Modeling the concept of genocide

This month I’ve talked a little about conceptual spaces, and a little about genocide, and a little about law and non-classical categories. Now I would like to tie the strings together by showing what use computer models might have in relation to those subjects.

This past week I have been graphing the concept of genocide for the sake of demonstrating the potential appeal of the conceptual spaces paradigm. The hope is to find some way of capturing the information that a person processes which underlie their judgments about how to categorize episodes of genocide, in the absence of classical category structures imposed by definitional fiat. From the jurist’s point of view, looking at concepts in this way is legally obtuse, and hence of at best indirect importance to a court — which, of course it is. On the other hand, if the conceptual spaces paradigm is a worthwhile attempt to describe psychological processing, it is of great importance to a people. And since virtually everybody in the history of the philosophy of law believes that law is only valid law when promulgated, and promulgation presupposes shared conceptual inventory… well, you get the idea.

In the previous post I took a look at Paul Boghossian’s (2011) critique of the concept of genocide. (I could have chosen any number of scholarly critiques of genocide to focus on — e.g., R. J. Rummel — but settled on Boghossian’s paper for the prosaic reason that his paper is available for free on academia.edu.) Boghossian offered a few cases which seemed to intuitively challenge the classical conception — the case of targeted warfare (Dresden), an imagined case of gendercide, and Stalin’s dekulakization. I take it that his remarks are not proposed in an effort to undermine the UN’s 1948 Convention on the Prevention and Punishment of the Crime of Genocide, but rather to perhaps complicate and enrich it by making its intrinsic motivations more defensible.

Fig.1. Venn. Classic boundary structure.

The classical concept of genocide looks something like the Venn Diagram we see to the right. Put succinctly, genocide is the use of atrocious means, against vital populations, with the intrinsic end of destroying at least some of that population (i.e., destruction of the group is an end-in-itself). These strict criteria tell us what the international court would have to say about Boghossian’s cases: that dekulakization and gendercide don’t count (economic classes and genders are not protected populations). Meanwhile, the facts about Dresden and Nagasaki are borderline cases, depending on the intentions of the Allies in charge of the war. But a reasonable person might wonder whether the underlying legislation is a result of political expediency and moral complicity as opposed to the strict and merciless requirements of justice.

To get a better sense of the psychological lay of the land, I decided to create a model of the conceptual space of genocide. The really wonky methods I used are discussed in the next section. For now, I’ll just discuss a few interesting implications from what I found.

Fig.2. Gephi, which is a networked concept. “Distances” are approximated by color groupings.

One potentially interesting result that I keep running into, at least for the latest iteration of the model, is that American slavery occupies a space relatively close to the Holocaust. (see right) This happens even though no direct analytical links force the two together, and despite the fact that this was not an effect I was expecting. Compare that to the classic categorization pictured in the Venn diagram (above), where slavery is treated as a definite non-case.

This might be worth noting, I think, because if the spatial analysis had any probative worth, then it might be an interesting part of a roundabout explanation of America’s long-standing hesitation to intervene in episodes of genocide worldwide, discussed by Samantha Power. You can tell a story where the American civil war places them on awkward footing with the idea of genocide, because they share the same conceptual space, though are not technically part of the same legal category.

Fig.3. VOSViewer. Genocide as a spatial concept.

But I should place emphasis on ‘if-then’. The use of the model is questionable, and depends on what you think of the methods behind the model. If you are interested in those, keep reading. Still, even if we think the model has little probative value, I would be satisfied to see more conversation in philosophy about the usefulness of conceptual spaces when thinking about how concepts and categories are received.

Notes on the concept of genocide

Remembrance Day has come and gone. I spent it in an Armory, listening to my parents’ choir, singing a rendition of Flander’s Fields and Handel and so on. All the hits, basically.

