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Re: We May Be Getting Somewhere

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Posted by Harvey on May 7, 2001 23:04:37 UTC

Hi Paul,

>>>H:"This makes Dick's model a foundationalist model." That may be so, but I am not sure. After being classified by you (again I thank you for that) I did some reading on the foundations of Mathematics and learned for the first time of the three-way disagreement between Logicism (Leibniz), Intuitionism (Kronecker, Brouwer), and Formalism (Hilbert). This reading confirmed my position supporting Kronecker and Brouwer, which I guess means that Intuitionism should be added to my list of labels. I read nothing, however, which gave me a clue as to how the name 'Intuitionism' was chosen.>With this new-found meager knowledge, I have formed some new opinions. I now see foundationism to be a point of view on the origin or starting point of some particular development. If the particular development is a field of mathematics, then the issues debated by those three above mentioned points of view are the issues seen to comprise the starting point for the field of mathematics. These are arbitrarily chosen, as the three different points of view on the foundations of mathematics attest.>As I see it, Dick has discovered a more general or more primitive starting point for developing the laws that govern the physical universe. In that sense, I claim it is a foundationalist model. That is, his model can be used as the foundation for the development of the laws governing physical reality.>He is not using the laws of symmetry that are already known. His model is simply general enough to allow for any and all symmetry that may be in the data. He only uses the mathematical system of numbers to develop his model.>H: "I'm not following you here. A mathematical model can't address the subjective issue since math has nothing very relevant to say about psychology (or at least what I'm aware of). When we do math we simply are solving analytical problems." P: Here is where I think I jumped out into a territory where you and Dick both didn't see where I went(...) But let's get past these questions and just assume that math is something "we can do". Who are the "we" that can do math? Can math just exist out there with no one "doing it"? I think Alex would say 'yes'. Just as Hilbert would say that numbers can be automatically generated in infinite quantities by some 'genetic' algorithm that sort of runs off by itself. Of course, lining up with Kronecker and Brouwer, I disagree and say that the only mathematical structures that get built are the ones that someone (we?) develops by actually "doing the math". So, "the 'particular development' I wish to pursue" is the system that contains not only the "math" but the "we" and the context in which we can "do" the math. I have no idea what this system is, but it is a super-set of physical reality and it is a super-set of mind. I think of it as all that is, was or ever will be whether anyone has ever perceived or conceived any part of it or not, or ever will.>I agree with this. I think there is something in that bigger context that is not describable and therefore cannot be reduced to or represented by numbers. Of course I can't tell you anything about it, because if I did, you would say Aha! you have given me a description of something indescribable.>So if I were to say "this description is indescribable" then you would immediately know that "this statement is a lie".>So, whatever this indescribable stuff is, it is outside of the (any) physical universe and does not have to obey Dick's equation or obey the laws of physics. And, we cannot apply math to it. In particular, we can't use a mathematical model to talk about it.

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