just quickly: "Is what a real problem?"
The problem that Dr. Dick imagined might come along. Any real puzzle.
"The problem of solving problems?" That is not an issue being adressed by Dr. Dick so much as "the defining of problems". In so far as definition is a first step toi solving, it is part of solving.
He avoids induction by refusing to go from the particular to the general; instead he goes for the general and comes back to a particular (specific physics laws).
However, his thought process was inductive in that although he started with the idea of "general"; he built up his "generality" by adding particular facets of generality into his mix.
He avoids induction by stating laws; by laying down his own law by definition.
"It seems you need a problem solving method to begin with before you can consider whether you have an appropriate problem solving method. Do you see the circularity in that?"
But he may claim he is not trying to solve; just to define.
"The problem with metaproblems (problems about problems) is that we need problem solving methods to consider a metaproblem."
True. Are definition stages considered part of the method?
"However, if we are questioning the problem solving methods, how can we even consider the metaproblem to begin with?"
The very act of questioning involves the comparing and matching of patterns. So one might investigate the nature of pattern-matching; and thus transcend problems and meta-problems issues.
"When you say it takes time to solve a problem, you are using your own inductive conclusions (part of the definition of problem solving through an inductive method is to make generalized conclusions from specific situation)."
True. But one could start from a general idea, then just reduce to a specific situation by defining it arbitrarily. One's conclusions will flow from the general start-point; so one is not going in the order particular-to-general; but in the order that is not inductive: general-to-particular!
Dr. Dick by-passes Hume's problem of induction by starting general; and defining particulars arbitrarily, by making laws.
You can say something meaningful about the world: you can say "If I take this general "encompass all possibilities stance, and make some laws, some definitions, this is what the interactions between those definitions and the possibilities, looks like."
The definitions themselves say a lot; Dick is not solving pseudo-problems; he is making laws and looking at the effects of that, starting from a general perspective.
He just defines a "problem" out of his general all possibilities field; so does not need induction.
He doesn't have a hierarchy of meta-problems because he just makes laws, creates definitions, then looks at their effects.
"In other words, you construct all the terms inductively and deductively so that the laws of physics are obtained, and then you have justified inductive and deductive reasoning as justified problem solving methods. Do you see anything wrong with that approach? "
But instead of that approach; he starts general so avoids the particular-to-general arrow of induction.
Ultimately though, he depends on his own judgement of his logical consistency and of others judgements.