Why A Posteriori Arguments Against God’s Existence Fail, pt. 2

A few weeks ago I posted my argument against any and all a posteriori arguments. I thought I would revisit the argument again today and try to spell it out more clearly and concisely.

By a posteriori argument, I merely mean any argument that seeks to disprove God’s existence on the basis of some fact of the world, be it evil, evolution, “divine hiddenness”, the success of the natural sciences, or the failure of mind/body dualism. These arguments essentially boil down to something like:

1. If God exists, we would expect to observe X.

2. X is not the case.

3. Therefore, God does not exist.

The argument is in the form of a modus tollens deduction, which is a perfectly valid form of argumentation. My response is a kind of dilemma that puts the atheist in the awkward position of defending the soundness of the argument. I contend that any successful defense of the soundness of such arguments requires one to commit an informal fallacy of begging the question.

But first I think it is important to unpack my concept of God. I believe God is the greatest conceivable being, a definition common to classical theism. Here, Dr. William Lane Craig discusses this concept of God, and its implications. I would agree with what he says:

Dr. Craig points that since God is conceived of as a necessary being, if God possibly exists, then God actually exists. Now my argument is much more humble than this, as I do not even suppose that God’s existence is logically possible. What I offer is the following dilemma:

1. If the a posteriori argument is to be sound, then the truth of the conditional premise must be based on appeals to possibility or impossibility.

2. If the truth of the conditional premise is supported on the grounds of possibility, then there must be a possible world where the antecedent and consequent obtain, be it a fact of the actual world or counterfactually.

3. If God’s existence possibly obtains, then God actually exists.

4. If God actually exists, then either the first or second premise of the a posteriori argument must be false and the argument unsound.

5. If the truth of the conditional premise is supported on the ground of impossibility, then there is no possible world where the antecedent obtains and this counterpossible conditional is trivially true.

6. If the conditional premise is true because it is a counterpossible conditional, then the support for the first premise is nothing more than the assumption of the conclusion, which is to beg the question.

7. Therefore, either the a posteriori argument is unsound or question-begging.

Now one might challenge my argument by saying that the atheist need not assume that God is possible or impossible at the outset. However, if the argument is to be any good, the atheist must provide reasons that compel her interlocutor to think there is epistemic warrant for accepting the truth of the premises. After all, the conditional premise might be false. If the atheist draws out implications from the concept of God, then we must ask how it could be that the concept of God supplies those implications. The atheist is limited here. She cannot admit that the implications are drawn from a coherent conceptual analysis of God, since this would suggest that in at least one possible world where God exists and such implications follow. That would mean that God is logically possible, and so actual. Thus, the only alternative is that the implication is drawn out of an incoherent or impossible concept. But then anything could be said to be implied by the impossible, so the implication is merely a trivial one. The atheist would have to admit that “If God exists, gratuitous evil would not exist” is just as true as “If God exists, light bulbs wouldn’t exist”. If that is all the atheist is saying, then the argument is no more interesting than its theistic cousin “Either God exists, or 2+2 is 5, and since 2+2 is not 5, God exists.” More to the point, if the conditional premise is trivially true because it is counterpossible, then the atheist’s argument is simply fallacious. Clearly the atheist intends to disprove God on a posteriori concerns, but she ends up appealing to the impossibility of God, a priori, as epistemic warrant for the truth of the conditional premise. Since no argument is given for the impossibility of God, and it is just smuggled into the first premise, this is textbook question-begging.

Let’s suppose that the atheist admits this much, but then claims that she will back up her a priori assumption that God is impossible by way of an argument. But then she is arguing about God’s existence purely on a priori concerns, and that is not the original argument offered at all. So, I think this adequately demonstrates that the atheist is limited to presenting a priori arguments in favor of that position and that a posteriori arguments are useless in disproving God’s existence.

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Posted on January 26, 2012, in Arguments for God and tagged , , , . Bookmark the permalink. 25 Comments.

