I just read an interesting paper by Eric Dietrich and Arthur B. Markman entitled “Discrete Thoughts: Why Cognition Must Use Discrete Representations.” In the paper, they first give a definition of general mental representations and make a distinction between discrete and continuous representations. Then they outline seven arguments for why they think discrete representations are necessary for any system that discriminates between two or more states.
Their definition of general mental representation is I think robust and conceptually useful. They define a representation to be any internal state that mediates or plays a mediating role between a system’s inputs and outputs in virtue of that state’s semantic content. They define semantic content in terms of information that is causally efficacious and in terms of what that information is used for. What this means is that representations have to be a part of mental causation. This approach reminds me a lot of Hofstadter’s work, which I have talked about here. Hofstadter emphasizes how mental representations, which mediate between the environmental stimulus and the behavioral output by virtue of being causal at the appropriate level of analysis. I take Dietrich and Markman to mean the same thing when they say that mental representations must be “psychologically real”. In Hofstadter’s terminology, the symbols must be active.
Next, the authors offers a definition of discrete representation. “A system has discrete representations if and only if it can discriminate its inputs.” If a system categorizes, then it has discrete representations. In contrast, a continuous representation would be more tightly bound to its correspondence with the environment. It would be coupled in such a way that it wouldn’t have the ability to make distinctions between its inputs. This is illustrated by the examples of a watt governor and a thermostat. In a watt governor, the arm angles of continuous representations of the speed of the fly wheel, and in contrast, a thermometer must make an on/off discrimination of the continuous representation of the varying bimetal strip. The discrete representation supervenes on the continuous representation.
Finally, the authors give seven arguments why cognition requires discrete representations. I won’t go over the arguments in detail, I will just list a brief summary taken from the text.
1. Cognitive systems must discriminate among states in the represented world.
2. Cognitive systems are able to access specific properties of representations.
3. Cognitive systems must be able to combine representations.
4. Cognitive systems must have some compositional structure.
5. There are strong functional role connections among concepts in cognitive systems.
6. Cognitive systems contain abstractions.
7. Cognitive systems require non-nomic representations.
In their conclusion the authors discuss the claim that it follows from the presence of discrete representations in the cognitive system that the best paradigm for cognitive science must be computationalism. They argue that any system that utilizes discrete representations must be finite and has deterministic transitions between states which can be constructed into an algorithm. Thus, the mind can be described as a computationalism system. I think this is a clever argument and places computationalism into its proper role as the dominant paradigm in cognitive science. Until conflicting evidence shows that when it comes to general mental phenomena there is a better methodological framework, we shouldn’t deny computationalism’s place as the best explanatory paradigm.