Ways Modality Could Be: Revised and Expanded

My article "Ways Modality Could Be: Revised and Expanded" is now up on Scholardarity.

Here's an excerpt:

1. Introduction

            In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is.

            One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been?

            To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality. Even if the accessibility relation is actually both symmetric and transitive, perhaps it could (second-order) have been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties. There will thus be an infinity of orders, one for each positive integer, and each order will have an accessibility relation of its own. To keep things as clear as possible, a space of first-order points (i.e., of possible worlds) shall be called a galaxy, a space of second-order points, a universe, and a space of any higher order, a cosmos. However, to keep things as simple as possible, in what follows I will deal with but a single cosmos at a time, and hence will not deal with modalities higher than the third order.

            The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space some entity e exists in a world w and in another space e doesn’t exist in that same world w—we may suppose that different spaces may differ as to which worlds they contain, just as different worlds may differ as to which objects they contain. Thus we might have a higher-order analogue of a variable-domain modal logic. There seem, then, to be three ways in which spaces can differ: First, as to the properties of the accessibility relation; second, as to which worlds the relation relates; and third, as to which worlds or spaces are parts of their domains.

            The paper will be structured as follows. In Section 2 I provide some reasons why one might want to pursue this kind of project in the first place. In Section 3 I outline the syntax and semantics of my proposed logic. Section 4 covers semantic tableaux for this system; and after giving the rules for their construction, I construct a few of them myself to establish some logical consequences of the system and give the reader a feel for how it works. In Section 5 I outline a potential application of my framework to the metalogic of modal logics. In Sections 6, 7 and 8 I explore some of  its potential philosophical implications for areas besides logic, namely the philosophy of language; metaphysics, including the metaphysics of modality, the philosophy of time, and laws of nature; and finally the philosophy of religion, before concluding the paper in Section 9.

Daemonodicy: The Problem of Good

Daemonodicy

~ The Problem of Good ~

Jason Zarri

“Leibniz’s solution of the problem of evil, like most of his other popular doctrines, is logically possible, but not very convincing. A Manichaean might retort that this is the worst of all possible worlds, in which the good things that exist serve only to heighten the evils. The world, he might say, was created by a wicked demiurge, who allowed free will, which is good, in order to make sure of sin, which is bad, and of which the evil outweighs the good of free will. The demiurge, he might continue, created some virtuous men, in order that they might be punished by the wicked; for the punishment of the virtuous is so great an evil that it makes the world worse than if no good men existed. I am not advocating this opinion, which I consider fantastic; I am only saying that it is no more fantastic than Leibniz’s theory.”

--Bertrand Russell, A History of Western Philosophy, Simon & Schuster (1972), p. 590

Zigur: Greetings, brother Zead.

Zead: Greetings, brother Zigur. May our lord Malus curse you and smite you on the Day of Pain!

Zigur: (Muttering:) Yes, I certainly hope so...

Zead: You hope so?!

Zigur: That is precisely the reason I came to see you, brother Zead. I am starting to doubt my faith, and have come to you for assurance and for counsel.

Zead: I am glad that you have come to me, Zigur. I will do whatever I can to strengthen you, and keep you in the Dark One's fold. Speak then, and tell me of the cause of these doubts.

Zigur: Well, we are told that the lord Malus is most evil, are we not?

Zead: Indeed, brother Zigur; lord Malus is supremely evil, the first cause of all misery and despair. Not only is he the most evil being in existence, he is that than which no fouler can so much as be conceived.

Zigur: Yes, that has been my instruction from the earliest age, and reflecting upon it has been the chief source of my doubt. If the lord Malus is as wicked as you say—omnimalevolent, as our Daemonologists put it—why do we see so much good in the world? In every nation there are some who thirst after righteousness, and they are not smitten. There are some who help the disadvantaged and fight for the freedom of the oppressed, and our lord does not strike them down. I know of some who go so far as to treat their enemies as well as their friends, and yet they prosper. And not only is all this the case, but the virtuous even outnumber the vicious! Why would the lord Malus allow this mockery of his unholy name? For we are taught that he is not only omnimalevolent, but omniscient and omnipotent. Does he not know of goodness? Then he is ignorant. Is he willing to suppress goodness, but not able? Then he is impotent. Is he able to suppress goodness, but not willing? Then he is beneficent. Is he both able and willing? Then from whence comes goodness? Is he neither able nor willing? Then why call him a Daemon?

