***There may be a double circularity: "induction" is itself a concept that requires "time"!... Deduction requires time too;***
One doesn't know what time is until after coming to conclusions about time, therefore if we are living for the first time at 6AM we must use inductive reasoning prior to coming to understand that time is passing. In Dick's case, he isn't defining time as a passage of experience but as having an exact mathematical definition (something that is not possible as a passage of time as if one were doing induction). So, I don't see the circularity as you do in this instance. The circularity I see is that to accept (1) requires reasons to accept (1) [I'm referencing my other post that break down Dick's step by step approach to formulating a solution to the problem as I recall in his paper]. Those reasons for  are choices dependent on inductive reasoning and blind sense impressions. That seems circular to me.
***Pattern matching (which perhaps Dr. Dick calls "definition") is automatically outside time or space. This is why there may be a very close parallel to something I did and what he did: by focusing on "definition" itself; on "pattern matching"; you actually remove the issue of induction as induction is a time-based issue.***
Maybe what I said above is what you are saying here? In any case, induction is required to come to the point of definitions and considering pattern matching which places induction as primary. Dick should construct his paper without any use of induction and sense impressions, but then he could not say anything meaningful about the world.
My complaint here doesn't completely dismiss results, but it weakens them considerably. I always have a stomach pain when meta-problems of any time are discussed (e.g., the Liar proposition, Russell's paradox, Hume's problem of induction, etc). If the last century has taught us anything it is that self-referencing systems often lead to semantic paradoxes and that these paradoxes are often unsolvable. It may be a fault in logic/math, induction, etc, or it may be that we cannot apply the techniques of reasoning without regard in issues of meta-problems. Dick is addressing a meta-problem which has all the ingredients of a self-referencing paradox.
***Dr. Dick might claim he is not solving a problem or even a meta-problem but is just talking about (I might as well use his words here) the consequences of defining reality.***
Reality is not a formal system that fits inside the heads of humans! Reality is much bigger than humans and that we can't begin to formalize that system. For one, we don't know what axioms to select. If we select only the math axioms (e.g., what Dick is assuming in his paper), then what about the logic axioms he is using (non-stated in his paper)? Also, why should reality conform only to the stated axioms of math and logic? What about future axioms that will create new mathematics and new logic? Reality is obvious to me to be much larger than what any one human could formalize into a formal system.
***I think actually he nonetheless IS solving a problem; but is effectively doing so from a "dimension" outside of induction/ deduction yet still using them both? Effectively is he saying: "time?" "induction?" "deduction?" these come from definition itself, from pattern matching, from joining the dots?***
I think I said this to Paul, whatever Dick has solved should be concentrated in terms of mathematics and not so much in terms of reality. He could create a mathematical paper that changes the references to a lattice (still using terms like t, x, etc so that the terms have more meaning when they become Dirac's and Schrodinger's equations). If he did this then he could leave the intelligent reader to make their own conclusions. Dick's problem is that he tries to hit you over the head with all this pseudo-philosophical statements that he loses the interested scientific reader.
I do believe that Dick has accomplished something. But, no one here is really qualified to determine what that is. It isn't a philosophical accomplishment, it is a mathematical accomplishment that has certain scientific curiosities that probably need to be entertained by a larger community. That can't happen as long as he hits you over the head with criticisms of science, unknown data of observations, etc. These terms do not belong in a peer review journal. I can't imagine a hard-nose scientist or mathematician wasting their time. He can look to the philosophical community, but generally his assumptions and reasoning is so unacademic that he isn't likely to get much interest.
Dick needs to rewrite his paper. This is something that he just refuses to do. Oh well, I'd do it for him but that is not in my jurisdiction. I really would like to see Dick do well in this aspect of his life. He is such a good egg and a fun guy to have around.
Warm regards, Harv