What’s Not Wrong with Jerry Walls’ Argument Against Calvinism

CASCADE_TemplateIn a guest post (here) on James Anderson’s blog Analogical Thoughts, Daniel Johnson, Associate Professor of Philosophy and co-editor of  Calvinism and the Problem of Evil, claims that a invalid argument lies at the heart of Jerry Walls’ new book Does God Love Everyone? What’s Wrong with Calvinism. I’m afraid that Dr. Johnson is quite mistaken on this point. Prof. Walls’ argument is demonstrably valid.

Johnson sets out Walls’ argument (from p. 30) as follows:

  1. God truly loves all persons.
  2. Not all persons will be saved.
  3. Truly to love somone is to desire their well-being and to promote their true flourishing as much as one properly can.
  4. The well-being and true flourishing of all persons is to be found in a right relationship with God, a saving relationship in which we love and obey him.
  5. God could give all persons “irresistable grace” and thereby determine all persons to freely accept a right relationship with himself and be saved.
  6. Therefore, all persons will be saved.

Johnson then lodges the following complaint:

Walls treats this argument like it is a logically valid argument. He calls it a “logical argument”… It is not. Walls must never have tried to formalize the argument and prove it valid; go ahead, try it – it cannot be done. It is a premise away from being a valid argument.

He goes on to say that unless Walls modifies his premise (5), “the Calvinist could consistently accept every single premise (all of 1-5) while denying the conclusion (6).” It’s even worse for Walls, since

Representing the argument in the body of the text – the argument without that (modified) premise – as a logically valid one when it clearly is not is an egregious philosophical mistake and amounts to an egregious misrepresentation of Calvinism and its philosophical options.

These are strong words. Since Jerry Walls is well known for his analytical precision—and not at all for making “egregious philosophical mistake[s]”—I  thought I would take up Prof. Johnson on his challenge to “go ahead, try it”—try to prove Walls’s argument is valid. “It cannot be done,” says Johnson. Well, let’s see.

Let the following values hold:

g =def  God
Bx =def  x has well-being.
Fx =def  x is truly flourishing.
Hx =def  x is a (human) person.
Sx =def  x will be saved.
Cxy =def  x can give irresistable grace to y.
Dxy =def  x desires the well-being of y.
Lxy =def  x truly loves y.
Pxy =def  x promotes the true flourishing of y as much as x properly can.
Rxy =def  x is in a right relationship with y.

Here, then, are Walls’ premises and conclusion once again–this time with their corresponding symbolizations:

  1. God truly loves all persons. (x)(Hx → Lgx)
  2. Not all persons will be saved. ¬(x)(Hx → Sx)
  3. Truly to love somone is to desire their well-being and to promote their true flourishing as much as one properly can. (x)(y)(Lxy ↔ (Dxy & Pxy))
  4. The well-being and true flourishing of all persons is to be found in a right relationship with God, a saving relationship in which we love and obey him. (x)((Bx & Fx) → Rxg)
  5. God could give all persons “irresistable grace” and thereby determine all persons to freely accept a right relationship with himself and be saved. (x)Cgx & (x)(Cgx → (Rxg & Sx))1
  6. Therefore, all persons will be saved. (x)Sx

The following deduction proves that Walls’ argument (as it stands) is valid:

snip20161011_4

A couple of things to note. First, premises (3) and (4) are actually unnecessary. You can deduce Walls’ conclusion from (1), (2), and (5) alone.  Johnson’s fuss about the ‘properly can’ locution—the one he finds in Walls’ footnote to premise (3), and which he thinks needs to be grafted into (5)—is therefore also unnecessary.

Second, contrary to what Johnson tell us, we don’t have to alter premise (5) at jot, in order for the argument to come out valid. It’s simply not true, therefore, that (as things in fact stand) “the Calvinist could consistently accept every single premise (all of 1-5) while denying the conclusion (6).” She can’t. The above deduction settles that. Of course, the Calvinist may well want to challenge the truth of (1), (2), or (5), but that’s another matter. The present point is: Jerry Walls is guilty of no “egregious philosophical mistake” in claiming that his argument is logically valid. And that’s because it is.2

Notes

  1. Here I’m treating ‘x freely accepts a right relationship with God’ as a stylistic variant on ‘x is in a right relationship with God’.
  2. This article has been reposted by the ‘Society of Evangelical Arminians‘ (October 11, 2016) here.

Interested readers may also wish to consult ‘The Calvinism Files‘ — a series of 8 posts on the coherence of Calvinism.

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65 comments on “What’s Not Wrong with Jerry Walls’ Argument Against Calvinism

  1. I’m certainly not going to attempt to symbolize the logic myself (at least not publicly), but I think the full argument might be found here (http://evangelicalarminians.org/jerry-l-walls-why-no-classical-theist-let-alone-orthodox-christian-should-ever-be-a-compatibilist/), starting on page 95. I didn’t see anyone link to it.

    It’s a bit late to the party, but this might resolve some of the issues?

    I do have Jerry’s book, and I think he does deal with some of the objections presented here in the text in a less formal manner. I have been following the discussion with interest.

    • Rich Davis says:

      Thanks, Andrew!

      Even a quick glance reveals that *this* is the argument we should have been focusing our attention on all along. The argument I originally symbolized is obviously the popular short summary of the longer, more detailed 15 step proof. I should have taken the time to get clear about that from the beginning.

      My apologies to Jerry!

