The problem with extreme skepticism, as I see it, is that the reasoning methods which one is skeptical is the very same methods one uses to arrive at one's skepticism. For example, Dick is very skeptical of the empirical process of experimental science because it uses theory to to to explain observations. He thinks that we don't know our theory is correct, so how can we immute our theoretical model upon reality.
This is a genuine skeptic concern (for everybody), but if you question the reasoning method of using theory to account for observations, then which observations are immune from a theoretical context? Every observable requires some language-laden construct by which to communicate those observations. Every human is given heavy dosages of parental influence prior to any analytical thinking such that any analytical thinking depends on language and it depends on the constructs provided by our parents, siblings, TV, etc. In short, there is no construct-independent observation of the world. If you don't theory, then you must for similar reasons doubt the constructs that were provided by our parents, teachers, etc. In short, you have no means to have a construct-free observation, so any skeptical concern must also be part of the very constructs that it is skeptical.
Well, even if we ignore this issue, Dick wishes to use mathematics by which to define certain terms and then develop these terms within a mathematical context (using numbers representing data of the world which he is able to construct into a wavefunction equation). What's the problem with this? Well, mathematics is also built on an empirical perspective of the world. The axioms of mathematics is what is apparent through our senses and the reasoning of our senses. The abstract concepts of mathematics is reduced to empirical observations.
If mathematics rests on empirical and inductive/deductive conclusions of that empirical data, then mathematics rests on the same clump of clay that science rests upon. Except science continues the process within the natural world of making constructs by which to derive further conclusions that are less obvious than the axioms of mathematics. Nevertheless, they are still determined using similar reasoning methods.
So Dick's approach doesn't satisfy the very thing that he wishes to accomplish. He wants to label translate concepts into an abstract mathematical approach, develop from first principles the laws of pre-1950 physics, and whola. We are supposed to believe that reality is a set of numbers? I don't think so.
Warm regards, Harv