  1. Looks good Dan. I reformulated the argument somewhat. The atheologian argues:

    1. If God exists, then x.
    2. not-x.
    3. Therefore God does not exist.

    Your argument:

    4. If (1) is true, then either: (i) there is some metaphysically possible world in which God and x exist, or (ii) the existence of God is impossible, or (iii) x is necessarily true. [by the truth conditions of strict implication]
    5. Either (i) there is some metaphysically possible world in which God and x exist, or (ii) the existence of God is impossible, or (iii) x is necessarily true. [by 1 and 4]
    6. (iii) is false. [by 2]
    7. Either (i) there is some metaphysically possible world in which God and x exist or (ii) the existence of God is impossible. [by 5, 6 DS]
    8. If (ii), then (1)-(3) begs the question.
    9. If (i), then God is metaphysically possible.
    10. If God is metaphysically possible, then God exists. [by the ontological argument]
    11. If (i), then God exists. [by 7, 8 HS]
    12. Either God exists or (1)-(3) begs the question. [by 6, 7, 9 CD]

    Everything looks solid to me. Just two questions: First, could (1) be formulated in terms of a subjunctive conditional instead of strict implication? I’m not sure what the truth conditions of subjunctive conditionals are though… Second, the move in (9) is not entirely valid, at least as its symbolized above. I imagine there is some rule in modal logic that allows you simplify “there is some metaphysically possible world in which God and x exist” to “there is some metaphysically possible world in which God exists.” I just wasn’t sure what rule it was. Either way, I don’t really have any substantial objections; looks good.

    — Xan Bozzo

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    • Hey Xan,

      Thanks for this reformulation. I think it presents my argument quite clearly.

      You ask, “: First, could (1) be formulated in terms of a subjunctive conditional instead of strict implication?”

      I don’t think either could be successful moves. Subjunctive conditionals are synonymous with counterfactual conditionals. They posit that there is a possible world close to the actual world where the antecedent and consequent both obtain. Of course, this would run afoul of the ontological argument, as you point out in your reformulation. Your reformulation also points out why a strict implication interpretation of premise one is no more successful. A conditional is necessarily, or strictly, true if the consequent necessarily obtains, which contradicts premise 2, or if the antecedent cannot obtain, which is to beg the question.

      You also ask, “Second, the move in (9) is not entirely valid, at least as its symbolized above. I imagine there is some rule in modal logic that allows you simplify “there is some metaphysically possible world in which God and x exist” to “there is some metaphysically possible world in which God exists.” I just wasn’t sure what rule it was.”

      Perhaps I am misconstruing your argument, but it seems to me that (9) is a de re rendering of the de dicto (i). One solution is to adopt just one consistent interpretation of modality, either de re or de dicto. I think this would avoid trying to force an inference between the two interpretations. But it is a point that is worth further consideration.

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  2. Hi Daniel. Suppose an atheist thought that God’s moral perfection precludes his being truly omnipotent. In this case he might argue that the first premise of the POE is true, but that it fails to refer to the maximal being described in the modal ontological argument, where “maximalness” is understood to include omnipotence.

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    • Adamoriens,

      Thanks for your comments.

      You write, “Suppose an atheist thought that God’s moral perfection precludes his being truly omnipotent. In this case he might argue that the first premise of the POE is true, but that it fails to refer to the maximal being described in the modal ontological argument, where “maximalness” is understood to include omnipotence.”

      I would agree with this point. If it can be shown that a maximally great God has attributes that are mutually incoherent, then such a God could not exist. I would take this to be an a priori argument against God’s existence, since it would be based on the very concept of God and not based on any fact of the world.

      Furthermore, I would agree with you that the POE can be used on certain other conceptions of God, but not on others. I do not take the POE to apply to the anthropomorphic Greco-Roman gods, for instance. It is possible that the POE would apply to a God that is omniscient, omnipotent, morally-perfect, and contingent. My point is that the God of classical theism has aseity and necessity. I interpret this to mean that if God exists, then God exists in all possible worlds. I am offering a particular conception of God, and my dilemma is meant to point out that only a priori arguments could count against such a conception.

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      • Thanks for your considered response. My point is that an atheist can plausibly hold that God as traditionally understood is capable and knowledgeable enough to prevent gratuitous evils, and compelled by his moral perfection to do so, and yet not agree that these abilities and qualities alone are sufficient to be maximally-great. Suppose he thinks that omnipotence entails being able deliberately bringing about gratuitous evil? In this case, he might be unsure whether the maximally-great being is morally perfect or “omnipotent”, but his POE depends only on there being a person who’s morally perfect and able to prevent gratuitous evil. What do you think?

