- #1
arupel
- 45
- 2
I can readily accept that the Godel sentence The theorem is that "This theorem is not provable" can be expressed in the language of Peanno Arithmetic.
2. Godel on the other side of a correspondence with the above, first translates the Godel sentence using the Godel numbering system
3. Having done this he translated the entire Peanno statement to the Godel numbering system.
This whole statement I think can be called a double diagonalization, in the sense that this is used in this content.
People use the diagonalization of numbers as an analogy to Godel's statement.
1. I cannot understand how translation of the Peanno statement to Godel's numbering system is diagonalization.
2. How does this procedure proves that the Godel sentence is neither provable and not proveable?
Thanks
2. Godel on the other side of a correspondence with the above, first translates the Godel sentence using the Godel numbering system
3. Having done this he translated the entire Peanno statement to the Godel numbering system.
This whole statement I think can be called a double diagonalization, in the sense that this is used in this content.
People use the diagonalization of numbers as an analogy to Godel's statement.
1. I cannot understand how translation of the Peanno statement to Godel's numbering system is diagonalization.
2. How does this procedure proves that the Godel sentence is neither provable and not proveable?
Thanks