The sorites paradox (also called the paradox of the heap) refers to a particular logical contradiction that arises from the analysis of vague terms (Sainsbury, 2009). Terms like ‘heap’, ‘bald’, ‘tall’ all fall into this category. We know a tall or bald person when we see one but what are the necessary and sufficient conditions for the transformation from hairy to bald or short to tall?

Take the concept of ‘heap’. If we were walking and came across a construction site with a huge number of piled up sand, it would be safe to exclaim “look at the heap of sand!” But what exactly is a heap? We seem to know one when we see them but what is the ontology of ‘heap’?

The paradox goes as follows:

One grain of sand does not make a heap.

If one grain of sand does not make a heap, then two grains of sand don’t make a heap.

If two grains of sand don’t make a heap, then three grains of sand don’t make a heap.

If three grains of sand don’t make a heap, then four grains of sand don’t make a heap.

If four grains of sand don’t make a heap, then five grains of sand don’t make a heap.

If 999,999 grains of sand don’t make a heap then one-million grains of sand don’t make a heap.

Therefore, for any number (N) of sand that is not a heap, N+1 is also not a heap.

It then follows from this that there is no such thing as a heap. But this is clearly not true. You were just able to point out a heap of sand at a construction site. This doesn’t only apply to heaps; it also applies to you. The proposition “I exist” also runs foul of the same problems seen by ‘heap’.

You began as a single fertilized cell (zygote). That cell divides through mitosis, you are eventually born, and you grow; all the while gaining and losing cells.

You weren’t you as a zygote.

If you were not you as a zygote, you were not you after one division.

If you were not you after one division then you were not you after two divisions

You see where this is going.

Therefore for any number (N) of cells that make you up, if you were not you, then after N+1, you don’t t magically become you. So… you don’t exist… neither do I! (Unger, 1979)

But hang on a minute! Who the hell is reading and writing this blog?! There seems to be a fundamental issue with the vagueness of the terms we are using. There is a ton of literature in philosophy trying to resolve this paradox and you can check out an overview at the Stanford Encyclopedia of Philosophy.

I don’t want to spend too much time discussing the sorites paradox so much as see how even words in science fall into it’s pitfall.

As a biocultural anthropologist, I have been caught up in the David Reich controversy surrounding his NYT article arguing that races are tenable biological units of inquiry and the subsequent responses. One response in particular (by John Terrell) made a point that I had taken for granted and got me thinking about it and the sorites paradox. I first wrote about it here but wanted to spend a little more time engaging with this idea (I’m totally burying the lead!).

See, in biology, we take for granted the term ‘population’. We define it simply as a group of organisms that breeds more within than out. This seems like a tidy little definition but can we operationalize it? This is where the problem lies. It seems to work fine for groups within a species (we’re not even going to get into the trouble with this word!) that are separated by some physical barrier.

However, when groups are merely separated by distance with subsequent groups in-between, where does the first “population” began and the second end?


If we were to talk about the “yellow” and “red” populations, it seems reasonable. Some within those groups are some 3000 miles apart and it’s really hard to mate over that kind of distance. However, I have constructed a particular narrative by only showing you two arbitrarily circumscribed groups. They are arbitrary because why are those boundaries where they are? Are the organisms immediately outside those boundaries really genetically distinct from those within? What does it look like if we fill another “population”?



Right, no problem? But again, I am constructing a particular narrative about the biological distribution of the sampled organism. This still doesn’t really reflect the reality. It is confusing levels of analysis and levels of reality.


It is often impossible to draw neat boundaries around a group. I study primates and we all have either experienced or heard stories about primate groups found far outside of their expected ranges. In the above example, where does yellow end and purple begin? This is a crude and basic illustration of the vagueness of ‘population’ and yet another narrative which isn’t really a reflection reality so much as a representation of a way of thinking about reality.

Now I want to revisit John Terrell’s point. He states:

Once upon a time, these supposed collectives would have been called “races,” at least in some contexts. Most of us know nowadays, of course, that we need to avoid using this word for politically correct reasons, if for none other. Hence almost nobody nowadays, for example, would write about Polynesian speakers in the central and eastern Pacific as a race. Instead, they are usually referred to as a population.

This may sound better, but let’s be honest. Distinguishing between races and populations is effectively making a distinction without a difference. If this comes across as sounding crazy to you, then tell me this. What is a population? How can you tell whether you are “inside” a population or “outside” it? How many of them are there “out there” in the real world? How many did there used to be? More than today, or fewer? (Now substitute in these simple questions the word “race.” Doesn’t make much difference, right?)

See, when it comes to humans, these terms get even more wuzzy. Within anthropology, we have long history of constructing races (if you want a brief overview of the history of the term race, see here). We homogenized entire continents of people into essential “types” and used the assumptions intrinsic to those types to make grand statements about the “natural” divisions in the human species and the value and meaning associated.

Anthropology has since moved on from it’s assumption that the human species is divided up into natural kinds and have generally (in biological anthropology) replaced ‘race’ with ‘population’. But what Terrell is saying is that we’ve merely replaced the term but the application is the same. Here is an example from PLOS:


We have the genetic analysis of several populations within South America (looking at the percentage of ancestry from three continents… which also happen to be three racialized groups). The narrative that this map is conveying is that these “populations” are actually distinct from one another. However, this is a confusion between levels of analysis (these geographic locations) and levels of reality (there aren’t sharp divides between these sampled groups as the map conveys). What about all the people in the intervening areas? How can we draw boundaries confidently between these groups?

I’m not saying that this work shouldn’t be done or using populations is bad methodology. Instead, we need to understand that the populations that we use are constructed, especially in the human species. We do two things: move around a lot and have lots of sex.

Population thinking and map-making like you’ve seen here obfuscates the reality of what is going on and makes it seem as if human groups are static when, in fact, they are not. We move around and do the sex. This means that what we see in terms of population genetics is always in flux and always has been. It’s yet another way of colonizing the genome of people but working under the assumption that indigenous groups somehow have experienced less genetic drift and gene flow than other groups.

To conclude, it’s always important to parse in our assumptions and take into account that our levels of analysis (the unit we are studying) may not represent reality. When we equivocate levels of analysis with levels of reality when examining human diversity, as Terrell says, we end up making a distinction between race and populations with no real difference. However, if we understand that the “population(s)” of interest are not reflections of reality, but merely constructed entities that represents an amalgamated web of kinship, political, biological, economic, and random histories at a particular time and place, we can avoid the trap of racial thinking (without using ‘race’) that some scholars fall in to.