Sorry for my delay:
***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.***
I have a problem with this paragraph. Let me reword it the way that I hear it:
"A game invented by primitive lifeforms called Monopoly has paved the way showing what kind of pictures in Pictionary (another game) can be drawn by these primitive lifeform's from their pure primitive thoughts. Dick has gone beyond that to show that the pictures in Pictionary implies necessary constraints on any words that come from the mouth of these primitive lifeforms. This without any appeal whatsoever to any data or information supposedly coming from any real universe experienced by the primitive lifeforms."
As you see, logic and math are too different games (e.g., Pictionary and Monopoly). Pictionary doesn't restrict Monopoly (or vice versa), but they may have rules in common. For example, in Pictionary and Monopoly there should be multiple players and they should take turns, etc.
***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.)***
I don't buy into this analogy since Faraday was able to make predictions as a result of his 'lines of force' model. Dick's model doesn't make any predictions, nor does it 'do anything' which a good invention should (as Dick claims his model to be).
***H: 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. P: 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.***
The reason I think the question is pertinent to Dick's work is because mathematicians may be muddling with limitations on what the laws of physics must conform, or equally - muddling with limitations on what we can perceive to be the laws of physics. If so, then don't be too surprised if muddling with wavefunctions, etc somehow generate the known laws of physics. For example, if we started to write a screenplay we shouldn't be too surprised if the movie idea we come up with has already been made. There may be a natural tendency to come up with what is already there. That natural tendency might be because the world is mathematical and pursuing a mathematical approach naturally leads to an emulation of the physical laws, or it may come because a mathematical approach naturally leads us to the most efficient understanding of nature.
Although, by saying that, I don't want to dismiss that Dick's work is probably heavily affected by what he knew of laws of physics as he was developing his model. Had we been sitting outside his home for those weeks that he was developing his model, we might have gone through his garbage and seen an inordinate amount of crumpled papers. Those crumpled papers would show all the equations that didn't obtain the laws of physics as we know them. He simply ignored those attempts, which would be a 'no-no' according to that 'fallacy of the enumeration of favorable circumstances' principle I mentioned to Alan a few days ago (citing Sagan's book).
***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.***
I'm not against proposing that consciousness is fundamental to reality, but I have some problems with the generation of mathematics as a result of consciousness. Mathematics is an result of certain axioms being true. All Consciousness had to do is generate the conditions for the axioms of math being true, and all of math is true. No need to create all various interesting 'games', they would exist instantly.
***Next (logically) Dick has shown that these "games" are necessarily constrained.***
Constrained by what? Dick is assuming that the axioms of math and the theorems of math are 'correct'. So, math already exists in his model.
***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.***
Why? What if mathematics is only one small 'room' where these rules apply, but they don't apply outside that room? For example, what if the principle of excluded middle is not valid outside this room? Then Dick's model falls apart outside that realm.
***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.***
Maybe, but why not take a more conservative approach and simply allow that our understanding in this area is very new and in future generations science will eventually make great strides in coming to a natural explanation for consciousness?
***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.***
As far as Dick's presentation is concerned, I only see the poor assumptions made by Dick as he brings his math game over into saying something about the world. I wish I could see more.
***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.***
It's an interesting possibility...
Warm regards, Harv