A Correction to a Penal Substitution Syllogism

I came across this syllogism by Tom Schreiner in his chapter on penal substitution in the IVP 4 views book on the atonement. It goes like this:

[1] One must obey the law perfectly to be saved.

[2] No one keeps the law perfectly.

[3] Therefore, those who rely on the works of the law to be saved stand under God’s curse.

But this is invalid. Here’s how the first two premises look more formally

[1] Necessarily, for any x, if x obeys the law perfectly, then x will be saved.

[2] There is no x such that x obeys the law perfectly.

It does not follow from these two premises that [3] those who rely on the works of the law to be saved stand under God’s curse. For if someone were to rely on it and obey it perfectly, they would be saved. That is just what premise [1] claims. Instead, the argument should look like this:

[1*] Anyone will be saved who obeys the law perfectly.

[2] No one keeps the law perfectly.

[3*] Therefore, no one will be saved.

Nonetheless, [3*] is not equivalent with

[3] Those who rely on the works of the law to be saved stand under God’s curse.

For it is not the case that

[4] No one will be saved if and only if those who rely on the works of the law to be saved stand under God’s curse.

Premise [4] is a conjunction of which one of the conjuncts contains:

[5] If those who rely on the works of the law to be saved stand under God’s curse, then no one will be saved.

And [5], according to Galatians, is obviously false. The antecedent is true and the consequent is false, because there are some who are saved by virtue of faith in Christ. Perhaps what is needed to get to make [3] equivalent with [3*] is another premise that states, “If everyone relies on the works of the law to be saved and not on Christ, then no one will be saved.” That would do the trick, but then that seems to be precisely what Paul is arguing for, so to assume this premise would make the argument circular. But at least it would not be invalid (circular arguments are true after all).

UPDATE: A Correction to “A Correction to a Penal Substitution Syllogism”

In the text above, I contended that the the first premise read like this:

[1] Necessarily, for any x, if x obeys the law perfectly, then x will be saved.

But I was wrong. After reading it more carefully, it actually reads like this:

[1] Necessarily for any x, x is saved only if x obeys the law perfectly.

Premise [2] is still right:

[2] There is no x such that x obeys the law perfectly.

Thus, it still doesn’t follow that

[3] Those who rely on the works of the law to be saved stand under God’s curse.

All that follows is

[3*] No one is saved (that is, there is no x such that x is saved).

And I still think it is right to say that [3*] is not equivalent with [3], but upon further reflection I don’t see how to make [3*] equivalent with [3], so I retract the rest of what I say in the original post.

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