        According to wikipedia, no quasiperfect numbers have been found to exist. A quasiperfect number is a “theoretical natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1.” If mathematical truths are necessary ones, then mathematicians must remain agnostic about the coherence/possibility of the quasiperfect number concept. But they are nonetheless able to prove that, if it exists, it is larger than 10^35 and possesses 7 unique prime factors:

        http://journals.cambridge.org/download.php?file=%2FJAZ%2FJAZ1_33_02%2FS1446788700018401a.pdf&code=7d2f1268a834c7d30e528452fc6608c7

        Isn’t this an exception to the principle that we cannot derive necessarily true conclusions from concepts of unknown coherence? If so, can we do this for posteriori arguments against God’s existence?

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  3. Adamoriens,

    You raise some excellent challenges, and I hope I address them to your satisfaction.

    You write that the atheist, “. . . might be unsure whether the maximally-great being is morally perfect or “omnipotent”, but his POE depends only on there being a person who’s morally perfect and able to prevent gratuitous evil.”

    I might still be misunderstanding your point, and if I am I apologize. Here is how I am understanding you. According to Plantinga, maximal greatness is maximal excellence exemplified in every possible world (I think this definition is confusing and possibly misleading). The atheist might contend that her argument only disproves maximal excellence as obtaining in this world, i.e. that there is not an omniscient, omnipotent, and morally-perfect being. If maximal excellence is not exemplified in this world, then a fortiorimaximal greatness is does not obtain. In this sense, the problem of evil could be seen as a defeater for the ontological argument. In fact, Michael Tooley raised this objection to Plantinga, though I forget the article (sorry).

    My response, and I think it applies to your objection, is that this atheologian is still not critiquing the God of classical theism. From Avicenna to Aquinas, classical theists have defended a doctrine of divine simplicity. Here is what the Catholic Encyclopedia has to say about this attribute,

    It is true that no single predicate is adequate or exhaustive as a description of His infinite perfection, and that we need to employ a multitude of predicates, as if at first sight infinity could be reached by multiplication. But at the same time we recognize that this is not so — being repugnant to the Divine simplicity; and that while truth, goodness, wisdom, holiness and other attributes, as we conceive and define them express perfections that are formally distinct, yet as applied to God they are all ultimately identical in meaning and describe the same ultimate reality — the one infinitely perfect and simple being” (P. Toner, 1909)

    If this is true, then God’s attributes cannot be parsed off from one another and remain as univocal expressions of those divine attributes that describe one identical nature. That is, a maximally excellent being is not in any way God, or a part of God, since that being lacks necessity. In lacking necessity, it is not possible that it could have some of the attributes of God, even if we stipulated that it had omniscience, omnipotence, and moral-perfection. That is why I said previously that we might be able to use arguments like the POE against certain conceptions of God, even a maximally excellent being.

    So suppose the POE disproved the existence of a maximally excellent being, I do not think this precludes the possibility of a maximally great being existing. I think an equivocation has occurred in the fundamental meaning of terms like “omnipotence” and “moral-perfection” if they are not taken as mere formal expressions of God’s simple nature, but separate predicates of a complex being. Otherwise, it seems that we are saying that God is a modal composite of maximally excellent beings ranging across all possible worlds, which is theologically incorrect and, in my opinion, misconstrues possible-world semantics. More could be said about this, but I hope this begins to answer your objection.

    You also write about necessary truths that would follow from there being quasiperfect numbers. Mathematicians are agnostic to the existence of quasiperfect numbers, yet we seem to be able to infer necessary truths if they happen to be discovered. I do not disagree with this at all. For the mathematician, the possibility of quasiperfect numbers can remain open. Whether or not they are possible, the statement “If quasiperfect numbers exist, they are larger than 10^35 and possesses 7 unique prime factors” can be true and necessarily true. Likewise, if God is an impossible being, the conditional “If God exists, there would not be gratuitous evil” is a true necessary conditional statement. I am not denying that counterpossible conditionals are true. If anything I am overly generous on this point and do not even require any relevance between the impossible antecedent and consequent for the statement to remain necessarily true.

    I do deny that the question of God’s logical possibility can remain open, if one is to defend the soundness of the POE. This is the fundamental difference between the math example and the POE.

