The author writes:
"...the question ' How can mindless mathematical laws give rise to aims and intention?' contains two markers of possible illegitimacy. The word 'mindless' is stated but not proven, and the phrase 'give rise' posits a stated but as yet unproven time sequence. There would be, for example, no a priori grounds to dismiss the remote possibility that, like humans and apes, both mathematical laws and mindful aims and intentions spring from an ultimately common source, rather than one from the other."
I took this question a different way. The principle of least action, for example, has no variables for representing intention, decision, information, possibilities, information channel, etc. Yet Richard Feynman has described a particle as "smelling" the possibilities in such a calculation, when the mathematics is "mindless" on this account. There is no "smelling" in the mathematical statements. But the idea is strongly intuitive for Feynman and he uses it.
Are there any categories of mathematics in which we could find such things as "goals," intentions," etc.?
Yes. Game Theory for example.
And-- there is another category where "information channel" is the central mathematical object. This is covered in Jon Barwise and Jerry Seligman's book "Information Flow: The Logic of Distributed Systems."
Relativity is a good example.
Water and air afford information channels for messages carried by sound. Applying this to space, the idea before Einstein was that the "aether" afforded a similar information channel, in the same way that water and air afford information channels.
But this does not work.
So the choice is either (a) give up on the idea that an information channel carries the message and signal from Einstein's clocks.
Or, (b) hold onto the principle of the information channel; but in relativity (and perhaps regarding intentions), look for an information channel to exist as something different from space.
That complex numbers can be used to model "possibility" allows me to take a next step (cf. An Overall Approach.)
An information channel comprises a system of parts, one part carrying information about another part. But in relativity, we cannot say that space is such a system. We have to expand the search.
Well, the wave function is a complex number. So say, for the moment, that there is a wave function for the Universe and that it is the system of possibilities we are looking for.
Then insofar as the wave function of a particle is part of the wave function of the Universe, the possibilities for, say, particle A can convey information about, say, the possibilities for particle B, by virtue of the system of possibilities (the wave function of the Universe) which now constitutes an information channel carrying information about possibilities from one particle to another.
Or, if you prefer something other than "wave function of the Universe," Bohm and Hiley's Holomovement also works as an information channel for broadcasting possibilities. (ibid. The Holomovement is a stream.)