This column contains references to abortion and sexual assault that may be troubling to some readers.

Abortion is one of the most ethically complex issues that we face, in part because it involves a number of difficult problems. Among them are balancing the life and rights of a mother against those of a fetus, relative burdens on mothers and fathers and considerations of rape.

But even if we oversimplify, if we abstract these issues away for a time, one of the central questions of the debate — “when is it okay to kill an organism?” — seems intractable. In particular, it suffers from a problem of vagueness.

Philosophers worry a lot about problems of vagueness. On a color gradient, at what point does it change from red to not red? If you need coffee, how much coffee is enough? An ancient example, called the Sorites paradox, comes from Greece: you have a pile of sand. You remove one grain at a time from the pile. When is the pile not a pile anymore?

We might be forgiven for observing that these don’t seem like real problems. We can simply stipulate that any amount of sand is a pile, or alternatively differentiate between “not a pile” or “sort of a pile” or “pretty much a pile” or “clearly a pile.” We acknowledge and understand that we are vague in how we use language, and this doesn’t impede our daily lives. Why should we care about vagueness?

We should care because ethical questions also suffer from vagueness, and in particular the question “when is it okay to kill an organism?” suffers from a vagueness with far higher stakes than the definition of a pile of sand.

Vagueness illustrates partway why both the advocate and the opponent of abortion have difficult arguments to make. Even the most hard-line proponent of abortion rights might balk at allowing the killing of a newborn, but it seems quite unrelated to the rightness or wrongness of killing a baby whether it is inside or outside its mother. If we go back in time, one minute at a time, no single change of one minute reasonably changes it from “okay” to “not okay” to kill a fetus. The opponent of abortion can follow this logic to argue that abortion is never okay.

But it works the other way as well. Both a sperm and an ovum are single human cells, and it seems no more wrong to kill these cells than to kill, say, cancer cells. At the moment of conception, a sperm and an ovum have fused to form a single cell, a zygote. Does this event have any moral significance? An argument that life begins at conception runs into problems here, because the very definition of life is vague. Any definition that says the zygote is alive would likely have to say that the sperm and ovum were also alive before they fused.

At any rate, what we care about is not a technical definition of life, but the question: has there been any change that would make it morally okay to kill the cells before, but not morally okay to kill the cell after? Asserting such a change is just as arbitrary as asserting that when a baby is born, killing it changes from “okay” to “not okay.”

But now we can run the argument forward: any single minute doesn’t seem to change it from “okay” to “not okay” to kill an organism, nor does it seem that an increase in the number of cells, or the development of certain distinctive features, has any moral significance. There is perhaps an argument to be made for “ability to live outside the mother,” but this is also vague: you could argue that, left alone outside, even a newborn would die; or conversely, that given the proper medical advances, you could fuse an egg and sperm and complete gestation entirely outside a natural womb.

We seem to have a contradiction. Running the argument one way, it is never okay to kill a fetus, and if we keep going, minute by minute, we might even think it’s not okay to kill any human cells. Running the argument the other way, it is always okay to kill a fetus, and if we keep going, hour by hour, we might even think it is always okay to kill a human, no matter how developed.

And unlike the case of a pile of sand, where it seems okay to wriggle out of the paradox, it’s less appealing to say that at some point killing an organism is “okay,” at some point it’s “sort of okay,” at some point it’s “rather not okay,” and at some point it’s “completely not okay.”

If even in this simplified scenario it is hard to find a satisfactory answer, it may seem to get worse when the complicating factors are reintroduced. For we begin comparing the badness of sexual assault to our judgments about abortion, or comparing the relative unfairness of the pregnancy burden with the vague notions of a right to life. If the problem seemed intractable before, it is doubly more so now.

But I think that in fact recognizing the intractable vagueness at the heart of the abortion debate can aid it. The discomfort of this vagueness can become common ground between friends and foes of abortion rights. I suspect that most people with opinions on abortion realize that the debate is not a binary between “life” and “choice.” My optimistic take, then, is that even dogmatically opposed opponents on both sides of the abortion debate can appreciate the inherent vagueness of the problem.

If an appreciation of vagueness can soften, at least temporarily, our more dogmatic positions, then there’s more room to consider the tangle of other considerations that arise in problems like abortion. We can realize that these other considerations, like medical complications in the mother, the distinctions between wanted and unwanted pregnancies and the differing burdens on men and women, may suffer from vaguenesses of their own. And we can attempt to address the pile of issues without the illusion that there is a simple, unambiguous solution to be found.

Contact Adrian Liu at adliu ‘at’ stanford.edu.