    • Andrew, I did in fact link that original paper of Jerry’s (it is the first volley in the exchange between him and Cowan/Welty that I mentioned). As far as I can tell the argument there is valid (or at least it doesn’t have the invalidity I mentioned). The objections I mentioned turn into objections to premise 19 in that argument. Cowan and Welty lay all of that out, which is why I said that I wasn’t adding anything of substance to their discussion. The reason I criticized Walls in the first place wasn’t that I didn’t think he could give a valid version of the argument; it was that he was misrepresenting the Calvinist’s options by not giving a valid version in that particular book and leaving out precisely the premise that the Calvinist would reject. The fact that he had a valid version actually makes that problem worse, I think.

    • Rich Davis says:

      I think ‘misrepresent’ is far too strong here. If I fail to represent X, it doesn’t automatically follow that I’ve falsely represented X.

      • “If I fail to represent X, it doesn’t automatically follow that I’ve falsely represented X.”

        That’s true. But by representing the argument as valid, he represented the Calvinist’s options as limited to denying one of the premises 1-5. (In the context, he clearly implies that the Calvinist has to deny a premise.) But the Calvinist’s best option (and the one a philosophically sophisticated Calvinist will take nearly every time) is actually to accept all the premises and deny that the conclusion follows. So he did misrepresent the Calvinist’s options.

      • Rich Davis says:

        I guess we’ll have to agree to disagree. I think it’s important to cleave to the principle of charity here. The popular level work should be viewed in light of the more detailed and sophisticated presentation. (For example, we read ‘God, Freedom, and Evil’ through the lens of ‘The Nature of Necessity’.) We should resist charges of misrepresentation whenever possible. And in this case, it’s possible.

  2. […] offered that argues that Walls’ argument is mistaken. However, a more recent post argues that Walls’ argument is sound and Calvinism is false. Yet another more concise post argues that Wall’s argument is mistaken […]

  3. James says:

    One further comment, which may be relevant for ongoing discussion of Walls’ argument:

    It seems to me that the “irresistible grace” business in premise 5 needlessly complicates the argument. Why not simply say that Calvinism entails that for any human S, God can ensure (or has the power to ensure) that S will be saved? (Add any suitable qualification about S coming to be saved freely, not being coerced, etc.)

    Adopt the following definition:

    Sxy =def x can ensure that y will be saved (where y ranges over possible humans).

    Then presumably Walls holds that Calvinism is committed to:

    (x)Sgx

    It’s worth noting, however, that it doesn’t follow from (x)Sgx that for any set of possible humans, God can ensure that *every member* of that set will be saved. Or more simply:

    (x)Sgx

    does not entail

    (x)(y)(Sgx & Sgy)

    Perhaps Calvinism is also committed to the latter claim; perhaps not. Either way, that seems relevant to the kind of argument Walls’ wants to level at Calvinism.

    • Chris Menzel says:

      (x)Sgx does entail (x)(y)(Sgx & Sgy) — if it’s true that, for every (human) person x, God can save x, then it’s true that, for every pair of persons x and y, God can save x and God can save y. I think what you are pointing out is that, from “for every person x, God can ensure that x is saved” it does not follow that “God can ensure that, for every person x, x is saved”. This is a well known “scope ambiguity” involving quantifiers and modal operators. I think we can formalize it in terms of the modal operator “◇” expressing “possibly” (which I believe is essentially what “can” contributes in your definition of “Sgx”). Then, letting “Hx” mean that x is human and “Egx” that God ensures that x is saved (so that we’ve pulled “can” out of your definition of “Sgx”), your observation, formalized, is that

      (1) (x)(Hx → ◇Egx)

      does not entail

      (2) ◇(x)(Hx → Egx).

      And, in standard first-order modal logic, that is true. This is especially clear when we express (1) and (2) in terms of possible world semantics: (1) says that, for each person x, there is a possible world in which God ensures that x is saved (and maybe some others, but, for all we know, maybe not) whereas (2) says that there is a possible world in which God ensures that every person is saved. It think that captures your point pretty well. (In fact, I still don’t think this formalization gets the situation *quite* right, but we’d need quite a bit more apparatus from modal logic to do so.)

      • Chris,

        Can you show me how (x)Sgx entails (x)(y)(Sgx & Sgy)? I ask because it seems easy to generate counterexamples. Here’s one:

        Sxy =def x can ensure that y is the first person to walk on the moon.

        Presumably (x)Sgx is true, but (x)(y)(Sgx & Sgy) is necessarily false (because only one person can be the first to walk on the moon).

        In any event, I agree with the remainder of what you say about the scope ambiguity. My point is that Walls needs to eliminate this ambiguity from his argument.

      • Chris Menzel says:

        James, you are assuming that x and y can’t be the same person. The semantics of first-order logic certainly allows that.

      • Chris Menzel says:

        James,

        Sorry, I was at lunch when I saw your post on my phone and I read it carelessly and responded hastily. My answer was not correct. Here’s the correct answer. You say: “Presumably (x)Sgx is true, but (x)(y)(Sgx & Sgy) is necessarily false (because only one person can be the first to walk on the moon)”. But your English rendering of “(x)(y)(Sgx & Sgy)” here is not correct. You are taking it to mean that, for any individuals x and y, God can ensure that *both* x and y are the first to walk on the moon. But that’s not what it says. It says that for any individuals x and y, God can ensure that x is the first to walk on the moon and God can also ensure that y is the first to walk on the moon. And that’s true.

        The problem here, once again, is that there is a modality smuggled into your definition of the predicate “S”, and that muddies the waters. Things are clearer if we make the modality explicit. So let’s define the predicate “F” such that

        Fzw = z ensures that w is the first to walk on the moon.

