Crosson, you are still requesting a type of mathematical formalism you yourself cannot provide, so I'm afraid your position is still utterly contradictory and self-detonates on deployment. Yet, despite being aware of this fact, you continue to assert it. That is intellectually dishonest. However, then you go on to state that we should just assume that your position is consistent and ignore any contradictions. Since mathematics is just another language, it is just as irrational to demand difficult mathematical formalism as demanding that all claims be in Spanish or else just labeling it as mere "hand waving". It reminds me of the neocreationist William Dembski's bold claim that all critics that where not applying rigorous mathematical formalism could be ignored with a similar reference to "hand waving".
You then go on to assert that your position is not based on a dichotomy between mind and matter. However, that is materialism by definition, so don't see what you are trying to pull with your crankery here. Your entire argument seems to be based on an argument from incredulity, that is, no one has yet perfectly understood everything there is to know about the mind and brain, so therefore, that which we do not currently understand must be magic. We do not understand everything there is to know about the formation of snowflakes, Does this mean that the formation of snowflakes requires that clouds have supernatural powers? Before we continue this discussion,
describe to me exactly why arguments from incredulity are invalid. If you do not understand this simple fact I'm not sure that a rational discussion is possible, since your religious dogmatism is getting in the way of evidence-based reasoning.
You then arbitrarily claim that the set of thoughts a human can have is somehow "infinite" and that this disproves materialism, yet fail to provide any evidence at all for this outrageous and untestable claim. It seems entirely reasonable to think that the mind is limited in its function and capacity. The burden of proof here lies in your corner. Moreover you utterly fail specify what you mean by "infinite" and why and how such a concept can even make sense outside of mathematics. David Hilbert, perhaps the greatest mathematician of this century states, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea."[1] Naturally, you cannot define "infinite" as "not finite", since that only tells us what "infinite" isn't, but nothing about what "infinite" actually refers to. If I say that X isn't a banana, then that gives us no information at all about what we mean by X. The same reasoning applies to the concept of 'immaterial'.
I hold neither a dogmatic nor religious position, since my position is based on the clear findings of cognitive neuroscience. I need not present a shred of evidence since my position is self-evident. All the findings of science as well as our everyday experience has confirmed that we live in a completely material universe. However, in the null zone of religious dogmatism, everything goes, apparently. Thus, you have the burden of proof to demonstrate that something more, in this case something you have described as "magic", exists. If not, your position fall. Since you so vitriolically reject scientific materialism, you are immediately faced with a long list of serious problems.
(1) If thoughts are not material, what are they exactly? How can thoughts be magical? What do they consist of? What is the fundamental unit of this 'immaterial' substance and how do you know?
(2) How does the interaction between the immaterial mind and the material brain occur? How do you know? It is self-evident that the material world can influence our thoughts but how does this occur? How can material processes influence something that you claim is not a material process and vice versa?
(3) How does the interaction between two immaterial mind work? How do you know?
(4) Where did this 'immaterial' substance come from? How do you know? Claiming that it came from another 'immaterial' substance is not an answer.
(5) Exactly when in our evolutionary history did organisms start to acquire 'immaterial' minds? What selective advantage can an 'immaterial' mind have for an organism? How do you know?
(6) Do other organism besides H. sapiens have 'immaterial' minds? Do bacteria or trilobites have 'immaterial' minds? Dinosaurs? How about chimps? Do they have 'immaterial' minds? Did H. Habilis have 'immaterial' minds? How about A. afarensis? How do you know?
(7) Where do these 'immaterial' minds go after the material part of you decomposes? How do you know?
(8) How are these 'immaterial' minds attached to the brain? Why do they not float away when you move your head? How do you know?
etc.
The answer to the analogous questions for scientific materialism are clearly explicable and, I dare say it, has already been pretty much solved or just about. However, on the magical position, it is abundantly clear that
these questions are in principle unanswerable and unsolvable was well as requiring mountains of shaky and unjustified ad hoc postulates. Not only does there not exist exist a set of valid methodologies for gaining knowledge about these 'immaterial' minds, there also exist no epistemology to figure what would constitute knowledge.
(9) What methodologies are valid for gaining knowledge about these 'immaterial' minds? How do you know?
(10) What epistemology or what set of epistemologies are valid for separating knowledge from mere predjudical assertion when it comes to 'immaterial' minds? How can you separate truth from falsehood when it comes to statements about 'immaterial' minds? How do you know?
Your question only pushes the problem back into a world of make-belief where, epistemically speaking, everything goes.
(11) What specific arrangement of this 'immaterial' substance corresponds to a specific thought, such as imagining the color red? How do you know?
Tell me what evidence is there that a specific arrangement of particles in my brain corresponds to a specific thought, such as imagining the color red.
It would argue that thoughts and experiences are processes or sequences of specific arrangement of particles and their interactions, rather than just a specific arrangement of particles. This is further supported by the fact that both the physical and mental processes in the brain are spatiotemporally smeared (Libet 2002, Dennett 1991, 2003, Pinker 1999 etc). In this sense, experiences are emergent properties of physical processes in the brain, so they key here seems to be emergence, rather than greedy reductionism. The electromagnetic radiation hit the eye and is transformed by light sensitive cells into electrochemical processes, which is what we mean by experience of "red". Now, when we remember something, we always remember in images, words, sound, touch or taste. For example, experiments have been done where a neurosurgeon found a particular location in a patient's brain, that if stimulated, a song would start paying in the patient's mind. Every time that same location was stimulated, the same song would play (Sacks, 1998). This makes perfect sense on materialism, but is inconsistent with magic. Chimps routinely out-perform humans on memory tests[2]. How is this even possible if materialism is false? Do they have 'immaterial' minds or is a material brain all they have? Yet again, you must appeal to even more
shaky theological ad hoc postulates to rescue your worldview. The positive evidence from mapping cognitive features of the mind to the brain alone is overwhelming in its support for materialism. There are plenty of good popular books on the topic such as
"Descartes' Error: Emotion, Reason, and the Human Brain" by Antonio Damasio
"Synaptic Self: How Our Brains Become Who We Are" by Joseph LeDoux
"Phantoms in the Brain: Probing the Mysteries of the Human Mind" by V. S. Ramachandran
"Soul Made Flesh: The Discovery of the Brain--and How it Changed the World" by Carl Zimmer
"Evolutionary Cognitive Neuroscience" by Steven M. Platek (eds)
I could go into more specific arguments later when you are done with the content in this post.
[1] David Hilbert, "On the Infinite", in Philosophy of Mathematics, ed. with an Introduction by Paul Benacerraf and Hillary Putnam (Englewood Cliffs, N.J.: Prentice–Hall, 1964), pp. 139, 141
[2]