End Notes from earlier portions of the Franklin chapter, on free will

1. Well, almost neither. Since writing the first draft of this chapter, I've
published an article in a philosophy of computing journal (Franklin and Garzon 1992).

2. A kind reviewer suggested I clarify the "essentially" that begins this sentence. I
have written several papers on artificial neural networks (in collaboration with Max
Garzon, John Caulfield, and others), one on genetic algorithms (with David Kilman and
others), and a couple in cognitive science (with Art Graesser, Bill Baggett, and
others). A sampling can be found under these names in the references. All this is in
order that you not take me for "a computer hack . . . spending his spare time writing
speculative pop science/philosophy." Still, I stand by my claim to amateur status.

3. The following account is taken largely from Armstrong (1987).

4. The first verse of the Tao Te Ching, the Taoist bible, warns us that the Tao that
can be spoken of cannot be the true Tao.

5. In the following description my mathematician self, who's gotten little exercise
so far on the tour, slips out to provide a mathematical definition of a continuous
dynamical system. This note is intended to explain some of the notation. [0,] denotes
the set of all nonnegative real numbers, t [0,] says that t belongs to that set. X
[0,] denotes the set of ordered pairs (x, t) with x in X and t [0,]. 36

The mapping T assigns to each such ordered pair some state in X. A vector space, in
this context, can be thought of as all vectors, that is, ordered lists, of real
numbers of some fixed length d, where d is the dimension of the space. Differential
equations can be thought of as equations involving rates of change whose solutions
are mappings.

6. My friend Art Graesser points out that cognitive scientists tend to
view the mind as an "abstract information system." While this certainly seems a valid
approach, the dynamical systems view might well prove more suitable for our endeavor
of searching out mechanisms of mind. The dynamical systems view can hope to take us
back to neural mechanisms for human minds, while the abstract information system view
must stop at least somewhat short.

7. I'm indebted to Phil Franklin for pointing this out.

8. Due originally to Frank Jackson (1982).

9. This seems to be the conclusion drawn from the thought experiment by many
philosophers of mind. An exception is Dennett (1991, pp. 398ff).

10. Science does study classes of subjective states. If a number of people were to
experience a particular stimulus, you'd get a class of subjective states, which may
have properties that you can study scientifically. Cognitive psychologists do just
that. They build theories that try to predict the properties of such classes of
subjective states resulting from the perception of a given stimulus.

11. Nick Herbert and Brian Rotman have kindly pointed out that this
description of information dates back to Gregory Bateson. Chalmers also.

12. Computer scientists speak of a Boolean variable, or just Boolean, as one that
assumes only two values, usually 0 and 1. A scalar variable, or scalar, assumes one
of some finite set of values.