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Posted by Harvey on October 9, 2002 05:36:27 UTC


A few questions. You said the following:

"No comment about how this labeling is to take place nor what meaning the labeling has nor whether the labeling is of any value; only one thing, "it is possible to label all of these 'things' with numbers". We are, at this moment, discussing these "things". All I said was, "it is possible to label all of these "things" with numbers". Let us use the numerical label 25 for each and every "thing". That is, for the moment, when ever I refer to the number 25, I am referring a "thing", some "thing" which is part of the "things" we are talking about! You should be able to comprehend that I have attached a numerical label (the number 25) to every "thing" under discussion... If you asked me to label the largest even number, I could just as well "label" it with the number 39. What you are doing is confusing the role as a label with its numerical meaning. So long as I am using the number as a label only, its numerical meaning is entirely beside the point. As a matter of fact, in this particular case, I arrived at the label 39 via the rule that it was the three words following nine words in your sentence (the rule is entirely open: I can use any rule that pleases me, including giving everything the same numerical label). All I said was, "it is possible to label all of these "things" with numbers". You keep trying to read more into that statement than is there... All I said was, "it is possible to label all of these "things" with numbers". I did not even say that it would be possible for you to decipher what thing the number stood for. You keep trying to read more into that statement than is there. (...) Now it seems to me here that you are constraining what a "thing" is. When I used the word, I had no intention of constraining it in any way. (...) If you insist on constraining the meaning of the word "thing", then give me a word to use which is not so constrained. (...) If your explanation refers to "infinite numbers, complex numbers, or even uncomputable numbers", those are certainly things which can be referred to! I can label those references 1,2 and 3. I can label any reference with a number!"

Dick, can you define the term 'number' for me? I only ask it because we obviously have entirely different concepts of what a number is.

Let me explain. The term 'number' is built on a set of axioms (called Peano's axioms). Whenever we speak of the term 'number' and attach the concept to a 'thing', we are assuming that Peano's axioms are true. For example, if Peano's axioms are meaningless with regard to Ultimate Reality, then so - ultimately - is the concept of numbers. If numbers are meaningless with regard to Ultimate Reality (mentioned in (5)), then (6) is meaningless.

Now, how do you know that Peano's axioms are true with regard to Ultimate Reality? How do you know the word true is even meaningful with regard to 'Ultimate Reality'?

Warm regards, Harv

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