Rabbi Eliezer offered an additional proof that "eye for an eye" means monetary compensation. His argument is an a fortiori — a kal va-chomer — that he considered logically airtight.
The Torah states in (Exodus 21:30): "When kofer is imposed upon him, he shall give the redemption of his soul." Kofer means an atonement payment — ransom money paid by the owner of an ox that killed someone. This is a case where the Torah explicitly requires a death penalty (for the owner whose ox killed), yet allows monetary payment as a substitute.
Now reason from the greater to the lesser: if in a case where Scripture makes the offender liable for death, he can escape by paying money — then in the case of blinding an eye, where Scripture does not impose a death sentence at all, how much more obvious is it that he pays only money!
Rabbi Eliezer's argument is elegant in its simplicity. The ox-owner faces death but pays money instead. The person who blinds another does not face death. If the more severe case is resolved with money, the less severe case must certainly be resolved with money. There is no logical space for physical retaliation to operate. The Torah's own system of graduated penalties makes monetary compensation the only consistent interpretation of "an eye for an eye." Anything else would mean that a lesser offense receives a harsher punishment than a greater one.