        So now, if we want to say that z CAN ensure that w is the first to walk on the moon, i.e., that it’s POSSIBLE that z do so, we need to use our modal operator “◇”. Doing so, we can make the distinction between the two readings in question more clearly. What you’ve written as “(x)(y)(Sgx & Sgy)” we now express as:

        (1) (x)(y)(◇Fgx & ◇Fgy),

        which says that for any any individuals x and y, it is possible that can ensures that x is the first to walk on the moon and it is possible that y is the first to walk on the moon; or in terms of possible world semantics, that there is a world in which God makes it the case that x is the first to walk on the moon and another where God makes it the case that y is the first to walk on the moon. That is clearly true (and clearly entailed by (x)◇Fgx). But this is not at all the same as saying

        (2) (x)(y)◇(Fgx & Fgy),

        i.e., that for any individuals x and y, it is possible that God ensure that *both* of them are the first to walk on the moon, i.e., that there is a possible world where God ensures that both x and y are the first to walk on the moon. And, as you rightly note, it is not entailed by (x)◇Fgx).

      • Chris,

        Your correction is correct. 🙂 I wrongly symbolized the point I was trying to make because of the concealed modality, and that took us down a sidetrack. But it looks like we agree about the original point.

      • Chris Menzel says:

        Not sure what happened after (1) there in my message, but I obviously didn’t proofread carefully. It should have read:

        What you’ve written as “(x)(y)(Sgx & Sgy)” we now express as:

        (1) (x)(y)(◇Fgx & ◇Fgy),

        which says that for any any individuals x and y, it is possible that God ensures that x is the first to walk on the moon and it is possible that God ensures that y is the first to walk on the moon…

    • Rich Davis says:

      James,

      Just thinking about Chris’

      (2) ◇(x)(Hx → Egx)

      and setting aside (1) altogether: what might be the (or a) reason a Calvinist might have for denying (2)? Your “perhaps not” hints that the Calvinist could have grounds for denying (2).

      • Rich,

        I don’t have a specific reason in mind. I’m only observing that there seems to be another logical gap in Walls’ argument: put simply, that God can save *anyone* doesn’t entail that God can save *everyone*. Thus if the Calvinist is committed to the former, it doesn’t immediately follow that he’s committed to the latter. If Walls thinks he’s committed to the latter (which appears essential to his argument against Calvinism) I’d say the burden lies with him to establish that. (Just for the record: I’m a Calvinist and I affirm both; but that’s irrelevant to the *logical* point I’m making here.)

        However, let me throw something further out. On the Calvinist view, people aren’t saved in isolation from their circumstances and their relationships with other people. God uses *means* to bring people to saving faith. Thus the salvation (or non-salvation) of one person may have significant implications for the salvation (or non-salvation) of another person. For all we know, in every possible world in which some people is saved, at least one person is left unsaved.

        All this to say, a Calvinist *could* respond to Walls by arguing it’s *epistemically possible* that there are no possible worlds in which God creates humans and all humans are saved. (There can be variations on this defense, e.g., it’s epistemically possible that there are no possible worlds in which God creates *a large number* of humans and all humans are saved.)

      • Rich Davis says:

        James,

        I’m intrigued by the defensive strategy you’ve proposed for resisting the inference from

        (a) God can save anyone—i.e., (x)◇Sgx

        to

        (b) God can save everyone—i.e., ◇(x)Sgx.

        As you and Chris note, (b) doesn’t follow modally from (a). And that’s fair enough. But there is also a system dependent reason, you suggest, for the Calvinist to deny this inference. Since (on Calvinism) “people aren’t saved in isolation from their circumstances and their relationships with other people,” it follows that

        (DS) It is epistemically possible that there are no possible worlds in which all humans are saved

        in which case (once again) the ‘anyone-to-everyone’ inference runs aground.

        Now here I’m inclined (at first glance) to agree with you: (DS) is true. I’m not sure, however, that just any and every Calvinist can avail himself of this defense. For suppose I not only affirm

        EVERYONE: ◇(x)Sgx

        but also claim to *know* that it’s true. In that case, I can’t affirm (DS); for there is something I know—namely, EVERYONE—that contradicts what (DS) says is true *for all I know*. For the proposition *There are no possible worlds in which all humans are saved* does contradict something I’m claiming to know. It contradicts EVERYONE. Hence, the proposition (DS) says is epistemically possible for me actually *isn’t*.

        If this line of reasoning is in order, a Calvinist may avail himself of (DS), but only if he lacks sufficient reasons—system dependent or otherwise—for knowing EVERYONE.

      • Rich,

        Well, sure — any Calvinist who knows (or claims to know) EVERYONE can’t consistently affirm (DS). I’m not sure why this would offer much consolation to Walls. After all, his argument is supposed to refute *Calvinism*, not merely the belief-systems of some Calvinists. Regardless of whether some Calvinists know (or claim to know) EVERYONE, Walls still needs to establish that Calvinism *as such* is committed to EVERYONE, either explicitly or by implication.

      • Rich Davis says:

        Hi James — in relation to

        EVERYONE: ◇(x)Sgx (translation: “there is a possible world in which God saves everyone”)

        you remark:

        “Well, sure — any Calvinist who knows (or claims to know) EVERYONE can’t consistently affirm (DS). ”

        But don’t we all know that EVERYONE is true? Think of a world W*, e.g., in which God creates but a single individual–Adam, let’s say–and then gives Adam irresistible grace. In W* Adam (and thus everyone) is saved. I think we can see (and in fact know) that W* is a possible state of affairs; it’s certainly non-contradictory. But this state of affairs entails–and we can see that it entails–EVERYONE. So we know EVERYONE is true, in which case Calvinism *does* materially imply this proposition.

        It therefore seems to me that the Calvinist cannot make use of (DS)–the defensive strategy you propose for evading Jerry’s conclusion.