Samantha Power’s “A Problem from Hell” (2002) is a history of the concept of genocide. She argues that the American government’s default attitude to genocide is ambivalence.* Even if you disagree with her assessment of American foreign policy, it is also a lucid and useful volume just for the sake of understanding the imperfect legacy of the idea.

In international law, genocide is any act which involves (a) use of at least some atrocious means, (b) against protected groups as such, with (c) the intent to eliminate at least part of those groups. The atrocities in question include: killing, serious bodily or mental harm, deliberately undermining conditions of life (e.g., ghettoization), forced sterilization, and forcible transfer of children. The protected groups are “national, ethnical, racial, or religious”, and to target these groups ‘as such’ is to treat their destruction as a worthy end in itself and not just a means to a further end. Notably, this definition applies even when the aggressor is the ruler or sovereign over the targeted peoples, and it applies during wartime.

In this conceptual space the Holocaust of the Second World War is the prototype of genocide, since that episode involved all of the atrocious means (killing, torture, sterilization, etc.) and was perpetrated against the protected groups as such. During the course of Power’s recounting, we learn of other definite exemplars of genocide in the 20th century — the Armenian genocide by the Turks, the Khmer Rouge’s assault on urban centers in Cambodia, Iraq’s use of chemical weapons against the Kurds, the massacre of Muslims in Bosnia, the Tutsis in Rwanda, and so on.

Though Power does not discuss this, it is noteworthy that the Canadian residential schools program was genocide. During that decades-long institutional crime against humanity, persons of Indigenous descent were sterilized and their children were forcibly relocated, notably during the period known as the “Sixties Scoop“. It has been alleged that episodes related to this event occurred up to 2017. To be sure, it is not be a prototype in the region of conceptual space of “genocide”, but it is a definite case.

**

For some Canadians this may be too much to take in. Nobody wants to be complicit in genocide, so denial of the facts is one strategy. However, there might be some problems with our grasp of the concept itself, which are getting in the way of getting accepted. That is, there might be features of the definition that hard to deploy in cognition, because our usage fails to meet the virtues of a well-behaved categorization.

So, for instance. Some time ago, Paul Boghossian suggested that the concept of genocide was irremediably defective. His arguments are reasonable. But is he right to suggest that the concept of genocide is especially hard to parse?

I must confess that not all of his arguments struck me as decisive. (1) So, for instance, the law requires actions that are intended to eliminate at least part of a protected group, and this “in part” clause is vague to the point of ambiguity. Boghossian argues that this is a major defect. But: for one thing, as many philosophers of law will tell you, that is one of the ambiguities that is strategic to lawmaking, as it affords a legal culture the opportunity to deliberate on the moral, political, and common-sense features of a non-obvious question in the mereology of social ontology. (2) For another thing, he argues that genocide is meant to be a distinctive injustice as a matter of analytical fact. But we can reasonably question whether genocide is distinctively worse than cases of mass killings without being incoherent, which (for classical conceptual analysts) should be sufficient reason to dismiss the need to establish that genocide is a distinct moral wrong. I think it is enough to establish that it is a wrong somewhere at the top of the heap of moral wrongs.

That said, many of Boghossian’s points are worth consideration. He identified several cases that are ostensibly excluded, but which ought to be included:

• Stalin’s dekulakization was directed towards an economic class of ostensibly well-off peasants, the Kulaks, that resulted in millions of deaths by way of forced redistribution of essential goods necessary for life (a). This apparently does not count as genocide because “economic class” is not a protected group, (b). (For the sake of completeness, we might also include questions about whether or not it is targeting “as such”, as opposed to instrumentally targeting for the sake of collectivization.)
• He wonders whether or not the intention of exterminating part of a gender would count. (e.g., we might cite sex selection and infanticide in the developing world.)

He also considered some cases that ought to be excluded, but are mistakenly included:

• Egregious wartime episodes like the firebombing of Dresden or the bombing of Nagasaki, targeted nationalities as such, using atrocious means. But (Boghossian suggests) this is an awkward fit, since the episodes occurred during wartime. For him, these are not obvious cases of genocide, since it is at least plausible to say that they were targeted as a means to an end, the end being to end the war.