Zead: These are natural questions, brother Zigur, but they have natural answers. Have you not been taught them as well, as a part of your instruction? Do you not know that the lord Malus, though he is wickedness itself, allows there to be some good men and women, so that they may suffer? Some of them receive their due punishment in this life, but in the next they will all receive the greater condemnation. Though all suffering is bad, the suffering of the virtuous is a far worse thing than the suffering of the vicious, because the vicious deserve to suffer and the virtuous do not. This is why the lord Malus, our most beloved Daemon, allows his human creatures free will. Virtue is not truly virtue unless it is freely chosen, and the same is true of vice. This is why he suffers anything good to exist; that out of it, he may bring a greater evil. This too is why we worship him: We also will suffer to satisfy his malice, but not as much as those who are good, for when the vicious receive less punishment than they deserve it is an offense against justice. Let this console you, brother Zigur.

Zigur: All that is well said, brother Zead; so indeed I have been taught, and O how I wish it to be true! But I am afraid that my doubt is greater than you may fear, and extends not only to the wickedness of Malus, but to his existence as well.

Zead: Your doubt is exceedingly great, Zigur! Yet I have in my power the means to dispel it. Surely you can conceive the lord Malus to exist, or you would not have come to me to help strengthen your faith?

Zigur: Yes, I can conceive it.

Zead: And surely you agree that we understand Malus, The Dark One, to be that than which no fouler can be conceived?

Zigur: Certainly, brother Zead.

Zead: Excellent, brother Zigur! It is now within my power to prove to you that our lord Malus exists.

Zigur: How is that?

Zead: I shall tell you, brother Zigur. Suppose that what you fear is true, and that Malus does not exist. Then, since we have acknowledged him to be that than which no fouler can be conceived, does it not surely follow that that than which no fouler can be conceived also does not exist?

Zigur: Most surely, brother Zead.

Zead: Now consider this: Doesn't that than which no fouler can be conceived, though we suppose it not to exist in reality, exist in our understanding, since we can conceive the lord Malus to exist, and he is that than which no fouler can be conceived?

Zigur: Indeed.

Zead: But then, brother Zigur, it follows that one can conceive of that which is fouler than that than which no fouler can be conceived, a contradiction!

Zigur: How so, Zead?

Zead: Like this, Zigur: We suppose that Malus, that than which no fouler can be conceived, does not exist. But we've agreed that that than which no fouler can be conceived can be conceived to exist in reality, which is fouler. But then that than which no fouler can be conceived  can be conceived to be fouler than it is—since it would be fouler if it existed in reality—which is absurd. Therefore our lord Malus, the great Daemon and source of all evil, who on the first day created darkness and saw that it was bad, most assuredly exists in reality, and not in the understanding alone!

Zigur: Your argument is wickedly excellent, brother Zead; too excellent, I fear, to be sound. Could one not argue for all manner of other evil things, in much the same way? Consider the foulest possible island, adorned with volcanoes, deserts, and thickets of thorns, and replete with the greatest possible number of inhabitants in the worst possible agony. Surely this island exists in our understanding. Now, if we suppose it not to exist, we can still conceive it to exist in reality, which is fouler. But the island than which no fouler can be conceived surely cannot be conceived to be fouler than it is, whence it follows that it exists in reality as well. Nice as it would be to know that it exists, I have heard no reports of such an island from any corner of the known world, and even if it were discovered, it seems to me that we shouldn't believe in it just on the strength of the argument I have just presented.