  4. Chris Menzel says:

    From my comments on Jerry’s Facebook wall. Sorry if this repeats anything above that I missed:

    I’m afraid there are some problems with both the formalization and the proof here. First, as the blog notes, premises 3 and 4 are never used. That alone should have been enough of a red flag to suggest that perhaps there are problems with the formalization. But premise 1 isn’t used either. So clearly there is something amiss here. Second, those intermediate steps 6-9 are simple logical equivalents of premise 2 that just clutter the proof and could be avoided just by using 9 (formalizing “Some human persons won’t be saved”) to start with as the second premise. However, even premise 2 in the proof is a fifth wheel. For the conclusion follows directly from premise 5 alone. Lines 10 and 11 follow from 5 directly, as in the proof. But now just instantiate 10 to Cga and 11 to Cga → (Rag & Sa). By modus ponens we have Rag & Sa and hence Sa. So by universal generalization, (x)Sx. (And note that this says that everything, including God, will be saved, which is not the conclusion of the original argument.)

    The heart of the problem is that the formalization of premise 5 is pretty clearly incorrect, as the premise (by virtue of the modal verb “could”) is a modal claim: Possibly, for all x, if x is human, then God gives x irresistible grace etc. Or perhaps it’s of the form: For all x, if x is human, then, possibly, God gives x irresistible grace etc (though that reading probably isn’t strong enough). Or perhaps it’s of the form: Possibly, for all *actually existing* x, if x is *actually* (hence essentially) human, then x exists and God gives x irresistible grace etc (requiring, that is, an actuality operator). Whatever the exact form, the stuff inside the scope of the modal operator is never going to be able to interact with any of the other premises, and hence (assuming premise 5 isn’t superfluous) the argument can’t possibly be valid, unless at least some of those premises are taken to be necessary truths.

    *****
    In a followup I noted:

    In the longer version of the argument that I’m looking at now, I see Jerry includes a premise in which the modal claim entails a stronger non-modal claim which, in turn, can work with the other, non-modal premises. So there does indeed appear to be a premise missing, although I’m not sure it’s the one Johnson points to (which I think Jerry addresses in his longer argument).

  5. James,

    Regarding your point about Walls’s argument being similar to the logical problem of evil, I think he would agree with you. His point, I think, would be that this is just another problem for Calvinism. The way libertarians resolve the logical problem of evil and the logical problem of “not everyone is saved” would be similar—it would make use of the presence of libertarian free will. But, of course, libertarian free will is not available to the Calvinist (if they want to do anything beyond offering a mere defense to the problems).

    • James says:

      Paul,

      Actually, I see it in reverse. 🙂 Insofar as Calvinists have resources to resolve the logical problem of evil (basically varieties of the greater-good defense) they have resources to rebut Walls’ argument. The free-will defense is just a particular version of the greater-good defense. But Calvinists have their own greater-good defenses.

      • Right! 🙂

        I suspect Walls might say this is where the comparison between the two arguments breaks down. The “quasi-logical rules” that someone like Mackie uses to try and show that an omnipotent, omnibenevolent God would prevent evil fail in their task whereas the rules regarding what it means to love someone (Walls’s (3) and (4)?) succeed.

      • James says:

        That’s a revealing way to put it, Paul. From where I’m standing, Walls’ rules do indeed appear to be “quasi-logical rules” regarding what it means to love someone. I mean, are we supposed to regard them as *logical* rules (on a par with modus ponens, say)?

      • Paul, he doesn’t, though. In that footnote I quoted, he says explicitly that you can love someone and not will (in the sense of ultimately choose) their good, if there is some greater good which is incompatible with theirs. That’s why he only says that love requires that you will the good of the beloved if you “properly” can do so, where you only “properly” will the good of someone if it isn’t costing some greater good. So Walls himself admits that his argument only works if we assume that there is no greater good which metaphysically necessitates that some are damned. Why does he think there is no such good? All he says is that it seems intuitively obvious to him. That, needless to say, is not enough of an argument.

        What this shows, I think, is that the love argument, once you admit the qualifications on love that Walls himself allows, just collapses into the ordinary axiological problem of evil, which is really about divine goodness generally (a good being needs a good reason to allow bad stuff to happen), not love. All this talk of love is a red herring.

      • Hi James. I don’t think they would be on par with modus ponens, etc. since they seem to have more to do with what we mean by the term ‘loving’. That seems to be consistent with how Mackie used the phrase “quasi logical rules” in his “Evil and Omnipotence.” There he seemed to be saying something along the lines of, “If we say something is good, we mean it’s going to eliminate evil as far as it can.” Now maybe a “meaning” reading isn’t quite right, but I think it’s something close enough. For Walls, then, it’d be something like “If we say God is loving, we mean if he could give irresistible grace to everyone then he would.”

        With the logical problem of evil, those quasi-logical rules are exactly what Plantinga attacked, noting that we have good reason to think they are not necessarily true. Here there *is* a parallel as you originally suggested to me in that the Calvinist would likely also attack Walls’s quasi-logical rules.

  6. I think I messed up posting this additional reply; if I didn’t, I’m sorry for the double post:

    Actually, I just realized something: your symbolization of premise 5 actually renders ALL of the other premises superfluous. Premise 5 by itself entails the conclusion. Proof:

    1. (x) Cgx & (x)(Cgx → (Rxg & Sx)) Premise
    2. (x) Cgx 1, Simp
    3. (x)(Cgx → (Rxg & Sx)) 1, Simp
    4. Cga 2, UI
    5. Cga → (Rxa & Sa) 3, UI
    6. Rxa & Sa 4,5 MP
    7. Sa 6, Simp
    8. (x) Sx 7, UG

    My use of Universal Generalization on line 8 is justified because the constant “a” was introduced only through the use of Universal Instantiation.

    Am I missing anything here? I’m not using a program, so this is off the top of my head. It looks good to me, though.