Ordinarily, this would be the place where I would argue for one or another categorization of the concept of genocide, such that these apparent exceptions are finessed into a rendering of a coherent whole, either decisively rejected as cases of genocide or decisively included.

But I will not do that. What I would prefer to do is examine the concept of genocide as a perspicuous region in conceptual space, following the methods in the previous post. Perhaps that will have to wait for a different installment.

**

*Her thesis has to be slightly complicated once you factor in G.W. Bush’s neo-conservative moralism when he argued in favor of the second invasion of Iraq in 2002 — but only slightly. History shows that that policy decision was driven by other factors — as I experience flashbacks to Condeleeza Rice’s “smoking gun mushroom cloud”, Colin Powell’s credibility-deflating testimony before the UN, and the bewilderment of the intelligence community reflected in the Downing Street Memo, and John Bolton’s ongoing impulse-control problems. Still, even if you grant that neo-conservatism certainly sold itself as a moralistic doctrine, it appears as a historical blip. And there is probably no surer evidence of this fact than Samantha Power herself was ousted from her position as representative to the UN during the crypto-isolationistic Trump administration.

Potted summary: “Reasoning About Categories in Conceptual Spaces”

What follows is a short summary of the main elements of a paper written by Peter Gardenfors (Lund) & Mary-Anne Williams (Newcastle) in their paper from 2001, “Reasoning About Categories in Conceptual Spaces”. It contains a way of thinking about concepts and categorization that seems quite lovely to me, as it captures something about the meat and heft of discussions of cognition, ontology, and lexical semantics by deploying a stock of spatial metaphors that is accessible to most of us. I confess that I cannot be sure I have understood the paper in its entirety (and if I have not, feel free to comment below). But I do think the strategy proposed in their paper deserves wider consideration in philosophy. So what follows is my attempt to capture the essential first four sections of the paper in Tractarian form.

1. An object is a function of the set of all its qualities. (For example, a song is composed of a set of notes.)
   1. Every quality occurs in some domain(s) of evaluation. (e.g., each tone has a pitch, frequency, etc.)
   2. A conceptual space is a set of evaluative domains or metrics. (So, the conceptual space around a particular song is the set of metrics used to gauge its qualities: pitch, frequency, etc.)
   3. Just like ordinary space, a conceptual space contains points and regions. Hence, an object is a point in conceptual space.
   4. We treat some objects as prototypes with respect to the part of conceptual space they are in (e.g., the prototype of a bird is a robin.)
      1. Those objects which have been previously encountered (e.g., in inductive fashion), and their location registered, are exemplars.
         
