***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.***
This is perfectly fine to do. It is the meaning of the definition with respect to the world and the conclusions about the world that is the problem. Dick is doing applied math and the rules of application are different than just doing math.
***"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"***
This is an error. Mathematical systems as a human activity doesn't need to be justified. Mathematicians define their use of terms, axioms, rules, etc, and they are perfectly able to play that 'game' without much objection from anyone. Dick goes further. He makes the assumption that mathematics is the attempt to map the real universe. Note his text (I'll also quote Dick since he likes to be quoted): "the reason mathematics is so important to science is that we are attempting to map the real universe". This assumption is a huge unwarranted assumption, and shouldn't be part of any pure mathematical work. It is applied mathematics gone headstrong into metaphysics, and that's a major reason why Dick's paper shouldn't be considered with any significant merit.
***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.***
This is just blatantly untrue Tim. Science uses mathematics to construct models because they are successful doing it. If science were successful using Alan's fly-by-the-seat-of-your-pants-make-comments-along-the-way type of investigation, then I imagine that Alan would be in large company. Unfortunately, scientific progress isn't achieved in such a loose and capricious fashion (otherwise I might take up physics for a profession...). Science has discovered that mathematics is helpful for developing models that have predictions that match our observations and that provide good explanations, and therefore science uses it. The philosophy behind mathematics is very contentious and divided. Even scientists disagree what mathematics is exactly, and no one has any supportable answer to the question. It can't just be definitions that should concern us, but the whole assumption that we are saying something about reality with our current understanding of math.
***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.***
The term 'our science' is imprecise. Dick's model has little or no theoretical physics beyond 1950's from what I can tell. Nothing about the physics that was developed using internal symmetries, just the external symmetry physics. It seems strange and coincidental that this is the case since he actually uses external symmetry arguments, but lacks internal symmetry arguments, don't you think so?