Harv and Paul,
With regard to the difficulties, I think Harv has hit the nail on the head with this particular comment:
I like your gusto... I noticed in your comments to Richard that Dick has not introduced his own formal system (i.e., there are no axioms in his model). That introduces a dilemma. If Dick is not introducing an interpretation, and he is not introducing a formal system (having axioms), then what has he introduced? You might reply that he has merely introduced theorems, but I think this would be faulty reasoning since Dick has defined terms that relate to the physical world (e.g., observation, time, reality, etc). Those are physical interpretations!
The central problem is that you both have missed exactly what I have done for very subtle reasons. As I have said many times, what I have done is "solved a problem"; the thing is, it is a rather subtle problem. First, what I have done is not a theorem (in my opinion) because there is nothing in my work (apart from the abstract perspective) which has not already been done by others. What I have actually done (if you could follow what I say in detail carefully) is that they (the others who have thought up these ideas) have missed some subtle but very important consequences of their work. You guys also are missing those same consequences by not putting the whole picture together.
And Harv, you are correct, I am introducing an interpretation; but not the kind of interpretation you are used to dealing with. The interpretation I am introducing is outside any interpretation you have yet to contemplate. That interpretation is itself abstract in that it is an abstract representation of all possible interpretations. The central issue is that such an abstract interpretation can be conceived and, having been conceived, yields far reaching consequences.
***** An apparent Paul/Harv agreement:
(7) Any interpretation that makes the axioms true with regard to the entities of some domain of interpretation, will make the interpretation of the theorems true with regard to the entities of the same domain of interpretation.
I have put forth an abstract interpretation of common ideas which makes the axioms of mathematics true. This makes the theorems also true with regard to the entities so interpreted. What I have shown is that my (abstract) interpretations (isomorphisms) yield as an inevitable result that "most of physics" is true!
I was referring to the esoteric epistemological issue. Not the physical or abstract interpretation issue. Don't forget, as far as we know, formal systems only exist inside the heads of humans and these can only be shown to only be inventions. A lot is going on in the heads of humans besides the idealizations and abstractions that we are able to do.
That is exactly why you completely miss what I am doing. I am not concerned at all with how I come to know what I know. What I am concerned with is, what can I make of what I know.
No one in the scientific community is using defined terms that Dick is using. In fact, he has been highly criticized for using those defined terms (and have criticized some reputable scientists for the continued use of terms that do not correspond to his - e.g., time). Paul, these are physical interpretation.
Harv is correct here! And Harv, I do believe that my definitions are far superior to theirs for the very simple reason that my definitions impose no constraints whatsoever on the possible explanations of "reality" and at the same time make much of what has already been discovered "True". Not by induction, but by deduction (a consequence of our definitions). Definitions which, by the way, have imposed no constraint whatsoever on the facts to be explained! Now, the fact that such a thing can be done is (in my humble opinion) quite an astounding discovery. Those who cannot see it have not looked.
Go back to the "public notes" I have posted and tell me where I have imposed a constraint on what may be so explained! -- There is more to come!! Next step is the resolution of Yanniru's complaint in a form you all should be able to comprehend.
Have fun -- Dick
PS Paul, would the italics be sufficient to set off the references?