    If your symbolization of premise 5 renders all of the other premises superfluous, then surely that is sufficient reason to find a different symbolization.

  7. Hi Rich, this is Dan Johnson, posting with my wife Sarah’s Facebook account, because I had to log in with Facebook to comment and I don’t have a Facebook account. (I think this is the very first time I’ve regretted that…). Anyway, thanks for this reply! This is exactly what I wanted from Walls or someone who could support him on this point; I’m glad someone took me up on my challenge. The nice thing about claims of validity is that we have some precise tools for evaluating them.

    The argument as you symbolize it is valid. And I agree with your interpretations of premises 1-4. With James, I think you haven’t properly interpreted premise 5 in your translation from English into predicate logic. Or, rather, your interpretation makes exactly the sort of modification I claimed was needed. So I’m making basically the same point James was, but with some more detail.

    Your interpretation of premise 5 is this: (x)Cgx & (x)(Cgx → (Rxg & Sx)). That says “Everyone is such that God can give them irresistible grace, and everyone is such that if God can give them irresistible grace, then they are in a right relationship with God and are saved.” The problem with your interpretation is the second conjunct, the conditional (x)(Cgx → (Rxg & Sx)). As far as I can tell, you just added that. That is nowhere to be found in the original argument. The original premise 5 is best interpreted as simply the first conjunct: (x)Cgx. That says “God can give everyone irresistible grace.” In Walls’ original premise, the clause “and thereby determine all persons to freely accept a right relationship with himself and be saved,” is best interpreted simply as a gloss on (an explanation of) what it means for God to give “irresistible grace” to someone. And, for the reasons I’ve mentioned already, the mere definition of irresistible grace plus the claim that God loves everyone does not entail that everyone is saved; one would need to add the claim that there are no sufficiently great goods which metaphysically necessitate damnation.

    Here are two arguments for my interpretation. First, Walls nowhere indicates that he thinks the clause “and thereby determine all persons to freely accept a right relationship with himself and be saved” would be at all controversial. All the contextual clues point to his treating that as an uncontroversial gloss on “irresistible grace.” But your interpretation makes that claim precisely the claim that every philosophically sophisticated Calvinist would reject, anything but an uncontroversial definition of irresistible grace.

    Second (this is the best reason), you yourself mentioned that your interpretation renders premises 3 and 4 superfluous. But Walls clearly does not regard them as superfluous. Nor does he regard them as simple supporting arguments for premise 5 — since he claims that one way out for the Calvinist is to deny premise 3, while claiming at the same time that Calvinists cannot deny 5! But if your interpretation is correct, then denying premise 3 is not sufficient to avoid the force of the argument, or if it is, it is only because it allows you to deny 5. So your interpretation also implies that Walls is mistaken as to the logical options for the Calvinist.

    Suppose I’m wrong in my interpretation of premise 5, and we were to accept your interpretation. Then, as you say, we should probably think of 3 and 4 as a miniature supporting argument for premise 5. But then my original objection just morphs into this: 3 and 4 by themselves don’t support 5! He needs also the footnote he made to premise 3, which is precisely the claim a philosophically sophisticated Calvinist will reject. And by claiming (later in the section) that a Calvinist has to deny one of the premises, and 5 can’t be the one the Calvinist denies because it is an obvious implication of Calvinism, he has misrepresented the Calvinist’s options. My fundamental objection to the argument is that it misrepresents the Calvinist’s options; the fact that the argument is invalid is really only a bad thing because of the misrepresentation it causes. Well, the misrepresentation remains in his text even on your interpretation of the argument. Also, giving a valid argument in which half the premises are superfluous (recall that 2 is superfluous as well, unless you want to cast the argument as a reductio) isn’t much better as a display of logical ability than giving an invalid argument.

    So even if your interpretation is right, Walls has made a serious misrepresentation of the Calvinist’s options by virtue of not properly constructing a valid argument without superfluous premises. But I think my interpretation is right. I think here’s what’s going on: in adding that conditional to your interpretation of premise 5, you’ve added exactly the sort of bridging premise (from the premises 1-5 to the conclusion, 6), that I argued was needed. You just cast it as a conditional instead of the adjective “properly” that I suggested. But the bridging premise you added was stronger than is needed, since yours renders premises 3 and 4 superfluous. Maybe a better way to help the argument is to interpret premise 5 simply as (x) Cgx, and adding the following bridging premise (call it 7) instead of the one you add:

    7: (x) (((Dgx & Pgx) & Cgx) → (Rxg & Sx))

    That says: “everyone is such that if God desires their good and does everything he properly can to promote their flourishing, and God can give them irresistible grace, then they are in a right relationship with God and will be saved.” That yields a valid argument as well, but the advantage is that it doesn’t render premise 3, at least, superfluous. (It does render premise 4 superfluous, but I suspect that it is premise 3 that Walls would say is doing the most work in the argument, so that’s the one we want to make sure we use in representing the argument. He says (rightly, I think) that no Christian will deny 4.) This, of course, is the premise the philosophically sophisticated Calvinist will deny; to defend it, Walls would have to bring his footnote to premise 3 into the text as a defense of this premise.

    Thanks for the hard work of the translations! I mean this as a friendly exercise in getting straight on the debate, and I can tell you do as well. I appreciate the work you are doing of trying to put it into a valid form. Valid arguments at their best constrain the options of those who disagree with the argument — if you don’t like the conclusion, you have to deny one of the premises. The troubling thing about the way Walls states this argument is that he buries (hides) the major option for the Calvinist (the Calvinistic claim that opponents cannot show that there is no sufficiently good reason for God to allow some to be damned). And he just doesn’t need to do that — he should bring out the major option for the Calvinist into the light of day and argue against it directly.