    Consider the following scenario. If the atheologian claimed to be agnostic towards God’s logical possibility, I would point out that if God is logically possible, then God actually exists. If God actually exists, then either 1) gratuitous evil does not exist in any possible world (the denial of the second premise), or 2) God’s existence must be somehow compatible with gratuitous evil (the denial of the first premise). I don’t need to prove which premise is false. I need only point out that at least one premise must be false. If the atheologian accepts this modal reasoning, then she must reject the logical possibility of God, if she is to press forward in defending the argument as sound. But rejecting the logical possibility of God requires an a priori argument. It cannot just be assumed so as to defend the POE. But then we are no longer talkin’ bout evil. We’re talkin’ the incoherence of a concept, which I think is a much steeper hill to climb.

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  4. Please forgive me if I misunderstand you; I don’t have any formal training here. But it seems to me that the atheist could perform roughly the same move in reverse, much like you mentioned with Tooley. Being agnostic about the possibility of God and agreeing that the conditional “If God exists, there is no gratuitous evil” is true, he could take the existence of gratuitous evil to indicate that, not only does God not exist, he is impossible. In other words, he could show that gratuitous evil renders the God-concept incoherent, even if he doesn’t know where that incoherence lies. Thus, the atheist may begin with the assumption that the “possibility of God is possible”, and conclude from the probable existence of gratuitous evil that the possibility of God is improbable, which looks like an a posteriori operation to me. Is that right?

    When I state that the argument from evil applies to a perfectly good God capable of preventing any gratuitous evil, I am in fact referring to the Anselmian God. But if an atheist supposes that there is a deity potentially more powerful than the Anselmian God, one that is capable of bringing about gratuitous evil, it’s no longer certain that the ontological argument’s maximally-great God and the Anselmian God refer to the same thing.

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    • Adamoriens,

      Thanks for these excellent questions. You’re pushing me to really think through my argument. This is the first time I’ve ever aired it publicly and it’s hard to anticipate all possible objections until you let other people try to find chinks in the armor.

      In response to this Tooley-esque challenge, I would have to say the following: one of the points of this dilemma is that it does not allow the atheologian to remain in a position of agnosticism towards the logical possibility of God, if they hope to defend the soundness of the argument. That is, in light of these modal concerns, the atheologian must specify exactly what his or her epistemic warrant is for the truth of the conditional premise. Thus my argument hinges on the following claim: the epistemic warrant for thinking a possible conditional is true is quite different from the epistemic warrant for thinking a counterpossible conditional is true. Furthermore, I think we can prove that the “agnostic” atheologian cannot offer any epistemic warrant for the truth of the conditional, if it happens that God is logically possible. The epistemic warrant for a possible conditional depends upon conceptual analysis of the antecedent and consequent which gives reason to think that there is an implication between the two in any given possible world. The epistemic warrant for counterpossible conditionals are quite different, especially if the consequent is not necessary. I don’t think that anyone would defend the logical necessity of gratuitous evil. Therefore, this counterpossible could only be defended on the logical impossibility of God–full stop.

      Here is why the atheologian cannot remain agnostic and also argue successfully for the soundness of the argument in light of these concerns. If the atheologian claims to be agnostic towards the logical possibility of God, then he must defend the truth of the first premise for entirely divergent reasons. He would have to say that it is true either because God is logically possible, and a consequence of the concept of God IS the absence of gratuitous evil, or because the concept of God is simply incoherent–and he doesn’t know which is true. If he does not know which is true, then could he really defend the truth of the conditional at all? It seems to me that if he admits that he does not know if God is logically possible, then he undercuts any reason to think his conceptual analysis provides any warrant, and so the theist does not have to accept the implication. The agnostic atheologian is essentially claiming that he has not, or cannot, think through the concept of God to develop a coherent picture of everything that concept might possibly entail. So why think that the implication of the absence of gratuitous evil should be the one shining exception? Such an atheologian is in the awkward position of saying something like, “If God is possible at all, then gratuitous evil would not exist”. The theist might respond with the following, “How do you know this? It could be that if God is possible at all, then gratuitous evil would exist!” But then the atheologian would have to simply shrug, admitting that he cannot provide any reason to prefer one over the other. For if he gives warrant to think one is true over the other, this could only come from God’s logical possibility. If he offers warrant to accept both as true, he is committed to God’s impossibility, which cannot be the epistemic warrant for the soundness of the argument. So to maintain his agnosticism, he must shrug and admit that it might be true that a conceptual analysis of the concept of God would lead to the implication that gratuitous evil would exist. In other words, he has no reason to think gratuitous evil would or would not obtain, if God is logically possible. This means that the only epistemic warrant for the truth of the conditional premise could come from proving the conditional to be counterpossible.

