Since my name was mentioned as not thinking, I thought it would be beneficial to respond to the pre-philosophical views presented here and why they amount to a misunderstanding:
***Fundamentally, taken as a whole, what we think is a valid interpretation of our experiences amounts to extraction of "information implicitly embedded in the data". There is a very important problem buried in this presumption. First, it is possible we are wrong. Historically mankind has been found to be wrong on a great number of occasions. How do we know they were wrong? Clearly we have come upon additional data which contradicted what we thought was true.***
The problem with the notion that our experiences can be presumptous is the following:
1) There is nothing you can do about it. Any notion that a mathematical model can correct our vunerabilities is itself based on our experiences on the axioms we select for the math model. If our pre-analytic experiences of the world are misguided, then so are any analytic thoughts that might be used to analyze the "extraction of information implicity embedded in the data".
2) Even identifying the 'problem of our presumptions' is itself sourced in our experiences. Hence if our experiences (or analysis of those experiences) are presumptuous, then so is the process of identifying and articulating this problem.
You can't offer to define a problem and offer a mathematical solution that is based on the very problem that you are trying to define and offer a solution to solve. Do you see how fundamentally flawed and self-referential that is??
***The other side of the coin is the fact that it is possible we are right: i.e., there actually does exist something we think is true which is true. Now, if that is the case, then contradiction will not occur no matter how long we wait and no matter how much additional data we obtain. These truths are what I am referring to when I speak of "information implicitly embedded in the data".***
Tim, this even goes one step further than a problem and solution that is based on the problem in question. Here there is an admission to the possibility that no problem actually exists, but the admission of this possibility is also based on the very same problem that we are trying to solve and provide possibilities in our solution. Hence there is no way to know if these possibilities that he is willing to admit as possible are restricted by the problem in question! Here, let me layout the logic on this so it is easy to understand and follow. This is not to suggest that our experiences can be so neatly divided, but it allows us to address the different kinds of experiences we have.
1) Raw Human Experience : First Order
This raw human experience includes your earliest memories, the sensations you feel this moment, the thoughts that you have right now, and everything that you can imagine. What is left out of this category is any analysis you might offer to understand this raw human experience. It is the incoming data so to speak. Let's call this a 'first order' experience meaning that the experience is not a reflection on the experience, it is just the experience - nothing more.
2) Review of our Human Experience: Second Order
This is when we examine our human experience, and make some conclusions about it. These are things that are not part of the original experience, these are things that you have to think about the experience before you can draw any conclusions. These are second order. For example, if you are chilly you might feel the cold, but at some point you realize that you are feeling cold and you realize that you are in fact cold. You have reviewed your human experience of something, and come to some conclusion. This is typically identifiable as thinking.
3) Analysis of your thoughts: Third Order
In this category you start to collect your thoughts. You realize you are cold, and you think about what it means to be cold, when the last time you were cold, etc. You are not just thinking about summarizing your human experience, but are recalling and considering the concept of being cold.
4) Abstraction of your thoughts: Forth Order
You are now no longer just considering the concept of being cold, you are thinking what the concept of being cold means. This is abstract thinking. You are thinking about concepts and dealing with them abstractly.
5) Logical/Mathematical thought: Fifth Order
Now you are no longer just thinking abstractly about concepts, now you are organizing your abstractions themselves into a manner that allows for you to play with the abstractions without being concerned about the concept of cold, or your thoughts about being cold, or the direct raw experience of being cold. You are representing the concept of cold with numbers (or what have you), and you are processing the numbers without meaning to what they originally meant in your pre-fifth order thinking.
6) Metamathematics/metalogic: Sixth Order
Now you start to consider what logic and mathematics actually mean in itself. You are no longer concerned about the abstractions themselves, but you consider the rules of abstraction.
7) Meta-metamathematics/meta-metalogic: Seventh Order
You are no longer concerned about the rules of abstraction, but whether there are any rules to the rules. This process of considering rules of rules could be ad infinitum, but it is clear that this is redundant and you don't need to consider anything beyond meta-metamathematics or meta-metalogic.
So, when we look at Dick's model, we see a big concern for (1)-(5). He has almost little or no concern for (6) and absolutely no concern for (7). But, here's the problem. He doubts (1). He thinks (1) is presumptuous. He especially doubts (2)-(4). BUT, what does he do? He proposes to solve his doubts of (1)-(4) by proposing (5)!! But, what he won't even consider is that his (5) is based on (1)-(4)!!!
This is totally beyond Dick's comprehension. It is simple metalogic studies, but he never studied metalogic. On the other hand, Tim, don't be fooled. I know its enticing to think that there is some fantastic proof in the squiggles and lines of his math, but you don't need to worry about the math. The issue he discusses is both best addressed and best solved using this meta-logic analysis of first order, second order, etc. Now, in real meta-logic, logic is first-order, second-order, third-order, etc. It does not match the above. This particular sequence was done for simplicity so it is easy to see why Dick's paper is a bunch of beewax.