Hi Tim,
Such apparent contradictions always remind me of the Wizard of Oz where a little water destroyed the witch. I hope it is not the case with my argument.
*it is surprising that you would take a stance that "then an abstract entity is about the world". i don't disagree with this but if i remmember correctly in a past post arguing against Dr. Dick's paper i thought you took a stance against the idea that mathmatics has to do with mapping reality.*
*"Dick goes further. He makes the assumption that mathematics is the attempt to map the real universe. Note his text (I'll also quote Dick since he likes to be quoted): "the reason mathematics is so important to science is that we are attempting to map the real universe". This assumption is a huge unwarranted assumption, and shouldn't be part of any pure mathematical work. It is applied mathematics gone headstrong into metaphysics, and that's a major reason why Dick's paper shouldn't be considered with any significant merit."*
There's a big difference between the two positions that I am holding here Tim. In the first position, I am stating that mathematics is not done in a complete vacuum from the world in which we live. There are traces of the world that find their way into mathematics. It happens in the manner in what axioms we consider important, what we generally mean by those axioms and 'undefined terms', etc. This is for the all the reasons we just discussed.
In the second issue, I am stating that mathematics is not a physical science concerned with making accurate statements about the universe. Rather, mathematics is a game that we play by adopting certain rules, and then we play our game. Just like any game, there are certain connections to the world we live (e.g., Monopoly money), BUT those connections are not meant to mean that we are literally deciphering real issues in the world. When we play Monopoly, we are not really buying hotels to place on Boardwalk and Park Place (the worst hotels that I always seemed to land on when owned by someone else).
This is not to say that mathematics cannot be about the world. For example, we might find that the laws of physics are theorems of some obscure branch of category theory. It might be that mathematics is not only a game, but is the rules of reality. However, we cannot make this assumption as some established fact. We do not know the full relationship of mathematics to physics. It might be that mathematics is the actual language of physics, or it might be that mathematics is one of a dozen or more other possible games that physicists from an extraterrestrial civilization use to describe their observations.
By Dick placing the role of mathematics as if it is some heir of truth, he introduces a subtle error in his thought. He goes from "it is a practical idea to use mathematics as a guide to designing a model of reality" to a position of "the mathematical model I have made is a model of reality that is necessarily true". The former position is fine as a model, however you need to substantiate the findings of your model with observational evidence in order to show that reality works the way you are saying. The latter position is just arrogance. It is based on the notion that because mathematics is used (assuming it is used properly), then the answer has to be correct even if nothing is observationally predicted. This is a wrong position since the history of physics has been that mathematical models are mostly incorrect in describing reality even when they match the results expected. Dick assumes that because he has used mathematics as his basis and he has matched the laws of physics that somehow he has escaped the requirements to produce new observables. This is failing science 101. |