      I went a little long on this explanation, but I think you were coming to this same conclusion in your own blog-post on this when you wrote: “So, to succeed with the argument from evil, I would have to show that I can remain agnostic about the coherence of the God-concept whilst drawing a necessary truth from it (namely, that God and evil cannot coexist in any possible world). But that would be very difficult without articulating a coherent notion of God.” I don’t think it would be difficult, I think it is impossible to succeed. He must come down on one side, and it’s going to require the denial of God’s logical possibility.

      As for your second point, I don’t think bringing about gratuitous evil is a great-making property. I’ve articulated reasons for this in my post on Stephen Law’s Evil God Challenge. I think it would be the atheist’s burden to argue for a conception of God that is more coherent or likely than the theist’s, and that it would be a great-making property. Still, I’m not sure that this would do damage to my dilemma. At best, we might say that God is free to commit gratuitous evil, should he want to. So there may be possible worlds where God does do this, but he decided not to actualize such a world. That’s the point of theodicies, I guess. But my dilemma is an attempt to rout the entire theodicy/anti-theodicy debate. The best defense is a good offense, and I think of this dilemma in this way. It puts the atheologian on his back heel, trying to provide warrant for their argument without appeal to logical possibilities. I’ve given reasons to think he can’t, so I’d want to see an atheist provide such epistemic warrant in light of these reasons.

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      • I’ll have to think a bit before responding. In the meantime, here are few arguments from Plantinga’s lecture notes, “Two Dozen (or so) Theistic Arguments”:

        1. If God did not exist, there wouldn’t be an infinity of natural numbers.
        2, There is an infinity of natural numbers.
        3. God exists.

        1. If God did not exist, there wouldn’t be objective moral facts.
        2, There are objective moral facts.
        3. God exists.

        1. If God did not exist, there would be no genuine difference between Mozart and heavy metal rock.
        2, There is a genuine difference between Mozart and heavy metal rock.
        3. God exists.

        On your account, it seems that these arguments are either unsound or question-begging.

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  5. Adamoriens,

    Going back to the quasiperfect numbers example, I would like to add one more point. I think it is significant that we can be agnostic to the logical possibility of quasiperfect numbers while defending a conditional that contains a consequence that would have to be the case were they to be possible at all. I take it to be necessarily true that there are no quasiperfect numbers smaller than 10^35. So there are significant epistemic grounds to defend the truth of the conditional statement “If quasiperfect numbers exist, they are not smaller than 10^35.” It can be defended on the necessary truth of the consequent alone, regardless of whether the antecedent is possible or not. However, in the case of the POE, the consequent “gratuitous evil exists” is, by all accounts, a contingent fact of reality. So we cannot defend the truth of the conditional statement on the grounds that, in any possible world, the consequent would be true regardless of whether God’s existence is logically possible or not. This means that the example is significantly disanalgous and cannot be used as an example of a conditional statement where the antecedent is not known to be logically possible.

    I think this might make what I am saying about why quasiperfect numbers don’t prove to be problematic for my dilemma, but let me know what you think.

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  6. I think you’re right there. But if my preceding observations are correct, there can be no successful argument that theism as a metaphysical system has unique features.

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    • Indeed, I don’t think there could be any successful argument for the existence of this God without presupposing the logical coherence of the concept itself. In effect, this dilemma forces the debate between theism/atheism onto the ground of a priori arguments and conceptual analysis alone. But to be clear, this is if we are talking about Anselmian theism. Perhaps these arguments prove the existence of some kind of generic god.

