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No, our economic theories are not symmetrical - 9/28/15
"If it were appropriate to pay taxes on capital gains, why wouldn't it be appropriate to pay negative taxes on capital losses? Economic theories tend to be symmetrical. And yet capital losses do not result in negative taxes, except in certain limited cases. And why only those cases?" - Scott Sumner
Insofar as economics is an actual science that expresses the elegant logic of the natural world, Sumner's premise here is probably correct: we should expect economic theories to maintain a certain symmetry! In fact, that's one of many good reasons for us to be skeptical of capitalism - because contrary to what Sumner seems to think, capitalist theory isn't symmetrical at all.

Consider the basic institution of property. It is from the supposedly empirical, value-neutral features of property that capitalism derives its moral authority; its characteristics are non-negotiable facts of the universe that can only be accommodated, and capitalism gains its legitimacy as the best system for doing so. For this reason, we would expect our theory of property to exhibit the same kind of symmetry that we find throughout nature.

But this is hardly the case! Just look at how property is bounded in geometric space. Horizontally, the rule is simple and somewhat intuitive: property is defined as every point within a simple, clearly delineated polygon. But how does this rule extend into the third dimension? Sometimes we go by some variation on the old ad coelum doctrine, which stipulates that property rights extend in an infinite ray extending perpendicularly from both sides of the property's two-dimensional plane. In recent years we've made all kinds of pragmatic modifications to this rule: for instance, my property rights only extend to a certain height above my house, which is why pilots don't have to ask for my permission every time they fly overhead.

Regardless, it seems clear that an entirely different regime of rules holds for the way that we vertically delineate property rights. This is like discovering that electromagnetism operates by one set of rules moving east and an entirely different set of rules moving south. Generally you would expect property to be defined by a single rule that extends symmetrically into every direction, but capitalism relies on a theory about the universe that's a lot more arbitrary and complicated.