And then comes the problem: you cannot explain any behavior of money that way. You cannot explain inflation or deflation. You cannot explain exchange rates between different monetary assets. If society owes me "a loaf of bread", but then they don't really owe me a loaf of bread, but rather whatever they are willing to give me in return for my unit of money, the concept of IOU with money goes beserk. There is no possibility to have inflation or deflation with such a view, as what society owes you can only do two things:
- remain constant (if society owes me a loaf of bread, then hell, it owes me a loaf of bread !)
- inversely change with economic growth (if society owes me a billionth worth of what is produced, hell, it owes me a billionth worth of what is produced).
You can accept abstract units when it suits you, but only when it suits you. The dollar doesn't need to have a fixed exchange rate to bread, nor does it represent a fixed fraction of all production, but it can have an abstract value of "whatever I can get for it". This does not depend on any particular concept of money.
If a mob boss owes you a favor, do you imagine that there is no debt because there is no fixed exchange rate between "a favor" and loaves of bread, or between favors and global production? You could argue that this isn't a debt for whatever reason, but if you ask a bunch of random people, I'm sure you'll find that pretty much everyone considers this to be "debt".*
I actually covered this, long ago, so I'm just going to recap and skip to the end. Debt is of the form "A owes B to C". Where we disagree is that you think that the essence of debt is in the nouns A, B and C, while I think it is the verb, "owes".
Mortgage: A=homeowner, B=cash payment stream, C=bank (in reality C is usually investors via a MBS)
Mob favor: A=mob boss**, B=(ABSTRACT), C=poor shopkepper
Bearer bond: A=bond issuer, B=cash, C=(ABSTRACT)
Dollar: A=(ABSTRACT), B=(ABSTRACT), C=(ABSTRACT)
*
You can define debt narrowly and declare everyone else to be wrong, but this is folly. Economics is ultimately the study of people. If you disregard them, you are just jerking yourself off.**
If the movies are accurate, A can be abstract here too, as a son may well honor a favor owed by his dead father, or an underling may attempt to extinguish the debt without letting it get to the top.