There's this battle of words that I have observed. "Faith teachers" say "1 Pet 2:24 refers to physical healing because it quotes Isa 53:5 'by his stripes we are healed'" and then the "old school" teachers respond by saying, "no, this refers to sins, because it says 'sins' right there in that same verse."
Well, first of all, we are not "healed" of our sins. We committed sins, but they were pardoned (not held against us), so we are exempt from the final judgment and wrath of God to come. We are "healed" of our afflictions (not forgiven of our afflictions). The sins are our fault, no matter how much the devil tempts us to commit them; the afflictions are the devil's fault, no matter how much we open ourselves up to allow and accept them. Both are paid for.
But it isn't "either/or." The first part of 1 Pet 2:24 addresses sins, as the first part of Isa 53:5 does, and the second part of the same verse addresses healing, as the last part of Isa 53:5 does.
Isaiah 53:3-4 (the two previous verses) is about Jesus bearing our sorrows, griefs, pains, illnesses, sicknesses, diseases, all the affliction of the devil, and is what is quoted in Matt 8:16-17. These speak only of our physical and other afflictions.
Isaiah 53:5 is about the whole deal. Literally, "and-he being-wounded from-transgressions-of-us being-crushed from-depravities-of-us discipline-of well-being-of-us on-him and-in-wound-of-him he-has-been-healed to-us."
The four things cited in Isaiah 53:5 are "transgressions" (i.e. breaking the law in a legal sense), "depravities" (i.e. actions and attitudes done from evil motives), "discipline" (like the "rod of correction" that we use on our children to inflict pain that results in their well-being or peace), and lastly our "healing."
What "healing"? Well, the previous two verses (verse 3 and 4) just explained that (as does Matt 8:16-17, which quotes them).
So, Jesus took upon himself our transgressions, our evilness, the pain that God would otherwise have used to chastise (force) us into obedience, and our physical and spiritual oppression.
The context of 1 Pet 2:18-24 is about slaves obeying their masters, including despite being mistreated (would typically be beaten) by their masters. He exhorts the slaves to make sure that they are suffering for doing good, not wrong, as Jesus did (1 Pet 2:20-23). Then he proclaims both Jesus' payment for sins and healing in verse 24.
So, 1 Pet 2:24 covers both sins (what would be our fault), and affliction (the unjust oppression of the "evil" one on us), just like Isa 53:5 does. Because our sins are paid for, we live for righteousness; because our afflictions are paid for, we are healed.
In context you can see all four points of Isa 53:5 in 1 Pet 2:18-24. Transgression, evilness, foolishness/childishness that would have evoked painful discipline, and the effect of physical abuse at the hands of the evil/unjust one. The slave would be able to see all four points in his own experience, and therefore how Jesus took care of the whole deal.
So, because the slave's sins are taken care of, (and the master's, for that matter,) they live for righteousness. Because the slave's just or unjust afflictions at the hands of their master are taken care of, healing is theirs. Both the sin problem and the physical mistreatment problem are taken care of, spiritually and physically, in 1 Pet 2:24.
So, 1 Pet 2:24 addresses both the sin problem and healing. And you can see the aspects of evilness problem and also chastisement covered in the context, as well.
[Note: Do not make this into some kind of "4-thing atonement" doctrine. I am simply showing how the points of 1 Pet 2:18-24 relate back into the points of Isa 53:5. There are even more parallels that you can get out of this if you read all of Isa 53:3-12 and compare with 1 Pet 2:18-25.]
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