John Calvin Commentary Hebrews 9:13

"For if the blood of goats and bulls, and the ashes of a heifer sprinkling them that have been defiled, sanctify unto the cleanness of the flesh:" — Hebrews 9:13 (ASV)

For if the blood of bulls, etc. This passage has caused many to go astray, because they did not consider that it speaks of sacraments, which have a spiritual meaning. They interpret the cleansing of the flesh as something effective only in human society, just as the pagans had their expiations to erase the disgrace of crimes. But this explanation is indeed very pagan-like, for it does injustice to God’s promises if we restrict their effect to civil matters only.

This declaration often occurs in the writings of Moses: that iniquity was expiated when a sacrifice was properly offered. This is undoubtedly the spiritual teaching of faith. Besides, all the sacrifices were destined for this purpose: to lead people to Christ. Just as the eternal salvation of the soul is through Christ, so these sacrifices were true witnesses of this salvation.

What then does the Apostle mean when he speaks of the purgations of the flesh? He refers to what is symbolical or sacramental, as follows: if the blood of beasts was a true symbol of purgation, so that it cleansed in a sacramental manner, how much more will Christ, who is himself the truth, not only testify to a purgation by an external rite, but also truly perform this for consciences? The argument then is from the signs to the thing signified, for the effect long preceded the reality of the signs.