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Hi Harv,
Sorry, but I don't check this thing often enough. Ask Paul; life gets very full after you are retired. We have house guests comming this weekend and I have had a lot of chores to do. And Aurino, I am glad that you are reading this as your perspective is quite different from Harv's and you might understand things he does not.
Harv, I get the impression that you think I am trying to slip something past you. That's not true; I take your comments very seriously and I think I understand quite well where you are coming from. What I am trying to do is explain my thoughts to you as clearly as possible. Even though I am not educated in philosophy, I take my logic very seriously and do my very best to avoid slips. One thing should be clear to you. Either my thought processes are quite alien to the norm or they are in error. If they were correct and not alien to the norm, what I have seen as quite obvious would have been seen by others a thousand years ago.
In that vein, this current discourse has not been wasted as you have pointed out to me a particular issue (very important to my deduction) which, though obvious to me, seems to be not at all obvious to others. That issue is that numbers (or numeric symbols if you prefer) can be used both as symbols representing the numerical concepts put forth by mathematicians and simply as tags or representations of things in general. Perhaps it is my significant background in machine language programming which made such things obvious to me. In order to represent anything on a computer, you must be able to transform it into a binary number (think of ASCII code).
I am surprised that you didn't find this alternate use of number symbols obvious as the advantages of such use bears very strongly on Godel's proof which I thought you had examined carefully yourself. I want to use numbers for essentially the same reason Godel did: because they allow abstract representation such that well understood procedures can be communicated easily. I hope that issue will become clear to you as we go on. If not, we will certainly have to come back to it.
For the moment, I will presume you have accepted #6 in the form "It is possible to label all of these "things" with the same symbols commonly used to label numbers" and move on to my next point.
Let us think about the beliefs of some particular individual at some specific moment. At that moment, he believes that some set of "things" exist.
***4. Fourth, at all times, from the ancient past to the far flung future, any rational person's idea of the universe will be based on things they think exist.***
Now those things which he believes exist consist of "things" which are indeed part of "Ultimate Reality" (a class which could, by the way, be empty: i.e., it is possible that nothing he thinks exists really exists) plus those things which are not actually part of "Ultimate Reality".
Per #6, these things can be referred to via labels chosen from the set of symbols commonly used to represent numbers. From this set of things referred to by these labels, I choose to omit entirely those which are not part of "Ultimate Reality". Now I will presume you will object to that with an argument that I cannot do it unless I have some way of determining which is which, something I clearly lack. I deny that outright. I claim that I can refer to things even if I have no way of determining what they are. All I am concerned with is that the portion of "Ultimate Reality" on which his beliefs are based can be seen as a set of symbols taken from that set of symbols used to label numbers.
So I arrive at point #7: It is possible to refer to that portion of true "Ultimate Reality" on which any individuals beliefs are based via a set of unknown numbers.
The set of numbers is unknown because I have no way of knowing what they are. They are defined via the following chain of thought: if I knew what these numbers were, the symbols used to represent them would be the labels of the "things" which are part of "Ultimate Reality" on which that individuals beliefs are based.
There is an important subtle point which must be made here or it will most certainly be missed. These "labels" do not identify these "things". They are merely attached labels and no more. As I said earlier, all that #6 says is that it is possible to attach labels consisting of the same symbols used to represent numbers. No mention was ever made that these labels provided any information at all, only that it was possible to attach them. For example, I can attach the label 25 to all the "things" the individual above believes exists. Having done that, I can then cut those things into two categories ("things" which are part of "Ultimate Reality" and "things" which are not). At that point, it should be clear that some of the things labeled 25 exist and some of the things labeled 25 do not exist: i.e., the label does not provide any information. All I am concerned with is that the labeling itself is possible.
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Harv: It is obvious that you need numbers and not labels, so I'll use this point later when you pull out your magic wand.
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I "need" labels, not numbers! I desire that these labels be numbers for a very simple reason. Using numbers for labels allows me a very straight forward way of assuring that I do not accidentally miss some possible way of attaching labels (that being the next major logical argument to be communicated). This is an important issue because we must satisfy the possibility that "Ultimate Reality" might someday be understood and, if understanding does ever occur, the set of labels attached to the "things which exist" would have meaning and that might require a specific labeling. We must be very careful so as to not omit that particular labeling procedure from our considerations.
I await your response -- Dick
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