I very much respect Dick, I just think he is not concentrating enough on the philosophical aspects of his interpretation. I'm concerned that he sees his philosophy as 'given' based on his results.
Also, I want to avoid 'counterbalance' discussions, so rather than comment line for line let me try to hit the gist of your argument. This means that I should 'drop' certain replies due to economy. I'll break your argument down into a few central points as follows:
1. 'How do you arrive at that correct derivation of how nature works in the first place, given the problem that nothing about nature can be known a priori?'
It's a trial and error process. For example, it is common knowledge that group theory has long ago worked out the types of lie groups that can logically exist in mathematics. Physicists have been picking and choosing from those groups the past 40 years or so to see how those groups match up with observations. It is a hit and miss process. Sometimes nature chooses the obvious group transformation to describe itself and sometimes it tricks us with using an unexpected group configuration. These issues are solved a posteriori - not a priori. Once the regularity of nature has been honed in on, physicists of a new generation will try to derive other mathematical means to derive the equations of physics. This sometimes leads to the conclusion that all is a priori about physics, but this is entirely misleading in my opinion.
2. 'The problem is that you cannot conceive of the universe being something entirely different from the way you see it, and that kind of argument has no logic.'
Only to a point can I make that visualization. A star is still a star, a planet only forms a certain way, etc. If the laws can be *restated* differently, then I have no objection. But, my view is limited to the laws being restatements - nothing more (i.e., they aren't matters of loose opinion or how we choose to define concepts what we want to find).
3. 'There is no such thing as a viable bias, all biases are undesirable distortions of the data and should be eliminated or at least kept to the minimum possible.'
I disagree. Biases are our means to find how nature works. Einstein, for example, had a bias using the equivalence principle which is why his relativity theory came so easily. Where biases hurt is when one cannot see they are out of joint with experiments or they are writing sloppy looking equations (or cannot see elegant equations developing from others). At that point, one should examine their biases. If one chooses to remain firm, then the absolute dividing line is when experiments fully contradict their view. For example, Dick is strongly contradicted by the experimental results of GR, but my understanding is that he refuses to acknowledge GR as valid. A bias has taken too much control.
4. 'If you think Alex is correct, why are you so often arguing with him? Because he doesn't believe in your particular conception of God which is completely irrelevant to Alex's model of reality? (...) You keep trying to convince Alex that HIS model of reality is inconsistent because it doesn't include YOUR concept of divine order. What both of you fail to realize is that your discussion completely misses the point and because of that you will never understand each other.'
Alex and I are really close in our views of mathematics in the world. The difference is that we are arguing about the implications of mathematics 'existing' in the world. It is purely a philosophical (oops! I'm sorry, a discussion of sound reasoning and implication) argument. We are merely arguing about interpretation.
5. Relationship of math to Dick's interpretations (of his math) versus my view of math.
You said 'so math is king but the king is just the king...' as (I believe) a sarcastic remark that when Dick discusses math I say it is 'just math' nothing more and nothing less, but when I speak of math I talk about it being king of the laws of physics. Well, let me clear up this apparent contradiction. When physicists use math in their equations, these equations are just math - nothing less, nothing more. In order to make math useful they should interpret that math by assigning physical concepts to that math and making predictions. Without an interpretation the math is always going to be math. Dick cannot let his math equations speak about philosophy, that is *his* job. Math says nothing - just math. Humans provide the interpretation. If humans interpret math in terms of physics equations, then the interpretation is science related. However, if humans add philosophical consequences to their math (such as me, Alex, and Dick), then the interpretation is a philosophical interpretation open for philosophical scrutiny. My philosophical view (and Alex's view) is that math is king. That is, it describes the inherent logical path of the universe. Dick's philosophical view is that math is not king, rather it is just our own axioms chosen by convention which is 'true' in that they are consistent. By developing physics equations from the math he believes that physics is 'true' in the same manner as is 'true'. The problem with this view is that it assumes that this somehow provides a foundation to physics, which I don't think it does (anymore than mine or Alex's view provides a foundation). No foundations are permissable (i.e., proveable) in the universe. That's just the way it is.
Warm regards, Harv