Jochen,
This is a very interesting essay. I'm especially enamored with your hard problems; however, I'm a stalwart fan of dual explanandum strategies for explaining mental causation, in particular the Structural Causation of Fred Dretske [FD]. I'm also a stalwart fan of mathematician and AI researcher Ben Goertzel's [BG] dual-network model of mind in which an ever evolving semantics obtains at the interface between the perceptual-motor hierarchy and the structurally associative memory.
I'm posting to this thread because it raises some interesting issues. You respond to Phil, "As for the philosophy of mathematics, the problem with Platonism is the problem I have with all kinds of dualism: the lack of a causal nexus to connect the two substances." I would point out that, in this case and many others, the causal nexus could very well be pattern, an abstract entity which is capable of INFORMING both the mental and the physical. The number three exists as a pattern in nature (3 indivisible objects) but also as an abstraction in mind (1+2, 5 - 2, √9, 18/6, the 2nd prime, the 4th Fibonacci, etc.). When you see a number three on a computer screen your eyeball generates a pattern in the perceptual-motor hierarchy and that pattern is REcognized in the structurally associative memory. Since the context depends on the relation between the pattern presented by perception and the pattern stored in memory, the semantics emerges at the interface between the perceptual-motor hierarchy and the structurally associative memory. In my humble opinion, the mental agent is necessary for making the relation,for example, in the distinction between the 2nd prime and the 4th Fibonacci. And of course mind can create patterns which are not acknowledged as existing in nature, primarily, it would seem, through analogy. Analogy is a mapping from memory to memory which, when cognitively successful, emerges in mental agency as introspective perception. How exactly this occurs is not well understood but without mental agency it would seem an incomplete and an underdetermined syntactical operation. Most scientists and mathematicians refer to such an experience as intuition; I refer to such as messages from the Muse.
As an argument for mental causation consider learning a new motor skill. I've been practicing yoga for a few years so I like to use the example of yoga churning in which one undulates ones stomach muscles from side to side; this is very counter-intuitive and, as such, it's obvious that the pattern doesn't exist in the perceptual-motor hierarchy. How does it find its way there? I read an abstract representation of that pattern in a book. That abstract representation becomes an abstract pattern in my structurally associative memory but the pattern is an abstraction, a condensation, of the full representation and this, I believe, is where mental agency enters the picture. It enters once again when I then imagine manifesting that pattern in the perceptual-motor hierarchy. Imagination is perhaps both a conscious and unconscious activity but certainly conscious, after all, I tend to imagine the full representation of the yoga churning not the condensed abstraction stored in memory. After a bit of trial and error it all of a sudden like falls into place and the pattern manifests in the physical; the causal nexus is the pattern! I would suggest the same holds true when practicing mathematics or science. Like the number three above, there are many different yet equivalent ways to generate certain concepts such as Maxwell's electromagnetic equations; these are all associated with the same patterns in memory and it would seem to be the mental agent which distinguishes between them.
(As an interesting and somewhat mysterious aside, in [DH pg. 7] neuroscientists have demonstrated intentional brain-body uncoupling in monkeys. I quote:
"In a closed-loop NIS paradigm, it remains a mystery as to how a population of recorded neurons can be co-opted to control an artificial device without moving the limb, which was, under normal circumstances, moved by the activation of the same population. Several studies have documented the fact that monkeys that are exposed to an NIS paradigm will eventually stop moving or minimally move their own limbs when guiding the artificial device through cortical control."
To me, this would seem to be the result of the mental agent re-informing the physical by the implementation of a new pattern although, as the authors state, this remains untested.)
And this is how one gets "semantics from syntax." Certainly the perceptual-motor hierarchy, presumably the structurally associative memory, and also, it would seem, nature, works purely on a syntactical foundation; semantics is in the REcognition of pattern. And you say that the syntax constrains the semantics but the opposite holds as well. Think of the software in a computer. The pattern in the software is the semantics; it distinguishes between Microsoft Word and Adobe Photoshop. The pattern is an abstract entity with "no mass, no energy, no location in space and time" but it manifests in the syntax and the syntax is representable in the physical circuits of the computer. It's the non-physical pattern, the semantics, which defines initial conditions and boundary conditions thus constraining those physical circuits to the will of the abstract pattern. The meaning resides in the pattern and the pattern constrains the syntax; the non-physical deploys the force of constraint!
In Mr. Goertzel's mathematical model of mind abstract patterns emerge and are maintained in the structurally associative memory as, interestingly enough, dual-networks. For example, a person's mathematical knowledge is organized in the memory both hierarchically and associatively. The master pattern in the memory he calls the "reality belief system"; it's what we use to navigate the world. These patterns are maintained and adapted in the mind by a system of functions mapping Pattern Space to itself. He refers to it as a system of magicians and anti-magicians, Fannie (f(x)), Hattie (h(y)), Geronimo (g(z)), etc. These magicians and anti-magicians run around casting spells on one another, in the process generating structural conspiracies - patterns conspiring to maintain themselves. When the conspiracy becomes threatened by something exceeding the limits of its adaptive capabilities, cognitive dissonance obtains.
Mr. Goertzel's mathematical model is a complex systems model utilizing attraction (the dual-network), autopoiesis (magicians and anti-magicians), and adaptation (evolution in real time). It's a complex and well fleshed out model encompassing four rather lengthy books: The Structure of Intelligence; The Evolving Mind; Chaotic Logic; From Complexity to Creativity. From Complexity to Creativity is "a book for thought and nothing besides" which culminates with some rather interesting conjectures. The dual-network is an attractor for his "cognitive equation" and he demonstrates how this dual-network/cognitive equation entity could very well apply to the Universe - the Universe as Mind! So from Mr. Goertzel's perspective your "web of relations" becomes an evolving ecology of pattern - pure maths.
And this reflects on the it from bit or bit from it question. Just like the abstract pattern (software) in a computer, it's not the circuits that define the pattern it's the pattern which define the circuits. This is the causal efficacy of the non-physical. It's popular amongst scientists to use Tierra and the Game of Life to demonstrate how true complexity can evolve from a set of simple rules but all of these simulations start with an ancestral pattern. So the question immediately obtains: where did the ancestral pattern underlying our existence come from?
References
[FD] Dretske, F., Explaining Behavior: Reasons in a World of Causes, MIT Press, Cambridge, MA, 1988; Mental Events as Structuring Causes of Behavior, in Mental Causation, Heil, J., and Mele, A., (ed.), Clarendon Press, Oxford, 1993.
[BG] Goertzel, B., The Structure of Intelligence, Springer-Verlag, New York, NY, 1993; The Evolving Mind, Gordan and Breach Science Publ., New York, NY, 1993; Chaotic Logic, Springer, New York, NY, 2010; From Complexity to Creativity, Springer, New York, NY, 1997.
[DH] Donoghue, J. P., and Hatsopoulos, N. G., The Science of Neural Interface Systems, National Institute of Health, Annual Reviews in Neuroscience, 2009, available at ( http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2921719/) accessed 03 May, 2013.
With regards,
Wes Hansen