Penal Substitution = Universal Salvation?

One  objection to penal substitution is that implies universal salvation, and we know that’s not right. According to Steve Jeffery, Michael Ovey and Andrew Sach in Pierced for Our Transgressions: Rediscovering the Glory of Penal Substitution, the argument can be laid out something like this: 

(a) According to penal substitution, Jesus’ death fully pays the debt of those for whom he died.

(b) Jesus died for all people.

(c) From (a) and (b) it follows that Jesus’ death fully pays the debt of all people. 

(d) But the Bible teaches that some people will pay their own debt in hell.

(e) From (c) and (d) it follows that God is unjust, for in hell he demands payment for a debt already paid in full by Christ. In other words, he punishes the same sin twice.

(f) This conclusion (e) is unthinkable, and so we must reject penal substitution (a) on which the whole argument rests.

But rejecting penal substitution (a) is not the only way out of this “unthinkable” conclusion (f). We could reject universal redemption (b) instead, and that’s what some—me, for instance—do.

Of course, those who reject universal redemption don’t do it simply to “prop up penal substitution.” 

Rather, particular redemption was part of the fabric of Reformed theology in the sixteenth and seventeenth centuries, and only when this was denied did some become uncertain about penal substitution.

There are, however, many people who hold to both penal substitution and universal redemption without holding to universal salvation. I’m guessing they just affirm it all without thinking too much about how it fits together. But traditional Arminians usually do reject penal substitution, holding to a governmental theory of the atonement, and the argument above is one of the reasons.