Paul kicked my spurs...
***i have trouble understanding the reason that you see Dr. Dick's presumption to use mathematics in his treatsise as a fallacy of assumption.***
What are the axioms of mathematics? There's a number of them for each branch so I won't ask you to recite them, however it has been shown before by greater minds than us how our current axioms can mislead us into how the world can best be described. The clearest such example is the age long view that Euclid's fifth postulate meant that space could not be curved such that two parallel lines would never meet or veer away from each other. All attempts to undercut that postulate came up empty until Gauss Riemann, Lobaschevsky, et al. were able to successful construct a geometry that didn't require the fifth postulate.
What is the lesson for Dick from this?
1) We do not necessarily have all the 'right' axioms, and that if we did it might change our view of the universe. If you build a model based on existing math axioms, then maybe all we've done is construct a model based on flat space which says nothing about the way the universe is and the limits we self-imposed on it.
2) Human math is finite based on our earthly experiences of the universe, however in terms of the exact character of the universe our mathematics might only represent a crude approximation - good enough for our survival and sciences, but deplete when it comes to describing the actual nature of the universe.
In my perspective, and I think most philosophers would share this perspective, using math in such a naive fashion is ill-founded from the start.