What kind of machines are men? During the past three decades, cognitive scientists and philosophers of mind have usually worked on the assumption that we are discrete automata, i.e., entities which have a countable (usually finite) number of possible internal states. Thus, men have variously been described as:G.J.C. Lokhorst. Analog automata and the foundations of cognitive science. In

Abstracts of the 9th International Congress of Logic, Methodology and Philosophy of Science, Vol. 3, p. 99. Uppsala University, Uppsala, August 1991.

- Turing machines, i.e., finite automata interacting with an unbounded discrete environment. This view is to be found in "Turing machine functionalism" (Putnam 1960) and in most of mathematical linguistics. (If natural languages are context-sensitive and we do master them, we are at least linear bounded automata.)
- Probabilistic finite automata (Putnam 1967).
- Indeterministic (or, equivalently, deterministic) finite automata (McCulloch & Pitts 1943, Kolmogorov 1956). Nelson 1989 has founded his whole philosophy of mind on this basis.
- Finite cycle-free transducers (Minsky 1967). Because we are mortal, such automata are sufficient to account for the whole of a man's behaviour during his or her lifetime, provided this behaviour is discrete. Since we have mentioned the four types of automata in order of strictly decreasing strength, this is the most conservative assumption one can make.

The supposition that we are discrete automata has recently come under attack from various circles:

- Contemporary "connectionist" models of cognitive and brain functioning are usually analog, rather than discrete.
- Physicists are becoming increasingly fascinated by highly non-linear, analog dynamical systems; they suggest that we are such systems ourselves.

Thus, it is becoming more and more plausible that we are analog automata (having a continuum of possible internal states) rather than discrete ones.

In this lecture, I will explore the implications the analog revolution may have for our basic views concerning human cognitive functioning. I will suggest that it may have less dramatic consequences than it might appear. On the one hand, there are some powerful theorems about the possibility of simulating analog automata by discrete ones. These suggest that both types of automata are approximately equivalent after all. (Vergis et al. 1986, Rubel 1989). On the other hand, the philosophical theories which have been stated in terms of discrete automata do not seem to depend crucially on the notion of discrete states. For example, Turing machine functionalism may easily be reformulated as analog automaton functionalism or analog neural network functionalism.

My conclusions are necessarily tentative. The theory of analog automata is still in an extremely underdeveloped state (less than half a dozen fundamental articles have appeared since they were invented by Lord Kelvin), and nobody can tell which surprises the future has in store.

30 Jan 1991

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