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One Should Be Careful!

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Posted by Richard D. Stafford, Ph.D. on March 15, 2001 14:41:10 UTC

I had always been a little bothered by what Godel was reputed to have proved as I had never actually seen his proof. A couple of years ago, I came across an English translation of his original proof in the local Barnes and Nobel bookstore. So I bought it and went through it very carefully.

Because I am not particularly bright, I often find things very difficult to understand. For this reason, I proceeded through his proof line by line making sure I not only understood exactly what each line said but could also come up with real examples which would defend the accuracy of the given statement. It was slow going but I did finally get to the crux of the matter (sufficient to convince me that I understood his proof).

Essentially, what he proved was that it is always possible to say, "this statement is false", in any completely closed logical construct where everything is internally defined (i.e., in any "language", even mathematics). I already knew that! I thought everybody did. It is my opinion that the trouble with many "experts" is that they often get so abstract with their deductions that they don't really know what they are talking about!

That is the true power of abstract logic: it is capable of carrying our deductions far beyond those relations we can comprehend directly on a conscious level. However, when we use that great power of abstract reasoning, we must be careful that the real meaning of our conclusions is not buried in abstract generalization beyond our comprehension.

Reliance on experts is a very dangerous mode of obtaining belief! I do not even suggest you believe what I have said; get a copy of the proof yourself and make sure you understand exactly what he has done!

Everything here is just an opinion you understand: I have lots of those!

Have fun -- Dick

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