      If Anselmian theism is true, it has to cohere with every possible metaphysical state of affairs. I’m not sure if that is what you mean by theism having no unique metaphysical features. I think God’s existence would have to be consistent with every necessary truth, i.e. mathematical propositions, and with every contingent truth. This coheres with the claim that God is perfectly free. For example, I do not think it is logically impossible for God to bring about gratuitous evil. I am of the opinion that there could be a possible world where God tortures innocent people for his amusement. However, I deny David Lewis’ brand of modal realism. I don’t think such possible worlds are real worlds like our own. I think they are just possible histories and God chooses to actualize this one freely (I think there is evil, but I think it only appears gratuitous from our vantage point). If God was forced to do so, he would not be morally perfect, omnipotent, and worthy of praise. So, yes. I think one would have to defend the logical coherence of the concept of a maximally-great God prior to defending the arguments you referenced above.

      However, I think we can point to features of the world that are inconsistent with naturalism/physicalism. This alone does not get us to the Anselmian God. The cosmological arguments of Aquinas/Leibniz might give cause to posit the existence of something supernatural, and that thing might be the Anselmian God, but cosmological arguments can’t get us all the way there. I’m roughly taking a position similar to ID when it comes to these arguments. We can have an argument to prove the existence of a cosmic designer, but is it God? They don’t answer. I think such cosmological arguments are deeply problematic for atheism/naturalism/physicalism, whereas it would be perfectly consistent with Anselmian theism. The problem with Plantinga’s arguments above, as I see it, is that they use the term “God”. Perhaps we could prove that there is a non-physical mind, to ground abstract mathematical facts. Perhaps we could prove that there is a non-natural source for objective moral facts. Perhaps we could prove the existence of a non-physical, timeless, extremely powerful, wise, and good being. I would say that it sure seems to fit with many varieties of theism, including the kind I advocate here. Atheists, on the other hand, would have to do some fancy footwork to explain how these conclusions could be true in light of the non-existence of any and all gods. But as I said above, there is always the possibility that some non-Anselmian god exists, while a maximally-great God is logically impossible.

      As for the last of Plantinga’s arguments. I reply thusly.

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      • Lol, awesome link.

        The arguments I offered are a posteriori arguments for God that suffer the same defect you see in arguments against God. For a theist to argue that a certain metaphysical feature is inconsistent with atheism requires that he offer some epistemic warrant for the conditional “if atheism, then x”, which can only be the result of a conceptual analysis of atheism, which commits the theist to the possibility of atheism and therefore it’s reality. In that case, either the first premise is false or the second one is. Or the theist is begging the question against the atheist.

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  7. Adamoriens,

    If there is a possible world where atheism obtains, then the Anselmian God certainly cannot exist. So I would agree that the debate between atheists and theists of my stripe has to be on the basis of a priori concerns, i.e. conceptual analysis and testing for consistency.

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    • A thought has occurred to me. See if you agree. I would say that the POE could be used to disprove God’s existence if the theist stipulates that the conditional premise is true. Obviously I have philosophical/theological objections to this conception of God, for this god would not be as great with regard to aseity and freedom. However, a theist is free to stipulate as he likes. And if the atheologian raises sound objections, so be it.

      I agree that the Anselmian would beg the question if he were to use a reductio against atheism. His arguments against atheism might be sound, but he could not provide any epistemic warrant for the conclusion, if the atheist simply disagreed with the conditional premise of that argument. The atheist could, in effect, escape through the same dilemma I set up. The question is whether the atheist is willing to stand his ground and demand that the theist proves the implications of atheism.

      So consider the moral argument. I find this argument very difficult to defend, especially if the atheist rejects the first premise. However, some atheists are happy to reject it. They stipulate that their atheism implies that objective moral values do not exist. So I think the moral argument is a powerful counter-argument to the atheism of Nietzsche and Sartre. But is it not so successful against the atheism of Peter Singer and Shelly Kagan. As a theist, I should respect this, and only engage with atheistic moral nihilists, specifically moral nihilists who argue that their nihilism follows from their atheism. They are putting an a posteriori argument on the table, and I am happy to oblige. Likewise, if a theist puts an a posteriori condition upon God’s existence, atheist should have at it. They should throw their best arguments against such a theist. In fact, I would probably agree with the argument, since I do not agree that such a god is God. But I am committed to a radical view of divine freedom which leads to what you describe as a metaphysical view that lacks uniqueness. I think God’s existence is compatible with every logically possible fact/state of affairs, but like Leibniz, I think God actualized those possible fact that the greatest conceivable being would.

