Saturday, July 15, 2006

Computation, Representation, and Teleology

Curtis Brown, "Computation, Representation, and Teleology," presented at E-CAP 2006, June 2006.

I just found the online (long) abstract of Brown's talk. Brown defends two necessary conditions for computation: it must operate on representations (semantic condition) and it must have the function to calculate (teleological condition).

I agree with Brown that there is a teleological condition on computation, at least in the sense of the term that is useful to computer science and cognitive science, and I have argued for this in some of my papers. I'd be curious to know more about what Brown means by "having the function to calculate". Since "calculate" is usually taken to be a synonym of "compute", Brown's teleological condition sounds circular. Unfortunately, the abstract doesn't say what Brown means by "calculate".

As to the semantic condition, I have argued at length that there is no such condition--on the contrary, in my view, computation does not require representation. One way to see this is by defining computations in terms of strings of letters instead of what the letters represent (such as, e.g., numbers). Defininig computations in terms of strings may be impractical when one is doing applications, but it is theoretically insighful.

Brown responds to my view by saying that even when computation is defined in terms of strings, the inputs and outputs of the computation are still representations. The only difference is that they represent strings instead of numbers or something else. This is an original reply, but I suspect it misses my point.

Strings can be seen as concrete entities (strings of concrete physical letters, inputs and outputs of concrete computations) or as abstract mathematical entities (strings of abstract letters, inputs and outputs of abstract computations). Either way, strings may or may not be semantically interpreted, and if they are, they can represent many things (including themselves, of course).

Here is an argument that would support Brown's conclusion. Consider a concrete computation defined in terms of strings. At the very least, it represents itself, or some abstract counterpart to itself. Strings must be represented no less than numbers or anything else does.

Yes, but the point of having a mathematical theory of strings is precisely to study certain properties of the strings without any concern for what (if anything) the strings represent. And one can do the whole mathematical theory of computation purely in terms of strings rather than in terms of what the strings represent.

So, of course, when you do the theory of strings, you need to represent the strings. But when you define computations in terms of strings, you can happily ignore what the strings represent, or even whether they represent anything at all. For all you care, they can be meaningless.

But, one might reply, once you have your computations defined over strings, don't they at least represent themselves (or some abstract version of themselves)? Sure, but everything represents itself (and many other things besides, depending on how it is interpreted). This notion of representation is not going to do the job that traditional supporters of a semantic condition on computation want such a condition to do (i.e., contribute to an account of mental representation).

Caveat: I haven't listened to Brown's presentation and I haven't read his paper. All I saw was the abstract linked to above.


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