A Cybernetic Theory of Representation

When it comes to mental representation, I think the teleosemanticists are largely right, except that they are overfocused on biology and evolution rather than the more general underlying principles that I believe are in play.

Teleosemantics is a theory of representation that says that mental representations reference the external world via their purpose, not their cause — that is, a mental representation is the way it is not because the thing it represents caused it to be that way, but because that’s the best way for it to achieve the function it was evolved to do. Teleosemantics was formulated as an alternative to causal theories of representation, which hold that a causal chain of some sort connects things in the real world to their mental representations. Imagine you see a snake and you think “snake”: a causal theory asserts that “snake” (i.e., the representation of a snake in your mind) means snake because it’s caused by an actual snake. A teleosemantic theory, however, asserts that “snake” means snake because you have evolved to react to snakes, and a mental representation of a snake such as the one in your head when you think “snake” is useful as a part of the reaction mechanism.

The notable advantage of teleosemantics over a causal theory is that it explains how you can see a rubber snake and think “snake”, without “snake” having to mean rubber snakes as well as real snakes. After all, if the meaning of any mental representation is the thing that caused it, then pretty much any mental representation means just about anything, because humans are very good at mistaking things for other things. Teleosemantics doesn’t have this problem, because if meaning derives from purpose, and the purpose of a mental image of a snake is to avoid real snakes, then it’s still about real snakes even when prompted by the observation of a rubber snake.

But teleosemantics has its own problems. For one thing, it seems too narrow: how could such a theory account for all the things we can think about that don’t have an apparent purpose? For another thing, it seems too tied to biology and evolution: teleosemantics says that mental representations are determined by biological needs and evolutionary history, and are only indirectly connected to the things represented, whereas intuitively it seems that the connection must be much more direct.

I agree with the critics that there must be a deeper connection between mental representations and their referents, something mediated perhaps by biological mechanisms but not fundamentally defined by them. But I agree with the teleosemanticists that the connection is by way of function. My solution is essentially to recast the teleosemantic explanation in cybernetic terms and transport it to the level of basic physics and logic, thereby becoming fundamental and universal (to a physicalist anyway).

To see how this works, let’s revisit the snake example. What is in your head when you see a snake, and what connection does that thing in your head have with the actual snake?

The teleosemanticists say, for starters, that what happens in your head is an evolved capability. I fully agree. Without doubt we are what we are because of evolution, including our mental faculties. If you see a snake and move carefully away, it makes perfect sense to say you are exhibiting behavior that was favored by evolution, and that what happens in your head has something to do with that evolved capability. But the fact that capabilities are evolved doesn’t tell us what they are and how they work. Evolution can tell you why birds have wings, but to know how those wings work you need to know aerodynamics. Likewise, it’s certainly true that you are able to evade the snake because of the abilities afforded you by evolution. That’s why you can evade the snake. What I would like to consider is how you can evade the snake. How is this behavior implemented? This is not a question evolution can answer.

Avoiding snakes is a directed cybernetic process. A cybernetic process is one that operates on feedback: the state of the system at time t + 1 is a function of the state of the system at time t and the state of the world, as sensed by the system. A directed cybernetic process is one that functions towards a goal, defined as a particular state of the world at time t + 1. In our example, the goal is the state of not being imminently threatened by snakes.

But we are not talking about hard-wired snake avoidance, we are talking about seeing something, thinking it might be a snake, and deciding to avoid it — in other words, not just avoiding snakes, but consciously avoiding snakes. Consciously avoiding snakes is a self-directed cybernetic process.

This is not to say that self-directed cybernetic processes are always conscious — but they always involve something similar to mental states: information about the state of the world, for one thing, and goals, for another. They are functionally similar, to be precise, which does not require being phenomenologically similar.

We can describe a directed cybernetic process functionally. The physical embodiment of the cybernetic process is a cybernetic system, conventionally referred to as an agent. Let p be a particular state of the world. Let q be a particular action by the agent. Let r be the state of the world that results. So, we can say: if p is the case, and an agent does q, the result will be r. We can also express this as a logical proposition:

p & q ⇒ r

Let m stand for the above proposition:

m = (p & q ⇒ r)

A directed cybernetic system works toward a state of the world. Let the function Φ(r) mean “works toward r”, or, in other words, the agent has chosen r to be a goal. Let the funtion α(q) mean that doing q is an available choice to the agent, that is, q is actionable. Let ε(p) mean that the agent knows p to be the state of the world., or one might say, the agent knows p. Let ε(m) mean that the agent knows m, that is, knows that if p is the state of the world, then doing q will result in r. Then the behavior of a directed cybernetic system may be described as follows:

Φ(r) & ε(m) & ε(p) & α(q) ⇒ q

Or, restated in plain English: if r is a desirable goal, and an agent knows that doing q when the state of the world is p results in r, and the agent believes the state of the world to be p, and q is an option available to the agent, then the agent will do q.

