1. If we're not justified to believe the Bible was inspired by a morally perfect God, then we're not justified to think it's reliable.
2. If we're not justified to believe God is morally perfect, then we're not justified to believe the Bible was inspired by a morally perfect God.
3. If God is not recognizably good, then we're not justified to believe God is morally perfect.
4. If we're rational to believe that God damns those he could have saved without violating their free will, then God is not recognizably good.
5. If it is rational to believe Calvinism, then we're rational to believe God damns those he could have saved without violating their free will (analytic truth).
6. If it is rational to believe in Calvinism, then God is not justifiably good.
7. If it is rational to believe in Calvinism, then we're not justified to believe God is morally perfect.
8. If it is rational to believe Calvinism, then we're not justified to believe the Bible was inspired by a morally perfect God.
9. If it is rational to believe Calvinism, then we're not justified to think the Bible is reliable.
10. We are justified to believe the Bible is reliable.
11. Therefore, it is not rational to believe Calvinism.
I: We are justified to believe the Bible was inspired by a morally perfect God. R: We are justified in thinking the Bible is reliable. M: We are justified to believe God is morally perfect. G: God is recognizably good. D: We're rational to believe that God damns those he could have saved without violating their free will. C. It is rational to believe Calvinism
1. ~I --> ~R
2. ~M --> ~I
3. ~G --> ~M
4. D --> ~G
5. C --> D (analytic truth)
6. C --> ~G (4,5, HS)
7. C --> ~M (3,6, HS)
8. C --> ~I (2,7, HS)
9. C --> ~R (1,8 HS)
10. R (axiom)
11. ~C (9,10, MT, DN)
I'll make a few observations:
1. The argument is valid in sentential logic. So what. I don't think his formalization is really going to capture the logic of the argument. There's all manner of modal terms that need epistemic logics to capture what's going on. The terms like 'rational' and 'justified' and 'believes' and 'think' are going to require a more powerful logic, like epistemic logic (as I said). Why would we need a more powerful logic? Look what happens in simpler logics when we present this argument
 Lois Lane believes that Clark Kent like coffee.
 Clark Kent = Superman.
 Therefore, Lois Lane believes that Superman likes coffee (by identity elimination).
Looks pretty good on some logics. So what. It wouldn't be if we formalized it with more powerful logics. The problem here comes in how we'd capture modal terms like 'believes that'.
2. As it stands, premise (1) seems false. Suppose there was a book that fell from heaven containing the answers to every weekly lottery. Suppose it has been right for every lottery since the first. Week after week. Pretty darn reliable. Suppose further that we found this line in the book, "Women should be treated like chattel, beaten if needs be." Not morally perfect. Here's the question: If Walls found the book, would he play next week's lottery? Yes. Why? Because he would believe that the book was reliable. So premise (1), as stands, seems to be a non-sequitur.
3. Premise (2) seems to be a tautology, i.e., "If we're not justified to believe [that the God who inspired the Bible] is morally perfect, then we're not justified to believe the Bible was inspired by a morally perfect God," simply expresses the truism that if you're not justified to believe that F is G, then you're not justified to believe that something that exists was created by an F that is a G. So (2) is uninteresting and, putting aside some other quibbles, we'll grant it.
4. I take (3) to be false. It seems to confuse epistemology with metaphysics. Why think what I (fail to) recognize is a valid indication of the way reality is? As a crass example, could I reason: if the stick is not recognizably straight, then we're not justified in believing that it is straight? What if it's half-way in water? Moreover, throw in our sin and desire to distort the nature of the true God, this premise seems even less firm. (3) needs to fill out the argument between the conditional. For one may not understand why God allows some evil, and be unable to recognize him as good, yet may still be justified in believing he is morally perfect by taking it on, say, the testimony of Scripture. Here one would appeal to models of knowledge by testimony. Here's an analogy: I grew up with a kid who was about 6 inches shorter than his peers and 20 lbs lighter. However, he could bring some fury. He was not a recognizable bad-a. But if the toughest kids on the block told a new kid not to mess with Carlos, the new kid would be justified in believing Carlos was a bad-a, even if Carlos was not a recognizable bad-a.
5. Of course, I deny (4). The sinner is a guilty criminal and deserves his punishment. Even if I grant (see #6) that God could save everyone if he wanted to, it doesn't follow that if he doesn't he is morally bankrupt somehow. If a governor allows a guilty and convicted child murderer to die by lethal injection even though he could save his life, is the governor morally suspect?
6. Of course, (5) this isn't an "analytic truth." The truth is not guaranteed by the collective meanings of the words in which it occurs. Moreover, I happen to think it may be false. In order to manifest God's holiness and justice in any created theatre, God may need to damn some actually guilty. So, (5) is not analytic and it may also be false.
7. Of course, the argument is reversible. Walls thinks that what us humans think of and call good is a pretty reliable indicator of what is in fact good. So, this would apply to a man who knows that his neighbor is going to murder his wife, the man can stop the murder, but the man refuses to do nothing (say, out of respect for the neighbor's libertarian free will). We would call this man morally depraved. But God does this all the time.
Moreover, it appears that God can stop people from sinning without violating their libertarian free will (cf. Gen 20:6), on Arminian assumptions. However, if God did violate Abimelek's free will, he could do this to others, and it appears to be a pretty inconspicuous acting on God's behalf. So what would be the loss of interfering with people's free will, especially for heinous sins? Abimelek didn't even know anything was up. Why did God stop Abimelek from "touching" Sarah but not the molester from touching "Susie?" What's the reason? However, aside from this, we might wonder why not violating free will is all-important? Let's see, the molester's libertarian freedom or little Susie's innocence. Indeed, we might wonder why a God who allows some people to "freely" go to hell when he could have stepped in and changed their will and made them "compatibilistically freely" choose him is considered more loving than one who would step in. I don't know, intuitions differ. Certainly thousands of Universalists don't "recognize" this God as good. So, there's several actions we could point out about Wall's God that doesn't seem to make him "recognizably" God, and so the argument turns on Walls. Yeah, he'll come up with his responses, just like the Calvinist does.