    • Actually, I just realized something: your symbolization of premise 5 actually renders ALL of the other premises superfluous. Premise 5 by itself entails the conclusion. Proof:

      1. (x) Cgx & (x)(Cgx → (Rxg & Sx)) Premise
      2. (x) Cgx 1, Simp
      3. (x)(Cgx → (Rxg & Sx)) 1, Simp
      4. Cga 2, UI
      5. Cga → (Rxa & Sa) 3, UI
      6. Rxa & Sa 4,5 MP
      7. Sa 6, Simp
      8. (x) Sx 7, UG

      My use of Universal Generalization on line 8 is permissible because the constant “a” was only introduced through the use of UI.

      Am I missing something here? I don’t have the program you are using, so I’m going off the top of my head.

      If your symbolization of premise 5 renders all of the other premises unnecessary, then surely that is a reason to find a different symbolization.

      • Rich Davis says:

        Hi Daniel: I think you intended (5) to read: Cga → (Rag & Sa). Otherwise, I agree that your proof is deductively valid. — Rich

      • Rich Davis says:

        Dan: I think this is a deep insight on your part. But I don’t think it’s a reason to look for a different symbolization for (5). Rather, it’s a reason for thinking that (1)-(6) are something of an argument summary — like Samuel Clarke’s Props. I-XII in his ‘Demonstration’.

        I’m now of the mind that the true architecture of the argument proceeds from an initial set of bridging premises to premise (5), and then on to the conclusion (x)Sx — via the argument you’ve so nicely laid out. The issue with *this* argument won’t be it’s *validity*, but rather those bridging premises.

        Thanks for your work on this! I haven’t laid my hands on your book yet. But once I do, I’ll try to blog a few things about it. Cheers!

      • Rich, so you’ll grant that Walls was wrong to say that 5 is a clear consequence of Calvinism and that the Calvinist’s options are only to deny 1 or 3, not 5? And that premises 1-4 are not sufficient to entail the conditional in your interpretation of 5?

      • Rich Davis says:

        I don’t know whether (5)–the original, not my symbolization–is a clear consequence of Calvinism. It would depend, I suppose, on the supporting (bridge) premises, and whether they are essential to Calvinism. Now are (1)-(4), as they stand, those bridge premises? That is, do they entail the right-conjunct of (5). I think the answer to that is ‘no’. But then, as I said earlier, I have come to think (1)-(4) are best taken–not as premises for a Copi-style proof–but as ‘signposts’ along the road.

        I’ll say something about the symbolization of (5) in a separate post.

      • Rich Davis says:

        Okay, concerning the symbolization of (5). You favour:

        (5a) (x)Cgx

        whereas I have plumped for

        (5b) (x)Cgx & (x)(Cgx → (Rxg & Sx)).

        It occurred to me last night that we’re both wrong. I think (5a) needs a right-conjunct since (5) has one. So your symbolization isn’t sufficient. On the other hand, my (5b) buries an ambiguity in the term ‘could’. Should we take this as a ‘logical’-could or a ‘power’-could?

        I think it is a mistake to read ‘could’ as expressing logical modality here. The reason is primarily textual: the right-conjunct of (5) mentions God’s ‘thereby determining’ such-and-such. So we’re looking at what it’s within God’s power to bring about, as opposed to straight-up logical possibility. (This ‘power’ interpretation also dovetails nicely with things James said earlier.)

        In any event, I’m now inclined to read (5) more along these lines:

        (5b*) Since it is within God’s power to bring it about that “God gives everyone IG,” it is within God’s power to bring it about that “Everyone is rightly related to God and is saved”

        where ‘IG’ stands for ‘Irresistible Grace’. Lying behind (5b) of course would be some power entailment principle or another which would then have to be argued for. The argument would then proceed from there.

      • Rich, I think that is exactly the right way to read it, though you’d need to specify what “everyone” means here. I think it needs to mean: “everyone is such that it is within God’s power to bring that person into a right relationship with God and save that person.” If it is read that way, then Jerry’s view that this is a straightforward implication of Calvinism is correct — which is a great exegetical argument in favor of this interpretation.

        But now the argument is back to being invalid, and my original objection to it stands. You need to add a premise to get from “for each person, it is within God’s power to save that person” to “everyone is saved,” which is the conclusion. The conclusion doesn’t say “it is within God’s power to save each person.” It says that God actually saves each person.

      • Rich Davis says:

        Hi Dan, you write:

        “The conclusion doesn’t say “it is within God’s power to save each person.” It says that God actually saves each person.”

        Yes. That’s true.

      • Rich, let me develop what I just said. I really like your suggestion; let me take a stab at symbolizing (5b) as you interpret it (and I’m inclined to agree with your interpretation). We can’t use R or S, because as you’ve defined them, R and S say that the subject IS or WILL be in a right relationship with God/saved, whereas (5b) says that God CAN (has the power to) save them. So we need to define a pair of new relations:

        Mxy = x can (has the power to) save y
        Nxy = x can (has the power to) bring y into a right relationship with God

        (5b) will be symbolized thus:

        (x)Cgx & (x)(Cgx → (Mgx & Ngx))

        That reads: “everyone is such that God can (has the power to) give them irresistible grace, and everyone is such that if God can (has the power to) give them irresistible grace, then he can (has the power to) save them and bring them into a right relationship with God.” I agree that this seems like the best interpretation of Walls’ argument. I’m willing to grant that it is a fairly obvious implication of Calvinism; it makes the conditional out to be a reasonable definition of “irresistible grace.” Do we agree on that?

