klein/stevin toward the divided line

by metalogike

They were speaking of Stevin’s analogy of zero to the geometrical point. “A valid analogy indeed,” said one, “but only one analogy. There is another, and if there is another, then perhaps there must be others…”

“You are thinking first of the one Stevin rejected, perhaps?” recalled the other.

“Yes”, replied the one, “the analogy of the point to the one, in which he saw the fault of the Greeks.  That he found it necessary to reject that one shows all-too-clearly his devotion to one all, even if its ground be shifted, to rest on zero rather than one.”

“A strange objection, if it is an objection,” said the other. “Do you point to the incompleteness of Stevin’s analogy? For that objection would seem empty, incompleteness being the condition of sense. Your pointing to it, as if there were another alternative, would be unjust.”

“No indeed”, replied the one.  “It is not the filling-in or filling-out of the analogical space that I have in mind, and the pathos of being unable to do so is banal. I have in mind rather the cause you have pointed to with your image of pointing – and with that you have opened a second and much deeper level of incompleteness. For where there are truly two analogies there is also an index.