I have already raised strong doubts about the soundness of marginalist analysis in economics even in the version presented by Murray Rothbard in Man, Economy, State.
Since then, my opinion that economists should abandon marginalism has grown even stronger. Most of our actual choices do not involve deciding whether to add an infinitesimal amount of good A to the stock of good A or an intitesimal amount of good B to the stock of good B, and this alone should give pause to any proponent of marginalism.
But I am sure that I will be asked at this point how we should deal with the famous water-diamond paradox which classical economists could not resolve. Does its resolution require marginalism, though?
The seeming paradox briefly goes like this. Water in general is obviously more important for humans than diamonds because it is indispensable for supplying many basic needs. Whereas diamonds are a mere luxury. Yet a minuscule diamond costs more than a liter of water.
The marginalist response to this was that humans are not choosing between all water and all diamonds, they are choosing rather among infinitesimal amounts of them. My point is that the first part of their response is correct but the second part should be changed.
Humans do not choose goods for their own sake, they pursue them for satisfaction of certain goals. Thus, what matters for a particular choice are not the volumes over which the choice is being made but the goals among which the trade-off is indirectly made by means of the trade-off among certain amounts of certain goods.
In other words, it is not impossible to imagine that humans will have to make a choice between large amounts of water or diamonds, for example if they in the future face a choice whether to colonize a planet rich in water or in diamonds. But nothing in the underlying basic structure of choice will change. Therefore, the notion of marginalism is not basic to economics, if it is a properly economic notion at all.