        If so, my original objection stands. For the argument remains invalid. What is needed to make it valid is a principle connecting the claims about what God can do with what God will in fact do. (x) Sx says “all are saved”, not “all can be saved.” That principle will ideally employ a conditional with the conjunction of the consequent of premise 3 and the consequent of premise 5b as the antecedent and the conclusion as the consequent:

        (7b): (x) ((Dgx & Pgx) & (Mgx & Ngx)) → (x) Sx

        This reads: “if everyone is such that God desires their well-being and promotes their flourishing as much as he properly can, and God has the power to save them and bring them into a right relationship with God, then all are saved.”

        Only with this premise is the argument valid. This is exactly the claim I argued from the start that he needs to add; he gives the (inadequate) beginnings of an argument for it in that footnote, and this is exactly the premise a philosophically sophisticated Calvinist will deny. Does that sound right?

      • Rich Davis says:

        Hi Daniel, you propose:

        “(7b): (x) ((Dgx & Pgx) & (Mgx & Ngx)) → (x) Sx

        This reads: “if everyone is such that God desires their well-being and promotes their flourishing as much as he properly can, and God has the power to save them and bring them into a right relationship with God, then all are saved.”

        Only with this premise is the argument valid. This is exactly the claim I argued from the start that he needs to add; he gives the (inadequate) beginnings of an argument for it in that footnote, and this is exactly the premise a philosophically sophisticated Calvinist will deny. Does that sound right?”

        I think so. I don’t have time to ‘crunch the numbers’ right now. (I have to teach at church tonight.) But the consequent should read ‘(x)(Hx → Sx)’. That’s my fault. I started out the proof w/ an open domain for the quantifier, but forgot that I did by the time I reached the conclusion. :-))

    • Alright, it seems Dan, james and I agree on the location(s) of the problem(s). Controversies over the word “properly” or on whether God “could” save everyone, ultimately boil down to the question: “is it possible that God have morally sufficient reasons to not save everyone, even as we maintain that He is all-loving?”
      Arminians say yes it’s possible, and the only sufficient reason is that humans have libertarian free will.
      Calvinists say yes it’s possible, and since I don’t think humans have libertarian free will, he must have other sufficient reasons (some of which could well be in the words of Rom.9 “what if God, willing to show his power, etc..”)
      Jerry Walls, much like the proponent of the problem of evil, needs to tell us why those morally sufficient reasons cannot exist.
      I have discussed these sorts of things here: http://theologui.blogspot.com/2015/06/reprobation-free-will-and-skeptical.html
      Guillaume.

    • Rich Davis says:

      Hi Daniel: thanks for this detailed and thoughtful reply. It’s very helpful in pushing things forward. Just a small point. You comment:

      “The problem with your interpretation is the second conjunct, the conditional (x)(Cgx → (Rxg & Sx)). As far as I can tell, you just added that. That is nowhere to be found in the original argument.”

      So you favour symbolizing (5) as simply: (x)Cgx. Of course, (5) seems to have a right-conjunct–“and thereby determine…. ” And that right-conjunct does involve people being in right relationship to God and being saved. Accordingly, I added the consequent to capture that expression. In that sense, I think your favored symbolization (x)Cgx is missing just a bit. But I guess you see the right conjunct of (5) as detachable, and factoring more into a supporting (bridge) premise–like your (7).

      The real debate, it seems to me, is over my ‘→’. If we don’t see (3) and (4) as supporting (5), I think the ‘→’ is a reasonable interpretation. If (3) and (4) are involved, as you suggest, then the ‘→’ is still justified, but then there are no doubt background (bridging) premises–as you and James are suggesting–linking that antecedent and consequent in my conditional.

      Wonderful to interact with you. Will you be at ETS/EPS in San Antonio? I’m reading a paper on Brian McLaren’s “Gospel” in the Church History group.

    • Hi Dan,

      Above you say,

      “But then my original objection just morphs into this: 3 and 4 by themselves don’t support 5! He needs also the footnote he made to premise 3, which is precisely the claim a philosophically sophisticated Calvinist will reject.”

      If I read you correctly, you agree that (3), (4), and the footnote to (3) do support (5). If so, then it seems a bit uncharitable to accuse Walls of employing an invalid argument since he himself provides (in the footnote) precisely what is needed to avoid its being invalid.

      I’m reminded of how many iterations of Mackie’s argument Plantinga went through before finally concluding that the argument failed. He didn’t simply say, “There’s an exception to the claim ‘A good thing always eliminates evil as far as it can'” and then conclude the whole argument fails to support the conclusion. Instead, he modified the argument in a way that Mackie would find acceptable and that prevented Plantinga’s own objection from working. Here the task should be even easier than trying to think of what Mackie might say in reply since Walls has actually provided the further explanation that would avoid the objection.

      Now, of course, it may be true that the footnote is something a “philosophically sophisticated Calvinist” would reject, but that’s beside the point when it comes to determining whether an argument is valid or invalid. It might be why you still reject the conclusion, but it’s because you find a premise false and not because the premises fail to support that conclusion.

      Best,
      Paul

      • James says:

        Paul,

        “If so, then it seems a bit uncharitable to accuse Walls of employing an invalid argument since he himself provides (in the footnote) precisely what is needed to avoid its being invalid.”

        Either Walls was aware that the central argument stated in the main text of the book was logically invalid (and needed to be supplemented with the footnote premise) or he wasn’t. If he wasn’t aware, it’s fair game for Dan to point out that the central argument *as stated* is invalid. If he was aware, why did he relegate that essential premise to a footnote rather than including it in the main text?

      • The argument that Walls gives in the text — the premises numbered 1-5, with the conclusion numbered 6 — is invalid. It is consistent to accept all of 1-5 while denying the conclusion, 6. (And I’ve argued in other posts that Rich reaches his contrary conclusion only because he clearly misinterprets premise 5.) Walls makes a lot of hay out of that — in the text, he says that a Calvinist has to deny one of the premises (he says 1 or 3; Rich, I guess, would say 5) to get out of the argument. But that’s false.

