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.
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Here’s a walkthrough of what I did to make the first version of the model (alpha 0.1, represented in Fig.3).
Before I do, I would like to offer a note on the nature of models. Modeling is in many respects more an art than a science, but (like philosophy) it is the kind of art that is supposed to help science instead of hurt it. To do it right, you need a non-trivial amount of work and training. Because I am a dilettente with the computer, I enlisted the help of my friend/collaborator Sasha Graham, who has a keen knowledge of computer modelling in the social sciences. I am much indebted to him for his kind help.
Initially, I used Gephi as a device to model the conceptual space, though on Sasha’s advice exported the data over to VOSViewer. Here’s why. Gephi is a wonderful tool for making graphs, and VOSViewer is a handy tool for doing corpus analytics. But while Gephi is useful for inputting data, it does not do spatialization effectively; and while VOSViewer is arguably more useful for visualizing spatial relations, it is meant to be used to co-locate word associations, which is not the point of this task. But if you put them together you will have hacked a way to model conceptual spaces.
The graphing is based on similarity relations, which are represented as edges (or lines between nodes). Each edge has a weight: stronger positive weights have a kind of ‘gravitational’ force, pulling on the edges (lines), like on a line of string. In theory, negative weights would “loosen” each string, which would have been nice, but it’s not clear this is functioning effectively in Gephi, so negative weights were omitted.
In this model, I placed three different kinds of nodes, using Gardenfors’s articulation of conceptual spaces: “Regions” (e.g., Fig.2., “atrocious means”, “intrinsically destructive ends”, and “vita populi”); qualities (e.g., “killing”, “intent to destroy”, and “race”); and cases/objects (“Holocaust”, “(Canadian) Residential schools program”, “Anomic terrorism”, “Cold civil war”, “Anomic racial hate speech”).
Edges are weighted on a scale of 1-10. For the most-part, edges are weighted depending on kinds of nodes related. So, q-R and R-R edges are always weighted 10 because they’re strong constitutive criteria, or “hard constraints”; e.g., “mass slaughter” is tightly related to “atrocious means”. Meanwhile, q-c edges are weighted 8 (being exemplars), and c-c edges are related 4 (being analogies between cases). No R-c edges are present, because we are trying to avoid uninformative analytical depictions of the concept. Those make up the bulk of the scoring, but there is one exception to the rule: I represented one q-c edge as a borderline case with weight of 1 — Dresden and “intrinsic targeting”.
The idea behind strong constraints (10) is to approximate the idea that these are constitutive criteria for kinds without forcing the issue, and borderline (1) is close to zero. The soft constraints in between were judgment calls but seem to make sense: an exemplar is better than an analogy, but neither are as strong as constitutive criteria.
The visualization was then run through the following layout parameters (Fig.2): Force Atlas2, scaling 2000, gravity 5, no overlap, in lin-log mode. The result is what we might call a “network concept”: it is not a projection into conceptual space, because too much information gets lost in an attempt to depict this many dimensions on a 2D graph. Coloring is community detection, and was done by grouping according to modularity class. The coloring, not edge distances, is what is worth paying attention to in (Fig.2). That information was then exported to VOSViewer (Fig.3), which can be read more intuitively, where space means distance.
Again, this is all worth taking with a grain of salt. It is a model — just one attempt to capture the flavor of what conceptual space might be like. It has many limitations, of course: e.g., a sparse population of nodes. I tried to choose one case per overlap in the Venn diagram, but imagination failed me. I am sure we can do better. If you’re interested in giving it a shot, click here to download the gephi file and try it yourself.
Benjamin L. S. Nelson 