They are abstractions that highlight an aspect of the thing being modeled.
That is why I deny that, by making a model of a recession in which "recessions are not about output and employment and saving and investment and borrowing and lending and interest rates and time and uncertainty... the only essential things are a decline in monetary exchange caused by an excess demand for the medium of exchange," Nick Rowe has shown that in real recessions, those are the only essential things.
For instance, what about the proposition that "The Ptolemaic model of the solar system proves that it is not about rock-and-ice-and-gas planets orbiting a giant plasma orb: The only essential thing is pure circular movement"?
But perhaps the problem there is that that is not a good model. So let's say we get a better one: Newton's. Now we have a planet as a point mass, orbiting the Sun, another point mass. Is this the "essence" of the solar system? That doesn't seem right at all: these point masses aren't the essence of planets and the Sun. They are just an abstraction of one aspect of these bodies, among countless others they possess. And for different problems, a model based on the idea of point masses would be disastrously misleading: You don't want to try to land your spacecraft on Mars based on modeling it as a point mass, nor would humans survive long if the Earth were one!
In particular, one may question whether, in Rowe's model which purports to show that recessions are all about "an excess demand for the medium of exchange," there is really a medium of exchange at all. Consider this quote from Mises:
"Thus the 'money' of this system is not a medium of exchange; it is not money at all; it is merely a numéraie, an ethereal and undetermined unit of accounting of that vague and indefinable character which the fancy of some economists and the errors of many laymen mistakenly have attributcd to money. The interposition of these numerical expressions between seller and buyer does not affect the essence of the sales..." -- Human Action
Let us look at what role "mangoes" play in the model economy Rowe has created. In his barter economy, he makes mangoes the "numéraie," and shows how the "price" of apples and bananas in terms of mangoes makes no difference to what trades take place at all. But in what sense, then, are these "prices" at all? What possible actors would choose to evaluate their trades in terms of a "price" that made no difference to what they traded? If we want to look at "essences," I would suggest that the "essential" feature of any price is that it enables us to evaluate whether or not some exchange is worthwhile.
Rowe then proceeds to a model where apples are not traded directly for bananas, but each are traded for mangoes. Why don't actors simply trade apples directly for bananas in this economy? He says:
"This means there is a market in which mangoes are traded for apples (the 'apple market'), and a market in which mangoes are traded for bananas (the 'banana market'), but no market in which apples are traded for bananas directly. The reason is that mangoes are portable, but apples and bananas must be eaten directly off the tree, or they taste bad, and agents are anonymous so can't swap IOUs for apples or bananas. So the only way agents can trade apples and bananas is by using mangoes as the medium of exchange."
Rowe recognizes that, even in the case where apples and bananas can only be eaten directly from their trees, IOUs could suffice to permit exchange: each actor could signal, through whatever IOU mechanism they employ, "You can go eat 100 of my apples, if I can go eat 100 of your bananas." And he tries to foreclose this possibility by positing that "agents are anonymous." But what in the world can that mean? I just go and dump 10 mangoes out on the beach, and trust that somehow ten bananas will appear in exchange? No, if transacting agents are anonymous to each other, then they must have some exchange through which they are transacting, and that exchange must know the identity of each transacting agent. If I offer ten mangoes for ten bananas, then for me to have any faith that I simply haven't lost my mangoes, someone or something (e.g., a computer) must know exactly who has accepted my offer, and have some way to ensure that non-anonymous agent actually delivers. In which case, we could simply transact through IOUs, and skip the mangoes.
Finally, let us assume that, for some unknown reason, mangoes would actually serve as the medium of exchange in Rowe's model. A recession sets in when people suddenly desire to hold more mangoes than they previously had held, raising P above 1. But what could possibly cause such a price change except increased uncertainty about the future? Indeed, what could ever create the need for a medium of exchange at all, except uncertainty about the future?
Rowe's model is interesting, and I am glad he has forwarded it. But it does not prove what he thinks it proves.