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Posted by Paul R. Martin on December 30, 2001 19:51:57 UTC

Hi Harv,

We could continue debating in this fashion, but I think it is clear where it would lead. It would either loop, or we would end up debating the number of angels that can dance on a pinhead. We have each made our points, we each believe our position has merit, and, if we look at it from the other guy's point of view, it should be clear that that, too, has merit.

For my part, you have helped me see that my insistence on strict categorization of contexts leads to an absurd position. In particular, in viewing mathematics as devoid of meaning, which is what my math professors demanded we do, we see that it is not consistent with what we find in real life. We know that the discoveries of theorems and solutions to many problems are not achieved by following the rigorous logical steps that the pedagogy forced us to learn and practice.

On the other hand, I stand behind the general idea of the backdrop I sketched. That is, that intellectual progress is made in large part by an interplay, or even an oscillation, between an approach generally from the top of my list to an approach generally from the bottom of my list. Both approaches yield progress, but each is limited without the other. We may learn a great deal about our world, as nearly all of our ancestors did for the past million years, without ever bringing formalism and rigor to bear on what we know. But, as the past 200 years has shown, by applying math and logic to what we know experientially, our knowledge of our world has been enormously extended.

As you point out however, the reverse approach doesn't really happen. Few, if any, mathematical concepts were developed without some correspondence (you called it a "reference") with something "real" (Evariste Galios' extensions to Group Theory come to mind as one notable exception).

So, at this point, Harv, I am willing to concede. I think we can step back and look at what we have written and maybe both learn something. It seems clear that the problem Dick has of getting his work read and accepted is largely the result of mixing up the contexts that I talked about. That is, taking a position in one context or the other and attempting to use that position to persuade someone from another context. Philosophical claims fall on deaf scientists' ears; mathematical claims are misunderstood by philosophers; scientific claims hold no interest for mathematicians; etc.

Thank you for the work you did in this dialog, Harv. I hope you are not disappointed that I didn't respond point for point to your last post, but I think it will save us both time if we let it go here.

>>>If Dick removed all the extraneous links of 'reality' to his paper (e.g., removed terms like reality, perception, observation, time, etc) then he would be left with a mathematical paper. It is too bad that he didn't take that approach, he probably would have been published eons ago.

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