Contrary to what I said, here I am again...
First, don't take Harv's criticisms too seriously. Harv doesn't understand what Dick is talking about, althought that is not his fault. For that matter, Paul Martin doesn't understand it either. Paul thinks Dick's paper is about God and physics - it is not. It is about communication. So let me tell you what Dick is really talking about. You seem able to understand the concept better than anyone else. Just let me state that I don't equate understanding with agreement. Keep that in mind.
doesn't he really just assume that reality, what ever it is, is communicable and then go on to define reality as a set of numbers?
In fact Dick is not assuming that reality is communicable. All he assumes is that any concept that is communicable (ie, any word) can be tagged with a number. That notion in itself is not as controversial as Harv thinks it is; all Dick is saying is that any explanation of anything can be converted into a series of numbers. That is exactly how we use computers to communicate after all.
in other words isn't the step of defining reality as a set of numbers actually a logical step following the assumption that reality is communicable?
As some poster recently pointed out, you can apply the same reason to "bananas". You can also define "bananas" as a set of numbers. Dick is not really concerned about reality, he's concerned about the kinds of relationships you can find between the symbols used to communicate a self-consistent explanation of anything, including "reality" and "bananas". That's the bit Harv doesn't get, mostly because Dick doesn't know how to explain himself.
Imagine you are given the task to create a new language from scratch. You have to invent words, give them meanings, and provide a way for other people to learn that language. However, you are not allowed to explain that new language in terms of any existing language. In other words, when you are done creating the language, you have to write some books that teach people how to use the new language... in the new language!
The task of creating a new language, you must agree, is trivial. The task of learning that language by reading books written in that language is extremely complicated, and to a good extent impossible.
The scenario above may sound exotic, but in fact every one of us had to confront it once in our lives. We were born without knowing a single word in English (or whatever your mother tongue happens to be), and you had to learn that language by listening to people talking in that language. How do we do it?
If you understood this so far, and are interested in more, I can tell you how this stuff is the essence of Dick's ideas. Let me know what you think.