      Can the atheist tow the same hard line? Can they claim that atheism is compatible with every logically possible fact? If so, then the battle lines will be a priori, for no matter which is logically possible, the law of the excluded middle does not permit both to be true. If atheists put a condition upon the truth of their atheism, I think theists should be able to disprove that form of atheism a posteriori. So if atheists claim “If atheism is true, then there is no first cause of the universe” then I think a theist could argue quite effectively against such an atheist.

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      • I was going to make a similar suggestion earlier. A theist might have beliefs about God which intuitively suggest that “if God exists, gratuitous evil cannot”, such that the atheist can point to the existence of gratuitous evil in order to show that an absurdity is implied; either God is compatible with gratuitous evil or God does not exist (or fails to instantiate moral perfection or omnipotence). And the same can apply to the atheist if he’s committed to some stipulation about atheism.

        I don’t know if this rhetorical strategy will work, though, since the theist or atheist can claim that their stipulation was the result of conceptual analysis, and the ontological argument will rescue them anyway, no matter what attitude their opponent has about the stipulation.

        It seems to me that there can be a non-trivial difference between conditionals with impossible antecedents. For example, some theists believe that there is non-trivial truth to the proposition, “if God didn’t exist, abstract objects wouldn’t exist.” This is an even stronger conditional than the POE, since both the antecedent and the consequent could not have failed to exist, and yet these theists wish to establish an asymmetric dependency between them.

        So non-trivial counterpossible reasoning could offer the atheist a way to use the POE as warrant for his own atheism.

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      • Adamoriens,

        You write “I don’t know if this rhetorical strategy will work, though, since the theist or atheist can claim that their stipulation was the result of conceptual analysis, and the ontological argument will rescue them anyway, no matter what attitude their opponent has about the stipulation.”

        I’m not sure that I agree. It’s not a matter of the opponent’s attitude. If the opponent can prove that the consequent does not obtain in this world, and that is a big if, then the concept of God, as understood by the theist, must be rejected as impossible. So an Anselmian theist might claim that if God exists, gratuitous evil would not exist, but he could only hold that position if he had good reason to think gratuitous evil is impossible. Maybe he’s right and all possible evil is of the non-gratuitous variety. I would say that the cautious theist could not make such bold claims, and it is not necessary to do so. One need only hold that God is morally perfect precisely because he did not actualize worlds with gratuitous evil, though they may be logically possible.

        You write, “It seems to me that there can be a non-trivial difference between conditionals with impossible antecedents. For example, some theists believe that there is non-trivial truth to the proposition, “if God didn’t exist, abstract objects wouldn’t exist.” This is an even stronger conditional than the POE, since both the antecedent and the consequent could not have failed to exist, and yet these theists wish to establish an asymmetric dependency between them.”

        It’s interesting that you went into this direction, because I have been researching this matter a bit lately, and I find it all very perplexing. Obviously this point should give me pause. But here is what I have been thinking about it.

        Non-trivial counterpossibles are accepted by some philosophers, especially in the relevance logic camp. I don’t think this is the consensus view, though I think it is a somewhat “sexy” view to hold in the philosophy of logic, if anything in the philosophy of logic could be considered “sexy”. Nonetheless, some philosophers, both theists and atheist/agnostics, hold that some counterpossibles can be non-trivially true and some non-trivially false. So the escape from my dilemma would be to say that “If God exists, gratuitous evil would not exist” is a non-trivial statement that is true. The problem with this view, as I see it, is that implication ceases to be truth-functional and we must do violence to our notion of validity in order to accommodate the possibility of false counterpossibles within deductive systems. Validity, as I understanding it, is a relationship between truth-functional propositions. So even if there are non-trivial counterpossibles, I find it dubious that we can make valid deductions with them, unless we stipulate a different notion of validity–which is what I understand the project of relevance logic to be. But this is why my eyebrow shoots up when people start talking about relevance logic. I see that they want to accommodate certain intuitions, but I think they do so at the expense of other intuitions.