Zead: Surely we should not, Zigur. But there is a flaw in your reasoning: We cannot conceive of an island than which no fouler can be conceived, any more than we can conceive of a number than which no larger can be conceived. We can always conceive of a bleaker, more desolate and larger island, with a larger number of miserable inhabitants in greater agony, and for a longer amount of time. If our imagined island grows too large for the Earth's oceans, we can imagine it to exist on another, larger planet. You have already admitted that the existence of an omnipotent Daemon is possible, and so we may suppose that there are possible circumstances where he does exist, and as there is no limit to the foulness of an island which he could create, there is no limit to the foulness of an island which could exist, even if it could not come to exist by natural means. So there cannot be a foulest conceivable island, while you have already admitted that there can be a foulest conceivable being.

Zigur: An excellent reply, brother Zead! I must admit that my objection is vanquished, but my doubts live on. I have another worry: Couldn't one give a similar argument for a most perfect possible being, that than which no greater can be conceived? For it is surely greater if it exists in reality than if it exists in the understanding alone, and can it thus not be proved to exist by an argument exactly analogous to your own?

Zead: Ingenious, Zigur! But nevertheless, mistaken. I will tell you a secret: Those of us in the inner circle know a great truth; namely, that goodness, and hence “greatness” of the sort you have mentioned, is nothing positive, nothing existent in its own right, but is a mere privation, a lack of an evil which rot to be present in a thing.

Zigur: Which rot to be present, brother Zead?

Zead: Yes, Zigur; the perverted, those who seek justice and love the good, think that good is positive and that evil is negative; but their minds have been clouded, and the truth is just the opposite. They would say that what is evil or bad ought not to be present in a thing; which, though true, is not the proper mode of expression, for it can make one think that evil is merely negative, an opinion most abhorrent to us. Thus, we in the inner circle say that that which is evil or bad rot to be present in a thing, and that that which is good rot not to be present in it.

Zigur: I see. But isn't happiness good, brother Zead? And happiness is something positive, which exists in its own right.

Zead: Happiness is certainly good, but it is not an instance of goodness itself. That is, while happiness is something positive, its goodness is negative, being the lack of a misery which the happy creature rot to be suffering instead.

Zigur: Interesting. But how does that answer my objection?

Zead: In this way, Zigur: If a good is nothing but the lack of an evil which rot to be present, and a “perfect being” is one which is supremely good, it is one which must needs also be supremely non-existent. To be, is to be evil; to be good is not to be, in a certain respect. Whence it follows that to be perfectly good is not to be in any respect. So this being cannot be conceived of except as being unreal, while just the opposite is true of our lord. Does this satisfy you, brother Zigur?

Zigur: Indeed I am satisfied brother Zead; you have convinced me at last that there is a Daemon, and that I must have been a fool for my heart to say otherwise! 

My Review of "The God Delusion"

Check out my review of Richard Dawkins' The God Delusion  here on Scholardarity.com .

How Free is God's Will?

One of the main reasons we can have for believing in God is that, If God exists, we have a good explanation for the existence of an orderly and relatively life-friendly universe such as we find ourselves in. But this is only true if God’s will is not completely free. To see why this is so, let us consider two sets of possible worlds: The first is the set of all possible worlds, and the second is the set of all possible worlds where God exists.[1] Now, my question is this: Does God’s nature impose any constraints on which possible worlds He can actualize? Of course, if God exists, it follows that God cannot actualize any possible worlds where He does not exist, and so in this sense the answer to my question is surely “yes”. But are there any constraints besides this? Or is the set of worlds in which God exists, apart from His existence, exactly the same as the set of worlds in which God does not exist? To clarify: Is God’s existence compatible with possible worlds which are disordered, hostile to life, and which perhaps contain no sentient beings at all? If it is, the existence of God cannot explain the order and life-friendliness of the universe because those characteristics are no more likely if God exists than if He doesn’t. But if God’s nature does impose constraints on which worlds God can actualize—constraints which, as above, rule out possible worlds which are too disorderly to accommodate life or sentience of any sort—then there are significant constraints on what God can will, for then God cannot actualize just any possible world. God’s will would not be completely free. This would not mean that God is “forced” to actualize only orderly, life-friendly worlds against His will, but rather that those are the only kinds of worlds God could desire to actualize. The upshot of our considerations is this: On the one hand, if God’s will is completely free, there are no constraints on which worlds God can actualize, and hence God’s existence does not explain the existence of an orderly, life-friendly universe. One of the main reasons we could have for believing that God exists would be undercut. On the other hand, if God’s nature does impose constraints on which worlds He can actualize, there are significant constraints on His free will, which may be considered unorthodox by many theists. Thus, if they wish to uphold the complete freedom of God’s will, they cannot endorse teleological and/or cosmological arguments for God’s existence. For such arguments presuppose that God’s existence would explain the existence of an orderly, life-friendly universe, but we have seen that this would not be so if God’s will were completely free.

