John Calvin Commentary 1 Corinthians 10:18

"Behold Israel after the flesh: have not they that eat the sacrifices communion with the altar?" — 1 Corinthians 10:18 (ASV)

Behold Israel after the flesh. He establishes this by another example, showing that the nature of all sacred observances is to bind us in a kind of fellowship with God. For the Law of Moses admits no one to a feast upon a sacrifice except the person who has properly prepared himself. I speak not only of priests, but also of those among the common people who eat the remains of the sacrifice. Therefore, it follows that all who eat the flesh of the sacrificed victim are partakers with the altar—that is, of the sanctification with which God has set apart His temple and the sacred rites performed in it.

This expression, after the flesh, may seem to have been added so that the Corinthians, by comparing the two, might place a higher value on the efficacy of our Supper. “If there was so much power in the ancient figures and in those elementary principles of their early instruction, how much more must we consider there to be in our mysteries, in which God reveals Himself much more fully to us!” At the same time, it is simpler, in my opinion, to say that Paul intended merely by this mark to distinguish the Jews who were still under the Law from those who had been converted to Christ.

Now, a contrast remained to be made: if the sacred rites appointed by God sanctify those who observe them, then, on the other hand, pollution is contracted from the sacred rites offered to idols. For it is God alone who sanctifies, and therefore all strange gods pollute.

Again, if mysteries unite and connect believers with God, it follows that the wicked are, in the same way, introduced by their superstitious rites into fellowship with idols. But the Apostle, before proceeding to this, answers by an anthypophora (anticipation) a question that might be raised as an objection.