Godel’s result about incompleteness COULD mean just that PA is inconsistent.
It would be an interesting way for the incompleteness theorem to be fulfilled. And become quite obsolete at the same time also. Except maybe as an early warning or sign that something is deeply wrong with PA.
Sure, that could be the case but that still is a much weirder situation than what Khoth is talking about. (Also, note that Godel’s theorems apply not just to PA but to the much weaker system of Robinson arithmetic so if there is an inconsistency it is probably happening at an even more fundamental level.)
I am skeptic about any infinity. I am not sure, if it is (always) paradoxical. But a theory which relates to an infinity related axiom is most likely too rich.
The concept of infinity and the concept an (infinite in any sense) god are both too ambitious for this finite world. But very persistent as we see.
Godel’s result about incompleteness COULD mean just that PA is inconsistent.
It would be an interesting way for the incompleteness theorem to be fulfilled. And become quite obsolete at the same time also. Except maybe as an early warning or sign that something is deeply wrong with PA.
Sure, that could be the case but that still is a much weirder situation than what Khoth is talking about. (Also, note that Godel’s theorems apply not just to PA but to the much weaker system of Robinson arithmetic so if there is an inconsistency it is probably happening at an even more fundamental level.)
Robinson’s arithmetic is still an infinite one. That could be the root of all evils.
How do you feel about the infinite cyclic group?
I am skeptic about any infinity. I am not sure, if it is (always) paradoxical. But a theory which relates to an infinity related axiom is most likely too rich.
The concept of infinity and the concept an (infinite in any sense) god are both too ambitious for this finite world. But very persistent as we see.