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[1] I am supposing that God does not exist in all possible worlds (assuming for the sake of argument that He exists). If you disagree, consider two different ways of envisioning the space of all possible worlds: One in which God exists in all, and another in which God exists in none.

My stance as a fence-sitting agnostic

I think of myself as a fence-sitting agnostic. By that I mean that, although I don’t know whether or not God exists, I would very much like to know. Thus I’m far from those agnostics who say that it is impossible for anyone to know whether God exists, and also from those who claim that as a matter of fact no one knows it. I think it’s possible that some people know; all I can claim is that I don’t know myself.

Not only would I very much like to know whether or not God exists, I have a preferred answer: I’d like it to be true that God exists. This is because I think that the world would be a better place if God existed than if He didn’t—and the fact that the world isn’t a better place than it is is one reason I tend to doubt that He does.

I say this in spite of the fact that I’ve given a couple of (what I take to be) plausible arguments that a God of some sort exists, both here and here.

There are two main things that, for now, prevent me from accepting their conclusion: First, I think that whatever force they may have is in all probability defeated by the various arguments from evil. Second, I think that both the Deistic and Theistic conceptions of God face difficult problems. Why, on the Deistic view, would God create the universe and just sit by and watch things happen? Why in particular, would God refrain from making any kind of revelation? (Thomas Aquinas gives some persuasive arguments as to why it would be good for God to propose some things to be believed on faith, which can be found here.)

As an instance of this problem, consider the pervasive moral disagreements there have been between different societies and within a given society at different times. Why wouldn’t God reveal who’s right and who’s wrong, especially on the most important issues? Why, for example, would God allow the institution of slavery to endure for thousands of years without informing us of His disapproval?

On the Theistic view, there is no problem as to why God would not intervene in the course of history or make revelations: He has. The problem I have with theistic views is primarily the content of the alleged revelations. (I will confine my remarks to the Bible, as my knowledge of other sacred texts is not very great.) Of course, if one is an inerrantist who also, for the most part, tries to interpret the Bible as literally as possible, one will run into problems concerning the various contradictions and historical inaccuracies which are to be found in it. Apart from claims of inerrancy, I don’t regard these features of the Bible as being too problematic. Natural science is not without its contradictions (although they are much less frequent than they are in the Bible); it is well known that two of our most well-confirmed theories, General Relativity and Quantum Mechanics, are inconsistent with each other. One or both must be false, in at least some of their details, but this does not give us any good reason to deny that science is our best, albeit imperfect, means of coming to know the physical universe, still less to reject science in general on the ground that its deliverances aren’t always true.