2. A concept is a region in conceptual space.
   1. Some of those regions are relatively amorphous, reflecting the fact that some concepts are not reliable and relevant in the judgments we make. (e.g., a Borgesian concept.)
   2. Categorization identifies regions of conceptual space with a structure. e.g., in our folk taxonomy, we have super-ordinate, basic, and sub-ordinate categories.
      • Super-ordinate categories are abstract (fewer immediate subcategories, high generality, e.g., ‘furniture’); basic categories are common-sense categories (lots of immediate subcategories, medium generality; e.g., ‘chairs’); and sub-ordinate categories are detail-oriented (few immediate subcategories, low generality; e.g., ‘Ikea-bought chaise-longue’).
   3. The boundaries of a category are chosen or “built”, depending on the structure that is identified with the concept in the context of the task. They can be classical (“discrete”) boundaries, or graded, or otherwise, depending on the demands of content, context, and choice.
   4. The structure of a conceptual space is determined by the similarity relations (“distances“) between points (or regions) in that space.
   5. One (but only one) useful way of measuring distance in a conceptual space is figuring out the distance between cases and prototypes, which are especially salient points in conceptual space.
      • Every prototype has a zone of influence. The size of that zone is determined by any number of different kinds of considerations.
3. There are at least three kinds of structure: connectedness, projectability (“star-shapedness”), and perspicuity (“convexity”).
   1. A conceptual region is connected so long as it is not the disjoint union of two non-empty closed sets. By inference, then, a conceptual region is disconnected so long as its constituents each contain a single cluster, the sets intersect, but the intersection is empty. For example, the conceptual region that covers “the considered opinions of Margaret Wente” is disconnected, since the intersection of those sets is empty.
   2. Projectability (they call it ‘star-shapedness’) means that, for a particular given case, and all points in a conceptual space, the distance between all points and the case do not exit the space.
      1. For example, consider the concept of “classic works of literature”, and let “For Whom the Bell Tolls” be a prototype; and reflect on the aesthetic qualities and metrics that would make it so. Now compare that concept and case to “Naked Lunch”, which is a classic work of literature which asks to be read in terms of exogenous criteria that have little bearing on what counts as a classic work of literature. There is no straight line you can draw in conceptual space between “For Whom the Bell Tolls” and “Naked Lunch” without wandering into alien, interzone territory. For the purposes of this illustration, “For Whom…” is not projectable.
   3. Perspicuity (or contiguity; they call it ‘convexity’) means all points of a conceptual space are projectable with each other.
      • By analogy, the geography of the United States is not perspicuous, because there is no location in the continental United States that is projectable (given that Puerto Rico, Hawaii, and Alaska all cross spaces that are not America).
      • According to the authors, the so-called “natural kinds” of the philosopher seem to correspond to perspicuous categories. Presumably, sub-ordinate folk categories are more likely to count as perspicuous than basic or super-ordinate ones.
4. One mechanism for categorization is tessellation.
   1. Tessellation occurs according to the following rule: every point in the conceptual space is associated with its nearest prototype.
   2. Abstract categorizations tessellate over whole regions, not just points in a region. (Presumably, this accounts for the structure of super-ordinate categorizations.)
      1. There are at least two different ways of measuring distances between whole regions: additively weighted distance and power distance. Consider, for example, the question: “What is the distance between Buffalo and Toronto?”, and consider, “What counts as ‘Toronto’?”
         1. For non-Ontarian readers: the city of Toronto is also considered a “megacity”, which contains a number of outlying cities. Downtown Toronto, or Old Toronto, is the prototype of what counts as ‘Toronto’.
         2. Roughly speaking, an additively weighted distance is the distance between a case and the outer bounds of the prototype’s zone of influence.
            • So, the additively weighted distance between Buffalo and Toronto is calculated between Buffalo and the furthest outer limit of the megacity of Toronto, e.g., Mississauga, Burlington, etc.
            • The authors hold that additively weighted distances are useful in modeling the growth of concepts, given an analogy to the ways that these calculations are made in biology with respect to the growth of cells.
            • In a manner of speaking, you might think of this as the “technically correct” (albeit, expansive) distance to Toronto.
         3. Power distance measures the distance between a case and the nearest prototype, weighted by the prototype’s relative zone of influence.
            • So, the power distance between Buffalo and Toronto is a function of the distance between between Buffalo, the old city of Toronto, and the outermost limit of the megacity of Toronto. Presumably, in this context, it would mean that one could not say they are ‘in Toronto’ until they reached somewhere around Oakville.
            • This is especially useful when the very idea of what counts as ‘Toronto’ is indeterminate, since it involves weighting multiple factors and points and triangulating the differences between them. Presumably, the power distance is especially useful in constructing basic level categories in our folk taxonomy.
            • In a manner of speaking, you might think of this as the “substantially correct” distance to Toronto.
         4. So, to return to our example: the additively weighted distance from Buffalo to Toronto is relatively shorter than when we look at the power distance, depending on our categorization of the concept of ‘Toronto’.
   3. For those of you who don’t want to go to Toronto, similar reasoning applies when dealing with concepts and categorization.