Harv,
***They[, mathematicians,] aren't eliminating meaning, they are eliminating tangibility. That's a totally different story. Meaning is still there, but it is an abstract meaning (versus a tangible meaning).***
I defer to your connotations of the terms 'meaning' and 'tangibility'. We have stumbled into the all-too-common trap of assuming that our listeners understand our own private connotations of key terms. Fortunately, we have beat this issue enough so that it is clear that we agree on the ideas we are discussing, but we used terms differently to describe them.
At this point, I am convinced that we agree on the empirical nature of the historical acquisition of knowledge, not only of the world, but also of mathematics. We also agree on the impossibility of making sense of any propositions that are devoid of meaning of any kind.
What remains somewhat of a difference between us, Harv, is our impressions of the extent to which references to the world can, and have been, eliminated from the formal structure of mathematics. I think this difference stems simply from our different educational experiences. When I referred to mine as "shocking" in my earlier post, I deliberately chose as strong a word as I could to emphasize the impact it had on me. I remain convinced that most people who have not seriously studied the foundations of mathematics don't really understand the intense focus and importance given by mathematicians to the removal of tangibility (thanks for giving me the correct word) from their theories.
I think physicists and philosophers, not to mention engineers and surveyors, are so engaged in the worldly aspects of their ideas, that they have no interest in this "shocking" distinction. They use mathematics simply as a powerful tool to help in their work. The "shocking" distinction I am trying to point out must seem silly to them and I suspect it usually falls on deaf ears.
Even though Dick has not formally studied the foundations of mathematics, he has nonetheless realized this same distinction, and he recognizes the profound impact it can have on the possibilities to answer a question posed by Einstein. I can't quote it exactly, but it is the question of what, if anything, can we know about our universe as a result of pure thought. Mathematics has paved the way showing what kind of logical structures can be developed by pure thought. Dick has gone beyond that to show that this strictly logical structure implies some necessary constraints on any possible communicable universe. This without any appeal whatsoever to any data or information supposedly coming from any real universe.
***A line has been crossed here that I feel is important to draw attention. We are concerned not about some mathematical problem, but we are concerned about the representation of reality. If Dick's work was limited to describing mathematical objects in terms of numbers (e.g., translating topological designs into numbers), then his thesis should be considered a mathematical work having nothing apparent to do with physics or science. But, this is not where Dick stops. He wishes to say something about reality and how reality can be represented. This is where that 'epistemological trail' becomes a significant issue. ***
That "epistemological trail" is significant if we are interested in the history of the development of the mathematics Dick uses, or in the personal history of how Dick came to make his discovery, or in the difficulty Dick has in getting other people, including you and me, to understand what he has done. And, if we are working on this latter problem (which I guess we are), then this epistemology may be important. As I write this, it slowly dawns on me that this may be the crux of the problem (I seem to find a new "crux" with each post I write). It now seems to me that Dick is trying to do two things at once: Explain what he has discovered, and explain how we should think about his discovery. The first has nothing to do with epistemology, but the second one gets all bolixed up in epistemological misunderstandings of the type we have just cleared up between the two of us, Harv.
Dick has given us a new starting point and methodology for examining the real universe we live in. He has even started from this point and shown how it can be used to derive some well known results. To fault his contribution by claiming that it has produced no new ideas would be like criticizing Faraday for not producing radios and computers. (I think some congressman even asked Faraday of what use his clever table-top experiments could ever be.)
As for your three numbered objections to Dick's work, I'll let him address the first two. I think your number 3 goes beyond the scope of Dick's work, but it rubs up against some of my own thoughts. Let me give you my take on number 3, which should probably spawn a completely new thread. Your objection was:
***3. 'Where do the laws of math and physics come from'? It is not an answerable question (at least in 2002). The laws of physics might come from our limitations at understanding nature, or they might 'exist'. Mathematics is the same situation (except it might be a limitation in our thought processes versus a limitation of our understanding nature). For that reason, we can't say that Dick's model does any epistemological service to science. Afterall, if mathematics is an invention, then so is Dick's model. It doesn't exist, it is merely a clever human invention.***
To my knowledge, Dick has never claimed to know where the laws of math come from. He acknowledges that the origins of some things, like our conscious and subconscious minds, remain a complete mystery -- his Great Original Dilemma. In an old thread, which you may have followed in the "General Interest" forum, I tried to extend the scope or context of Dick's discovery to include this Great Original Dilemma. Briefly, here is my approach.
Since we know without a doubt that thought exists, it seems logical, when speculating on an ultimate explanation of reality, to suppose that consciousness is primordial. If we make that our basic assumption, or postulate, then it seems to me that we can deduce a sensible explanation for everything else. As mathematicians have finally shown, the concept of numbers and the logically consequent structure of mathematical analysis can be developed by pure thought alone. (I know, I know. That's not how it WAS developed, but that's not what I claimed.). Thus, logically, that primordial consciousness could certainly have "done mathematics". Then along the lines Alan keeps suggesting, various interesting "mathematical games" could be invented and played as well. Next (logically) Dick has shown that these "games" are necessarily constrained. Next, as George Berkeley pointed out, what we think of as physical reality could logically be explained as simply a mental "game" played by this primordial consciousness, but of course, it must behave within the constraints discovered by Dick. Finally, to explain all these other consciousnesses (us) in the face of science's inability to do so, and to remain as parsimonious as possible, we may speculate that they are simply manifestations of tiny parts of that primordial consciousness operating as "drivers" of us organisms in a manner similar to our own VR and remote-controlled devices.
This gives us a picture of reality as being continually created and extended by this primordial consciousness. It is always finite, never perfect, but nonetheless continues to increase in complexity and grandeur. This is essentially the same picture Chris Langan has developed in his CTMU theory. To me, it is logically the way it has to be and that it is completely within the powers of our "human" minds to discover this necessity. Dick has provided us with an important link in that chain of discovery.
So, to say that mathematics is a human invention, well,...,yes that is accurate to the extent that you identify our human minds as being unique, and that the mathematics you are talking about is what is written into human literature. But, I expect that the primordial consciousness, when pondering this position, would do the human equivalent of smiling and winking.
Warm regards,
Paul |