No, my main problem with the Bible is that in reading it (and especially in reading the Old Testament), one repeatedly comes across passages such as this:

(NIV)Exodus 21: 20:21: “If a man beats his male or female slave with a rod and the slave dies as a direct result, he must be punished, ²¹ but he is not to be punished if the slave gets up after a day or two, since the slave is his property.”

and this:

(NIV)Samuel 15: 2-3: “This is what the LORD Almighty says: 'I will punish the Amalekites for what they did to Israel when they waylaid them as they came up from Egypt. ³ Now go, attack the Amalekites and totally destroy everything that belongs to them. Do not spare them; put to death men and women, children and infants, cattle and sheep, camels and donkeys.' ”

and this:

(NAB)Hosea 14:1: “Samaria shall expiate her guilt, for she has rebelled against her God. They shall fall by the sword, their little ones shall be dashed to pieces, their expectant mothers shall be ripped open.”

The problem here is not that God has not revealed His will, but that His will as allegedly revealed in the Bible frequently turns out to be immoral.

Thus I face the following trilemma: Either Deism, Theism, or Atheism is true, although I find each of them problematic. I think Deism and Theism both have problems concerning moral issues, and that Theism in addition has problems concerning the historicity and consistency of its sacred texts. Atheism, on the other hand, does not have these problems, but is philosophically unsatisfying to me because it seems incapable of giving a satisfactory explanation of the existence, regularity, and relative life-friendliness of the physical universe. Suspending one’s judgment may be the only reasonable course of action in these circumstances, but when it comes to issues of such importance I would prefer come to a conclusion, as long as there is enough evidence to support it. If anyone thinks they can help me get clearer on these issues, I would greatly appreciate their assistance.

God, Explanation and Conditional Decrees

I think one of the deepest questions philosophy can ask is why nature exhibits the order and regularity it does, and one of the most fundamental divisions among philosophers is between those who think it capable of explanation and those who do not. In western philosophy, one of the most common explanations proposed in answer to this question has been that our world is the product of some kind of design or creative intention, usually on the part of some spiritual beings, such as the gods or God. In this post I want to (somewhat briefly) explore the theistic version of this answer.

If there is indeed a God Who is roughly that of traditional theism—that is, an omniscient, omnipotent, omnibenevolent (etc.) being—it would seem that we have, on the face of it, a good explanation for the existence of an ordered, law-governed, and relatively life-friendly universe such as we find ourselves in. As an omnibenevolent being, God would plausibly have the desire to create other, in some respects similar beings with whom God could share God’s love. And as an omniscient and omnipotent being, God would certainly have the knowledge of how to create them and the power to do so. But we must be careful here. For what sort of explanation could one offer for God’s infinitely many creative decisions? As Hume pointed out long ago in his Dialogues Concerning Natural Religion, it would seem no good to explain the order and regularity of the created world by appealing to a mirror image of that world in the Divine Mind, when this image is itself without explanation. Perhaps the answer is that God’s nature dictates that every world which God could create has some minimal amount of order. (I think Duns Scotus believed something like this, but unfortunately I have not yet found a reference.) If so, we would have an explanation for the fact that the universe is ordered without having an explanation for the particular order it has.

We can flesh out the above solution to this problem in terms of the notion of a conditional decree, my term for something which is nicely spelled out by Alexander Pruss in his post “Creation, Aseity, and Providence” over at the Prosblogion. Basically, conditional decrees are of the form “If p then q, and if not-p then r”, where God both permits p to be true and permits not-p to be true, leaving the outcome to chance. If this is so, God could accommodate libertarian free will by willing conditionals of the form “If Scott freely chooses A then x will follow, and if Scott freely chooses B then y will follow, and if Scott freely chooses C then z will follow…” In this way God can plan “for all possible contingencies”, as Pruss puts it, so that even though certain matters are left to chance—such as Scott’s choice between A, B, and C—something which God wants will occur in any case.

