Lev,
I've looked at (and around) page 29 as you suggested. At first glance it appears not entirely unrelated to my "Automatic Theory of Physics" based on automata theory as the most promising means to understand both "the unreasonable effectiveness of mathematics in the sciences" and as the model of how physics theories are generated from observations. I'm sure there are significant differences in our approaches, but I do not at the moment have time to study your 98 dense pages.
You reference "the lack of any fundamental mathematical models whose roots are not directly related to numeric models," and appear to lament that, "during mankind's scientific history, we have dealt only with numeric models and, during the last century, with their derivatives."
If I understand you so far, your goal is to replace the role of numbers in scientific theory with a non-numerical approach. I do not see the need, nor the likelihood of success, for such an undertaking, but I wish you well in your endeavor.
In reply to your remarks above, I am not sure that it makes sense to state that a representation exists in which "syntax and semantics are the same". Meaning seems to be inherently related to contextual framing, and I'm unclear as to how one can combine the object and its context in one representation.
Do we see reality, or is our view unreal? Matthew Crawford, in "Shop Class as Soulcraft" has elegantly pointed out that it's possible to view exactly the same scene with two different interpretations; this doesn't refer to well-known optical illusions, but to the meaning of what we see. For example, while cleaning parts, "Previously... I had held one of those valves in my hand and examined it naively, but had not noticed the mushrooming. Now I saw it. Countless times since that day, a more experienced mechanic has pointed out to me something that was right in front of my face, but which I lacked the knowledge to see. ...the raw sensual data reaching my eye before and after are the same, but without the pertinent framework of meaning, the features in question are invisible."
This bears repeating: "the raw sensual data reaching my eye before and after are the same, but without the pertinent framework of meaning, the features in question are invisible."
In other words, the truth is the same for everybody, but it is not seen by everybody.
The meaning does not come from the visual data or information, which is the same before and after. It comes from the framework of meaning... the knowledge of the system, of which the piece being viewed is a part. The same truth or visual data is seen each time, but the meaning of what is seen changes, depending upon the framework in which it is understood. Meaning seems to derive from the real physical world. In his example, the meaning of the 'mushrooming' seen on the valve depended upon the design, construction, and operation of the physical motorcycle. Awareness of the visual data without the understanding of the system of which it is a part imparted no meaning.
In physics this may apply to something like 'fine tuning'. In one framework, this is understood in one sense. In another framework, one postulates a mega-verse.
That you believe that there is only one such formalism is sufficient explanation for me. It has also become clear to me over the last year or so on fqxi that almost all of us have developed our ideas and understanding over many years, and no one is really convincing anyone else to change their ideas. But we do seem to serve a worthwhile purpose in getting each other to clarify our ideas.
Thanks for your comments.
Edwin Eugene Klingman