You're a circle, I'm a square and that's okay

One of the most fertile re-conceptualizations in abstract mathematics is the shift from the question, “Does x equal y?” to the question, “Do x and y share enough properties that, as far as their membership in a particular class of objects is concerned, they’re equal?” This might be a little abstract, so let me give an example that might help clarify the point. Consider the circle and the square. As sets of points in the plane, they’re obviously not the same object. But one can be continuously stretched into another without “ripping” or “glueing.” This makes them the same object as far as a field of mathematics called topology is concerned. Topology studies only those properties of mathematical entities which don’t distinguish between objects that can be continuously morphed into each other—a square and a circle, or a donut and a coffee mug.

You might ask, “What’s the point of studying something like topology if the entire field ignores the difference between objects as different as a square and a circle?” There’s certainly a reason that even preschoolers are taught to distinguish between the two, but they also share quite a few similarities—you can walk around both and get back to where you started, for example. If you only care about the properties that topology keeps track of, then there’s no need to bother with the extra information that a square has four corners and a circle none.

I think a similar concept is tacitly at play in political language surrounding equality. When we make an argument such as, “all humans are equal,” we don’t mean that every human is exactly the same. In other words, we’re not all squares—some us are squares, and some of us are squares of a different size, and some of us are circles. What we really mean by “all humans are equal” is that all humans share certain properties relevant to the moral argument that we’re about to defend, i.e. that all humans metaphorically have the same topology. For example, an argument for a right to life, as I see it, is based on the fact that almost all humans share a similar interest in their lives, and that this interest ought not be subordinated to anything else. All that is needed for such an argument to work is not that all humans are exactly the same, but that they are the same with regards to holding an interest in their own lives. We might not all be squares, but our differences are flexible enough to be “continuously morphed” away when we think about the right to life.

The problem is that I don’t think we’ve been explicit enough about this way of thinking, so we still disagree strongly about what sort of equality we’re committed to. Distributive equality is probably the most contentious arena. People aren’t similar enough in the right ways to justify total resource or income equality. Here, the fact that some of us are squares and some are circles becomes relevant—some might be better at turning raw materials into goods that improve others’ lives. They might also require some sort of incentive to convince them to put in the labor to make those goods. We’d therefore be justified in giving them both the resources necessary for the production of their good and whatever extra incentive they need. Don’t consider this a ringing endorsement of the free market, though—I merely wanted to point out that, with regard to resource distribution, humans are unequal in relevant ways, and that those differences are also relevant to the collective good. Sometimes, topology doesn’t cut it—we need to actually study the geometry at play.

So, what is the relevant way in which humans are equal as far as distributive justice is concerned? I take a utilitarian stance—humans are equal in that they all have a capacity for happiness and suffering. Their happiness and suffering therefore ought to be taken into equal account when performing the utilitarian calculus, which is to say that a given “amount” of happiness shouldn’t count more because it comes from one person rather than another. I’m well aware of the philosophical difficulties associated with quantifying happiness, but the utilitarian version of equality is the only way I’ve been able to make sense of distributive equality that doesn’t ignore relevant differences amongst humans.

We’re still a long way off from a consensus on the subject, but I think that understanding equality in this new light will help us move forward not just in the debate over distributive justice, but in all political spheres where equality is invoked. It could help us better understand issues like marriage equality, equal protection under the law and more. We would still have a difficult task ahead of us—deciding which level of detail to keep track of and which differences to ignore isn’t easy. In fact, it’s probably the meat of the task. But at the very least we won’t be shoving a square peg into a round hole when we say “All humans are equal.”

Eugene Rabinovich is a Trinity senior. His column runs every other Friday.