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Sounds good! The last para particularly is promising. Could you expand it?
– Rushi
Commented Apr 6 at 9:18
Tnx the link is garbled but I think its this haimgaifman.net/wp-content/uploads/2016/07/22odel-to-kleene.pdf?? I'll take a look
– Rushi
Commented Apr 6 at 12:22
We can clearly see the symmetry of columns and rows in a 2D array of binary digits. The nature of the potential infinity of the strings in both directions should obviously be the same (I am talking about the strings themselves with no reference to any semantic 'meaning' attributed to them). Therefore, their 'completion' must stand or fall together...and by the diagonal argument they cannot be complete. Supposedly, Russel got his idea for his famous paradox while considering Cantor's proof...see haimgaifman.files.wordpress.com/2016/07/22odel-to-kleene.pdf
– 21stCenturyParadox
Commented Apr 6 at 12:26
Yes, If you search 'Gaifman Naming' you will find links. In it is one of my favorite quotes: "Peano [1906] classified the paradox as linguistic, not mathematical, a view that is more or less accepted nowadays: ‘definition’, it is argued, is relative to language and the definition of g is carried out in a language that is on a higher level than the language whose definitions were previously enumerated. What is overlooked in such accounts is the fact that the argument from linguistic levels and the argument from circularity are two sides of the same coin."
– 21stCenturyParadox
Commented Apr 6 at 12:29
Thank you very much for this excellent answer. I have to read your links. The quote from Wittgenstein is hard to understand for me. I remember that before dozen of years I tried to read philosophical remarks from this author and he gave an example "can you imagine a man coming to you and saying that he comes from an infinitly far point.
– kouty
Commented Apr 6 at 18:26

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