Hi Paul,
***H: Here I think your analogy breaks down from what I am saying. The analogy with ET might better illustrate what I'm saying. P: I'm not sure what you mean by "breaks down", but it occurs to me that both of our analogies have a flaw, or a feature, that makes them not applicable to what Dick is trying to say.***
Meaning that with ET we know for a fact that we can never fully comprehend their full mental model since their evolution is so far removed from our evolutionary developments. On the other hand, we might be tempted to think that we can fully share the same mental model as the kid in the box.
***In my analogy, there are two sentiences: you and the kid. In yours, there are also two: me and the alien. We both described a particular communication situation between two sentiences. In Dick's model, there is only one sentience: you. The communication problem Dick describes is you taking information from some unspecified source and logically deducing what you can without knowing anything about the information.***
I agree that multiple individuals do not play as prominent a role for Dick's model, but in principle the same rule applies. Any interaction we have with the Universe is via our mental model, and that mental model is more than just what is communicable (i.e., what we would communicate to someone else if we could), but it also includes all the stuff about us that we are unaware of or do not realize how it affects our view of the Universe. In that sense, the ET analogy is helpful, I think, since we should be humble in our estimation of how a communicable mental model might be skewed by factors that we are completely aware of.
***H: Hence, I am willing to consider abstract concepts if you and Dick are willing to concede that all abstract concepts require some epistemological basis for those concepts. P: Here is where we are stuck, at the moment. Dick and I are not willing to concede what you ask. And, from your statement, "I think anyone who tries to totally divorce themselves from the tangible world is deluding themselves", I take it that even though you might be willing to consider abstract concepts, you are not willing to let go of the "herbs and spices". We may be able to get around this impasse, however, if we realize that there are the two separate contexts of communication. One between a pair of us sentient posters (you and me), and the other between a hypothetical "scientist" and the "universe".***
Unfortunately, for me, this only delays the problem by one step. Rather than having to share my mental model with another individual, I must somehow try to sort out what part of my mental model is communicable and what part isn't. For example, are the axioms of Peano Arithmetic (PA) communicable? What about my sense impressions and internal inferences within me that suggest that there are independent objects in the world? This might seem trite, but I don't think it is. There is evidence in quantum field theory that there are no truly independent objects in the world, and that our sense impressions are wrong. So, any mental model needfully has both communicable and incommunicable concepts all intertwined. All we can hope to do is bounce off our concepts on others to see what is communicable and what is not.
***But in the context of a hypothetical "scientist" trying to model the "universe", it is entirely possible to do so by considering concepts completely devoid of meaning.***
I know we've gone through this disagreement before. I can only think we are not communicating since I cannot understand how you could believe that a meaningless concept is entertained by scientist or mathematician. Professionals (should) spend very little of their time analyzing meaningless concepts (unless they are numerologists).
I think you are actually meaning that abstract concepts have no tangible meaning. If that is what you mean, then I agree only to a point. The meaning of an abstract concept (e.g., a mathematical point) is meaningful but in a different sense than a physical point is meaningful. The 'physical point' is not really a point (in the mathematical sense) but rather is only analogous to the way humans conceive of points. The issue is rather reversed since mathematical points actually come from our abstracting from 'physical points'. That is, we look at only certain qualities of a 'physical point' and we pay no attention to the elements which distract from our concept of a mathematical point. Eventually with enough mathematical learning, mathematical concepts become so abstract that they no longer hold any tangible meaning in the formal mathematical sense. This is what I believe you are talking about, right? Well, I am not concerned about the formal mathematical sense of meaning. I am talking about the epistemological sense of meaning. Epistemology is concerned about how we know what we know. The epistemological issue becomes: how can mathematicians treat certain concepts as meaningful (i.e., useful to be discussed in mathematics) and yet place no tangible reality to those concepts. The answer, I believe, is that they place meaning on other abstract concepts and equations which 'sit on top' of a whole slew of other abstract concepts. At some point lower in this hierarchy (near the axioms) we see the tangible concepts that all the above is sitting upon. This is why mathematics is taught very tangibly to young children. They are taught to count objects (people, pens, dogs, etc). Only after all these tangible things are related to in a mathematical manner, do we finally leave the tangible things and just focus on the abstract things. After many years of all abstract concepts someone might feel that all these abstract concepts are 'meaningless' in terms of a tangible world, when in reality there is simply a distant connection of learning that it just appears that these abstract concepts have no meaning. When in fact, we are quick to connect those concepts to the tangible world if we are so lucky as to teach young children. This, I think, is the epistemological issue.
Since, Dick is concerned with epistemology (i.e., how do we know what we know, and what can we know for sure), he must also confront these other epistemological issues. He can't just be content with the mathematical approach to abstract concepts which ignore the tangible things of the world. You can't mix formal mathematical practice with epistemology.
