i can find no problem with your arguments with respect to a cautious approach of using mathematics in scientific problems.
i do have one small argument with respect to the implyed idea that Dr. Dick is attempting to build a model based on existing math axioms. he is attempting to build a model based on certain definitions that he has proposed. he then uses mathematics to develope those definitions into a self consistent model. so in essence he has allowed mathematics as ONE of his definitions through which his model is constructed.
the reasons for doing so are very clearly stated in the quoted material below:
hmm, i hope i don't get in trouble with Dr. Dick for quoting so much from his paper with out permission.
"I will make much use of Mathematics without defense or argument. In essence, it is quite clear that mathematicians are very concerned with the exactness of their definitions and the self consistency of their mental structures. I suspect mathematics could probably be defined to be the study of self consistent systems. At any rate, their concerns are exactly those which drive my work; I am merely attacking a slightly different problem. I hold that the reason mathematics is so important to science is that we are attempting to map the real universe (which is assumed to be self consistent) into a mathematical system (which is self consistent by construction). In accordance with this view, I will hold that the fundamental mathematical relations require no defense by me. I will leave that defense to others far more qualified than myself"
in conclusion Harv, Dr. Dick's use of mathematics is nothing more than any scientist might do when attacking a problem, just as his use of language and logic are acceptable vehicles in the presentation of his ideas so is mathematics. if we find his language, logic and mathematics correct then all we have to attack is his definitions. that for now i leave open to debate. but i would state that if he can honestly derive our science from his definitions then those definitions should be of interest to any one with an interest in science.