I'm going to say he's an INFj.

I think Socrates is an ENTp actually and it would make sense that they shared some common views but I bet ya there were some fundamental differences.

He was a minimalist as many INFjs tend to be. He didn't seem to want to even consider improbable possibilites. An ENTp, while not seriously considering them, would never actually rule them out completely.

I'd say that puts him the 'j' category definately. Just his view in combination with the 'j' I would say indicates more of an intovert. I say intuitive because his beliefs do have some merit, just too narrow and focuses what is known rather than questioning what is unknown.

While it might work much of the time, oversights would inevitably happen. He also seemed to be a bit of a non-conformist.