To be sure, this is a simplification. For one thing, it’s just a snapshot; in reality, the state of the world, the available actions and even the goals change over time. For another thing, the state of the world is too complex to consider in its entirety; in practical terms, only a relatively small number of properties of the world can be considered at once. Finally, there are many goals and actions in play at any given moment, and they are not guaranteed to be consistent or compatible.

But such complications don’t negate the fundamental principles expressed in this simplified formulation. One such principle is that what the system needs to know is not the same as what the system’s goal is. Or, in terms of the formula, to achieve r, the system needs to know p and m. This explains the apparent disconnection between a functional explanation and the intuition that a representation is related to what it represents: in a cybernetic system, while the function of a representation does determine content, the content is not of the function, but of the state of the world that causes or enables the function. I call this a reverse-causal theory of content: the mental chain of causation, from function to representation, is the reverse of the physical chain of causation, from content of representation to function.

So the cybernetic model explains why the cause of our mental representations can be so different from their content. As stated so far, however, it doesn’t explain why there are mental representations in the first place. After all, it holds for thermostats as well as human minds, and themostats do not need mental representations.

Still, the cybernetic model is the starting point for such an explanation, once we examine the complexities and opportunities the human cybernetic system has evolved to handle.

The first complication is the fact that our knowledge of the world comes to us in bits and pieces over time. This means that ε(p) — our knowledge that the state of the world is p — will in general require memory and integration of sense data over time. A mental representation of some sort seems a natural model for storing the result of such a process.

A stronger rationale for mental representation comes from a consideration of the practical limitations of the cybernetic model as described so far. When we talk about the state of the world, of course we don’t mean every single detail, or even every single detail it is possible for us to know; there are simply too many. Luckily in practice most of the details we might consider will be irrelevant for most purposes. In the snake example, what counts is a fairly small subset of details: those that determine that a snake is within striking distance of us. Even so, the possible combinations of details this encompasses is astronomically large: think of all the ways a snake might look, all the sizes, shapes, colors and patterns in all the possible orientations and contexts. And this is just for a single snake: of course we want the same behavior to hold if we see two or more snakes, or, for that matter, if what we see is not a snake but another animal that poses a similar risk.

The only practical way that I can think of to handle such complexity is through some kind of generalization. Let’s define P as a set of world states that includes p, Q as a set of specific actions that includes q, and R as a set of world states that includes r. Let’s stipulate that the relation p & q ⇒ r holds for any p ∈ P, q ∈ Q and r ∈ R; we will call this proposition M.

We can now write a generalized version of the cybernetic formula:

Φ(R) & ε(M) & ε(p) & ε(p ∈ P) & ε(q ∈ Q) & α(q) ⇒ q

Or: if R is a desirable type of goal, and an agent knows that doing an action of type Q when the state of the world is of type P results in a R-type state, and the agent believes the state of the world to be p, and knows that p is a P-type state, and knows that q is a Q-type action, and knows that q is an option available to the agent, then the agent will do q.

This may be more complicated to describe, but is much easier to implement on a practical basis. Without generalization of this kind, an agent would have to essentially relearn a lesson for every minor variation of the relevant factors. But it does impose an additional requirement on agents: they must have an understanding of types. A type is by definition abstract: it encompasses many instances, including the possibility of instances that have not yet been encountered.

Whereas a system that deals only with concrete instances could conceivably work entirely with sense data rather than representations, this seems less feasible in the case of a system that also deals with abstractions. On the other hand, if a system uses mental representations to deal with concrete instances, handling abstract types may be a small step: all the system needs to do is to reuse representations. If “snake” is a representation, and this representation is applied whenever the sense data fit certain criteria, and a number of different concrete instances can evoke the suitable sense data, then “snake” is a type, and the system is capable of generalization.

I will look at one more factor that argues for the existence of mental representations. The value of a cybernetic principle expands enormously if it can be created proactively rather than in hindsight: i.e., if the agent can come up with new formulas based on existing formulas, existing knowledge and mental processes (logic, intuition, etc.). In fact, we do this all the time, by using our imagination. We imagine possible future states of the world; we imagine possible actions we might take; and we imagine the result that might occur from an action. What could imagined states and actions and results possibly be, other than mental representations?

Note that none of the foregoing requires biology or evolution; rather, biology and evolution take advantage of possibilities inherent in the way the world operates.

In short: the laws of physics predict the power of imagination.