        My second reason for thinking that this would not be a great way out for the theist or the atheist is that the whole question of God is controversial and unsettled. Relevance logic relies on intuition pumps that I already find bizarre, e.g. “If you square the circle, then I would be surprised.” Some relevance logicians take that to be susbstantively true. Is it? Would I be surprised if you were to do this impossible feat? I have no idea why relevance logicians seem to think that is intuitively true. It’s not to me, and there are no possible worlds that are even remotely close to this one where squaring the circle occurs, so how would I know what my reaction should be in impossible worlds. Frankly, if this is the only way to keep the POE on the table, I’m happy to concede that POE relies upon relevance logic, and the controversial claim that it is intuitively and substantially true that “If God exists, then there would be no gratuitous evil”. The argument would only carry over people who already share that intuition, but it would not carry for those who lack such an intuition. But where is the epistemic warrant to convince people like me? How could you prove that it is actually non-trivially true?

        I’ll have to think about this a bit more, but that’s me shooting from my hip.

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  8. Would you agree that it would only serve to weaken the POE if it can only be plausibly carried through on the basis of a controversial non-classical version of intuitionist logic? On one level, these are just systems of logic. You can do whatever you want to make a system, and see what kind of results pop out. You could have a system of logic that restricts disjunctive syllogism, or introduces non-truth functional operators. But it is a metaphysical or philosophical issue to say which system of logic truly reflects good inferences.

    To me, intuitions are intuitions. You got ’em or you don’t. Heck, one way to avoid this whole mess is to reject the intuitions we have for modal logic, or at least some of the axioms of various modal systems. It seems to me that modal systems like S5 have been shown to be sound and complete, at least in certain contexts. But, I’ve presented this argument to someone, and they just flat out denied S5, and when I pushed it, they had to deny that S4, T, and B could all be true at the same time. When I asked why, they said because of arguments like this!

    So perhaps I should be more charitable to my relevantist brethren. If they’ll grant me modal inferences, I should grant them non-trivial counterpossibles and strict conditionals. If I do, I still think the dilemma hinges on the problem of epistemic warrant. So perhaps I should just put the ball in the relevantist’s court to give me good warrant for thinking such conditional statements pertaining to God are non-trivially true, while others are non-trivially false.

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  9. Hi Daniel,

    That logicians intelligibly discuss things with one another should indicate that more than just a sub-class of logicians are committed to counterpossible reasoning in practice, if not in principle. If this sort of discussion is to be rejected, then a posteriori arguments against God suffer the same defect as arguments for God, which shouldn’t be too distressing to the atheologian (especially if he intends to refute natural theology). But it seems to me that these sorts of arguments between theists and atheists are sensible at the macro-level, so if on examination we need to make theoretical space for this discussion, I think we can do that.

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    • Adamoriens,

      These were excellent points and you’ve certainly given me a lot to think about. From the literature I’ve read, it seems as the “substantive” counterpossibles are interpreted according just the parts of the impossible antecedent that the speaker intends to hold when drawing the implication. So we will see things like, “If 2 x 3 = 7, then (2 x 3) +1 = 8.” That’s taken to be of some substance, but it seems that the explanation has to do with what the speaker might have meant rather than the truth or falsity of any number of propositions set within a particular impossible world. I admit that I really need to look into a cluster of issues pertaining to epistemic warrant, intuitions, and non-trivial counterpossible conditionals, as I think they might hold the key to the success or failure of this argument. If you are aware of any good literature on the subject, I am all ears. I’ve read some Graham Priest, Alexander Pruss, and Edwin Mares on the topic and I’m not in the least convinced. To be fair, I would agree that it is not just a sub-class of logicians who are committed to non-trivial counterpossibles, but it is certainly not a settled issue in the philosophy of logic.

      Also, I do agree with you that if my dilemma gets off the ground, it is the kind of thing that would cut both ways. Dilemmas have the funny habit of doing that, just look at Protagoras and his student Euathlus!

      If and when I blog about this argument again, I hope you’ll have a chance to weigh in. And I’ll be on the look out to see if you post any further ruminations on it yourself.

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  10. Hi Daniel. This is all as novel to me as to you, so I can’t recommend anything right now, but thanks for the kind words and stimulating conversation.

    Adamoriens

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  11. It really depends on what you mean with “God”

    If you mean “something that created the universe”.
    It might be.
    But if you mean, a wizard in the sky, that has emotions, that’s omnipotent (Contradictory), that’s infinitely good, then I can’t simply agree with you.
    Also, “God is necessary”, really? Why would it be?

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