***Alan has given us some insight as to how this may be done. His "games" of "musical chairs" etc. are meant to be meaningless concepts, even though he uses familiar analogies, which of course have meaning to us, to describe the concepts.***
Here's a case in point. Musical chairs are not meaningless concepts (as you also implied), they are tangible concepts. This demonstrates the epistemological connection that exists between tangible things and abstract things. Once this relationship is forged, it is permanently 'there'. You can't ignore it, and can't remove it. Those particular abstract concepts are reducible to the meaning obtained from this exercise of using musical chairs (to use Alan's example).
***H: However, what you cannot do is divorce the original meaning that imputes those numbers with human meaning. It might look that way to someone who knows for a fact that they are thinking abstractly, but this is only fooling oneself. P: Yes, I know you disagree with my previous paragraph, but I think you are wrong. I think the great mathematicians have succeeded in divorcing meaning from their concepts. Are they fooling themselves? I don't think so. They freely acknowledge that even though you may impute some "meaning" to their formal statements, there is in fact none.***
What mathematicians are doing is climbing a ladder to a certain height, and then they kick the ladder to the ground once they no longer need that ladder. Now, we can look at it from the mathematicians viewpoint as to why they kick the ladder and why they say that the concepts they have climbed hold no meaning. This is fine to say when teaching mathematics to higher level students, but it is not epistemologically true. The fact that they used the ladder of tangible concepts to use undefined abstract concepts means that they are forever dependent on the ladder in some epistemological sense. For example, we are dependent on the sun for our sense of time even though we can know the time if darkness fell upon the earth due to a nuclear winter. The dependency of the sun has nothing to do with knowing the time of day, rather it has to do with as an explanation as to how we know the time of day. Knowing the time of day (without the sun) is merely a matter of setting certain standards among us so that we all agree on how the time of day should be defined. Knowing the time of day (in terms of how we actually know it) is an epistemological issue having to do with the transition from sun clocks to digital clocks.
***What Dick is offering, is a new method to augment this traditional method. His method starts with nothing from the traditional source, except for mathematics. And as I have tried unsuccessfully to convince you of, mathematics today is based on a foundation that has been swept clean of any taint of herbs and spices from our tradtional "knowledge" of reality. It is based on a strictly abstract and meaningless set of concepts. Dick starts with that basis, and derives constraints on what is possible for a physical universe that are surprisingly like the "traditional" laws of physics.***
There's assumptions which do not work from my perspective. For one, if mathematics is formed from our sense impressions and inferences as I suggest, then Dick is obtaining his mental model from the same traditional source as science (sense impressions and inferences). Although, his mental model purposely excludes any information which is not pertinent to mathematics. For example, Dick's model cannot utilize experimental results since mathematics is not an experimental field (well, that's not entirely true, but for our purposes he doesn't rely on experiment). This is problematical since this throws out a great deal of information of the world. Hence, if there is something major about the Universe that can only be known from experiment (e.g., physical constants, etc), then Dick's model ignores it.
Another weakness is that we have no way of validating the identity of his variables with physical concepts since he has no new predictions about which to speak of. He matches current physics as he probably knew as a grad student, but much of the physics since is not part of his statement that 'much of physics is a tautology'. Our only means to validate his defined concepts is to confirm that he arrives at much of physics. But, this is not helpful since we know that one can reconstruct known laws and equations of physics simply by manipulating the model.
Starting at the level of math and defining concepts is fine as a game, but when actually trying to form a better understanding of the Universe and the laws of physics we think 'work' for that Universe, then we can't rely on methods which only validate what we already know. We need scientific models that give us new predictions so that we can validate the model. It is a known problem within the philosophy of science where theories are modified to explain contradictory data. If pressed far enough, one can keep an existing model indefinitely (even though it is wrong) simply because the theory can be modified over and over to explain all the inconsistencies that occur over time. At some point enough is enough and the model must be overturned completely.
In Dick's case this could never happen. There can never be a point to where the model is overturned because its only justification for being right is what we already know (Dirac's equation, Schrodinger's equation, etc). At no point can the model be shown to be false. If we cite that more and more physics has been learned that his model says nothing about (e.g., QED, QCD, etc), then this means nothing to the model.
Yet, another problem, is that the whole issue of the universe simply being mathematical is not even addressed by Dick. What if Schrodinger's equation, Dirac's equation, etc is all the case simply because the universe must conform to mathematical principles and equations? In such case Dick should be credited with helping to show that 'math rules', but this isn't what Dick wants to say. He doesn't want math to rule, rather he wants to say that our laws of the universe are mostly tautological (i.e., true because of our own definitions). This isn't the same as saying that 'math rules'. Rather, it is saying that 'we rule' since we make the definitions what they are. He really has never shown to me that this is the cause for the Universe conforming to some fundamental equation.
Warm regards, Harv |