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Gödel's Proof
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Gödel's Proof
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Bill's
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Feb 01, 2019 11:36AM
This is our book discussion for Feb 2019.
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Wonderful book ! Clear, well written and concise. A basic grounding in mathematics would be good to read this book but with some help from the net I don't think this is a problem.For some reason after I finished the book - I kept remembering the Heisenberg uncertainty principle and Schrodinger's cat !
Weird !
There is only one problem I have with Goedel's proof as explained in the book. It assumes that you can actually construct a G statement along the lines described in the proof in PM, but as far as I'm aware there is no guarantee that such a G statement can be written down in finitude. In fact, the number denoted by sub(n, 17,n) itself looks like it needs to have a greater Goedel number than n, which is by definition the Goedel number of the entire G statement! And it appears to me that you would encounter the same problem regardless of what formal system you use. Using the sample PM the authors introduce would get you stuck writing the statement ad infinitum!
Weird indeed. :)
