Communal Norms of Representation are Conceptual

The thrust of the previous post is that there are two main levels of analysis when discussing representation in science: relevance and accuracy, or what a representation is about and what it says.

Let us focus first on conditions of relevance. Consider any model M, and any object O. The question I want to ask is: in what sense might we say that it is possible that M represents O, or that it must be so (independently of whether it represents it well)?

We should first dispell an ambiguity in this question. Are we talking in general, or in a particular context? I have argued in my past research (Ruyant 2021) that there is an important difference between two senses of “represent”: either it refers to norms at play in the epistemic community (such as: the Lotka-Volterra model represents a prey-predator system), or it refers to a specific use in context (the model of the pendulum that I’m using represents the oscillation of my clock). However, the first sense is generally more prominent. In the contextual case, we are more likely to say “being used to represent”, or “represents for its user” than “represent” simpliciter.

In the generic, normative sense, models usually represent kinds of objects, or generic. In the example above, “a prey-predator system” does not refer to one system in particular, but to a type of system, as when we say “a triangle has three sides”: we are not referring to one specific triangle, but talking about triangles in general. The same goes when we say that a model represents the hydrogen atom, or oscillators. These are generic locutions, as in “the dodo is extinct” or “Tigers are predators”.

There are exceptions to this: when a model represents one particular object, for example, the solar system or the Sun. However, these are rare in science, and even the model of the Sun is often thought to inform us about many similar stars. So, I will neglect these cases and consider that scientific models represent kinds.

Now, let us reformulate our initial question. It becomes: consider any model M, and any kind object K. The question I want to ask is: in what sense might we say that it is possible that M represents Ks (or the K or a K), or that it must be so? And I would say that the sense of possible or must in which we might say that is conceptual. It is a matter of applying norms to our representations, of understanding these norms, and both the source and target of necessity are internal to our representations.

Consider potential objections:

• Aren’t there external sources of necessity? After all, we can refer to a kind without having a full description of its nature. Must it not be the case that M correspond to characteristics of Ks that are only known a posteriori in order to represent it? I don’t think so. If misrepresentation is possible, then there need not be such constraints. Whether M is accurate depends on the characteristics of Ks, of course, but this is a matter of accuracy, not relevance.

• Can’t the model be normative in some cases? Can’t the aim be to tell how we want Ks to be, not how they are? Perhaps, but again, this is not captured at the level of relevance. A model in electronics that represents how transistors must be, for example, does this by means of its content, which reflects the aims of modellers, but the fact that it represents transistors to start with is independent from what these aims are exactly. It is a conceptual matter.

Note that I don’t consider that a model of K can also represent a sub-kind or a super-kind of K. I understand “represent” in a very specific way. Otherwise, we could claim that a question such as “does a model of a whale represent a fish?” or “can a model of a mammal represent a whale?” is an empirical matter (because it depends on the fact that whales are mammals or fish). But it seems to me that these questions trade on an ambiguity between the two senses of representation mentioned above (the communal norm / contextual use distinction). In this respect, the locution “The K” is more appropriate, if sometimes not very natural: it is clear that a model of the whale does not represent “the” mammal, and conversely.

My conclusion is that whether a model represents a kind (communal norms of relevance) is a purely conceptual matter. If there are apparent exceptions to this, this is to the extent that we focus on particular uses on concrete objects instead of communal norms that concern kinds. There can be epistemic uncertainty about whether a model should be used to represent a particular object, or our aims can matter when selecting this or that object as a target of representation when using a model, but we are no more considering the level of kinds here.

Having said that, the use-level is also interesting, so we will consider it in the next article.