foreign-currency-denominated debt.
That's an overly simplistic view of the value of money. If the value of money were only based on belief, then one would except sudden collapses of monetary value without any connection to the real economy quite regularly. In a sense, money would be like the cartoon character who defies gravity until he looks down.
In reality, the value of money is based on people's demand for money. This demand is largely circular (the store wants money in exchange for goods because that's what the suppliers demand, and the suppliers demand money because that's what their employees demand, who demand it because that's what the stores want, and so on).
However, there are two decidedly non-circular sources of the demand for money. One of these sources is taxation: If the government decides that you have to pay your taxes in currency X, then there will always be demand for that currency. Even if your employer pays you in Bitcoin, you will still have to pay your income tax in whatever the local fiat currency happens to be.
The other source is debt payment: If you are in debt, you have to make certain payments (under threat of losing your house etc.).
These two belief-free sources of demand for fiat currency are the "base case of induction" for why fiat currency has value. They ensure that the viability of fiat currency does not depend on belief.