        The reasoning he gives in his footnote is the bare beginning of the reasoning he would need to give in order to support the inference from his premises (1-5) to the conclusion. But he doesn’t point to his footnote and say “or, hey, the Calvinist could reject my reasoning here instead of rejecting one of the premises!” That’s what makes his logical mistake so egregious. He buries the real issues in a footnote, without acknowledging that the footnote needed to be a premise in the argument for the argument to be valid, and never comes back to it. In reality, his whole book should just be an expansion on and defense of the reasoning in that footnote.

        Your point about Plantinga and Mackie is a good one; that’s why I relegated my critique of Walls to a blog post, where my published treatment of the arguments from evil against Calvinism treats a version of the argument from love (and other problems evil poses for Calvinism) other than the one that Walls gives. Walls’ versions of the arguments aren’t very good, and in my published work I treat the best versions of those arguments I can think of. It is just that enough people are misled by this kind of sleight-of-hand in Walls’ presentation of these arguments that I thought it needed a stand-alone criticism. The substantive issues are still there and haven’t been touched. But that’s exactly the problem with Walls’ treatment: he leaves the substantive issue — the question of whether we can rationally judge that there are no great goods other than free will which would metaphysically necessitate damnation — completely unexamined.

      • Rich Davis says:

        Hi Dan! You write (to Paul):

        “It is consistent to accept all of 1-5 while denying the conclusion, 6. (And I’ve argued in other posts that Rich reaches his contrary conclusion only because he clearly misinterprets premise 5.) Walls makes a lot of hay out of that — in the text, he says that a Calvinist has to deny one of the premises (he says 1 or 3; Rich, I guess, would say 5) to get out of the argument. But that’s false.”

        Well, I don’t think I’ve *clearly* misinterpreted (5). :-)) You’re right, though, that I think a Calvinist must deny (5)–at least as I’ve symbolized it. This is because, as you have shown, (5) entails the conclusion of Walls’ argument, (x)Sx, all by itself.

    • Ok, Rich, great! So it appears we’ve reached agreement: on the best interpretation of premise 5, the argument is invalid. It can be made valid fairly easily, but the premise that must be added will be a controversial one.

      Once you’ve number-crunched everything to your satisfaction, are you willing to post these conclusions up in the original post and retract your claim that the argument is valid? (It would be good to make the same retraction on the Evangelical Arminians site.) It can be a model of what Christian philosophers, using logical tools, can achieve, when they really listen to each other. We can actually persuade each other of things, something sadly uncommon. 🙂 Thank you for your graciousness.

      • Rich Davis says:

        Hi Dan: Alas, it’s far too soon for that. :-)) At any rate, it’s an ongoing conversation–as opposed to the Convocation of 1714! Cheers, Rich

  8. James says:

    Rich,

    It appears to me that your symbolization of Jerry’s premise 5 is incorrect. As you have it, the mere fact that God *can* give irresistible grace to S *entails* that S will be saved. But that’s not what premise 5 states or implies, nor is it something that the Calvinist ought to grant.

    • Rich Davis says:

      Hi James,

      Thanks for this good observation. You are quite correct about (5). The wording is tricky and I am trying to be as charitable as I can in my interpretation. So I took ‘and thereby determine’ as ‘in which case’ — hence, the material conditional. We’d have to check w/ Jerry on this, I suppose.

      Cheers,
      Rich

    • Rich Davis says:

      Here’s another possibility. My symbolization of (5) is what Jerry intends, but there is a supporting argument for (5)–running in the background, as it were–which employs certain bridging premises. These would be premises that connected antecedent and consequent in (x)(Cgx → (Rxg & Sx)).

      In that case, the argument (as I symbolized it) would be valid, but the Calvinist would take issue with its soundness–in particular, the supporting (bridge) premises for (5).

      • James says:

        Rich,

        Well, I thought the point of 3 and 4 was to bridge that gap from what God can/could do to what God will/would do. That’s why I was surprised to see your claim that 3 and 4 are superfluous to the argument. The question isn’t why Johnson would ‘fuss’ over them, but rather why Walls would include them in the first place!

        Walls’ argument is basically a reworking of the logical problem of evil:

        1. An all-good, all-powerful God exists. [assumption for reductio]
        2. If an all-good, all-powerful God existed, he *could* completely prevent evil.
        3. If an all-good, all-powerful God existed, he *would* completely prevent evil.
        4. Therefore, evil is completely prevented (i.e., evil does not exist). [from 1-3]
        5. Evil exists.
        6. Therefore, evil exists and evil does not exist. [reductio]

        Walls’ variant:

        1. An all-loving, irresistible-grace-giving God exists. [assumption for reductio]
        2. If an all-loving, irresistible-grace-giving God existed, he *could* save everyone.
        3. If an all-loving, irresistible-grace-giving God existed, he *would* save everyone.
        4. Therefore, everyone is saved. [from 1-3]
        5. Not everyone is saved.
        6. Therefore, everyone is saved and not everyone is saved. [reductio]

        Walls’ argument is vulnerable in much the same way that the LPE is vulnerable.

      • Rich Davis says:

        Okay, that’s interesting. I don’t have Jerry’s book yet. However, the way Daniel Johnson set out the argument, (3) and (4) certainly looked like stand-alone premises in the main argument. For example, there is no conclusion indicator (e.g., “Therefore”) at step (5)–as there is at (6)–to indicate that (3) and (4) should be understood as playing a supporting role for (5).

      • Rich, the argument as “I set it out” was copied and pasted from the book. He didn’t make 3 and 4 out to be support for 5. That’s actually the problem I have with your symbolization of the argument.

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