It is a well-understood principle in Jewish thought that while the Temple is no longer standing, our prayers and acts of charity serve as equivalents to the offerings that were brought in the Temple.
How can we understand this? Are we saying that the sacrificial service has been replaced or superseded by prayers and charity? No; but prayers and charity, when properly done, accomplish some of the same ends as the offerings.
Were the sacrificial offerings ever meant to take away sin? According to the letter to the Hebrews, no.
"It is impossible for the blood of bulls and goats to take away sin." (Hebrews 10:4)
If not, then what did they do?
"Temple and Offering do not in themselves bring about the grace of G-d, but are only to be, and only wish to be, means of showing the way to gain the grace of G-d." (Rabbi S.R. Hirsch)
If offerings are symbolic, then we have to ask ourselves: What message was the offering was supposed to impress on our minds and hearts? And the next question is: can we continue impressing this message on our minds and hearts even when we no longer have the ability to bring the offering?
The essential point when someone brings an offering is faith, the acknowledgement of the symbolism of the offering, and the subjection of the heart to G-d.
"The sacrifices of G-d are a broken spirit: a broken and a contrite heart, O G-d, thou wilt not despise." (Psalm 51:17)
These acts of the heart, made concrete by a physical act, can be mirrored in our prayers (subjecting our heart) and in charity (using our bodies and possessions in accordance with His will).
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