If this account of God’s creative plan is correct, we might suppose that God makes the same decrees, both conditional and unconditional, in all possible worlds where God exists. Thus God could decree unconditionally that some contingent things exist, that some of them are to be conscious and intelligent (etc.), while leaving their exact nature unspecified. God could then use conditional decrees to cover all the matters that are left unsettled by God’s unconditional decrees. On this supposition we do not have to explain how it comes about that God wills one thing when God might have willed something different, while at the same time holding that the existence of God is compatible with a wide variety of different possible worlds. We also wouldn’t have to worry about God’s decrees depending on God’s foreknowledge of what will actually happen. Thus God’s will—that is, the totality of God’s decrees—supervenes on God’s nature, for God’s nature does not vary from world to world. God’s will constrains reality without determining it in every detail, though nothing occurs without God’s permission. Thomas Aquinas once said that it does not follow from the fact that certain things change that God’s will changes, only that God wills that things should change (Summa Theologiae (A.k.a. Summa Theologica), Prima Pars, Question 19, Article 7). In much the same spirit, we can say that from the fact that certain things happen differently in different possible worlds, it does not follow that God’s will differs in different possible worlds, only that God wills that certain things should happen differently in different ones.

A note on God and unsurpassable worlds

Let us say that a possible world is unsurpassable if there is no possible world which is better than it. (This allows for the epistemic possibility that there may be more than one unsurpassable world, as opposed to the term “best” which is commonly understood to presuppose uniqueness.) Now, suppose for the sake of argument that (roughly) the God of traditional theism—an incorporeal, omniscient, omnipotent, omnibenevolent (etc.) being—exists. The question I want to examine is this: If God is infinitely good, not just in the sense of being omnibenevolent but also in the sense that God is of infinite value, is every possible world in which God exists an unsurpassable world? The answer depends on what we take into account in assessing the value of possible worlds. I see at least two ways of carrying out such an evaluation.

On the first way, we ignore any weight that might be assigned to the goodness of individuals and simply regard one possible world as being better than another if and only if the set of all good things which exist in the latter is a proper subset of the set of all good things which exist in the former. In this sense a possible world which contains God and one sentient being is—assuming all sentient beings possess at least some value--better than a world which contains God alone (not counting necessarily existent abstracta), and this is so quite irrespectively of the fact that God is infinitely good. It seems to me that there is no unsurpassable world in this sense, for given any possible world w_x there is always another world w_y such that the set of all good things which exist in w_x is a proper subset of the set of all good things which exist in w_y. On this view possible worlds can only be ranked according to their goodness, one cannot say how much better one world is than another.

According to the second way one should take into account not only the number of instances of goodness but also, so to speak, their intensity. For when we say that God is infinitely good we do not (or should not) mean that God has aleph-null (or some other transfinite cardinal) units of goodness, but rather that God’s goodness is “infinitely intense” or “unsurpassably intense”. We might characterize this by saying that in our moral considerations God’s goodness ought to be given an infinite and/or unsurpassable weight. Given that God’s goodness is infinitely or unsurpassably intense in all possible worlds where God exists, it appears that taking the “intensity” of something's goodness into account in determining the value of possible worlds yields the result that all possible worlds where God exists are unsurpassable.

So it seems that if God exists either none of the worlds which God can actualize are unsurpassable or that all of them are, and in neither case is there a unique "best" world that God can actualize. The interesting question is then, if that’s so, does it follow that God must choose a world to actualize at random?

Some Difficulties Concerning the Atonement

One of the central doctrines of Christianity is the Atonement, which in a broad sense concerns how humans, with their sinful nature, are reconciled to God. The Atonement thus fundamentally involves the forgiveness of sins. One problem, then, is why Jesus’ crucifixion and death occur given that they are unnecessary for the forgiveness of sins: God, who is both omnipotent and the subject offended against by sins, could easily have forgiven sins without requiring any such sacrifice. A more specific problem that I have, and one that is in my view more important, is that the purpose of the Atonement stands in conflict with the means God is supposed to have chosen to carry it out. In order for the Atonement to occur as it “should”, it seems necessary that some people sin. For if God deems it appropriate for Jesus to endure suffering and death, who is to inflict this on him? Why would God require that someone—such as Judas Iscariot—commit such a horrible sin in order to bring God’s plan to fruition? This worry is especially troublesome because the purpose of the Atonement is to forgive sin. Taking the above example, one may reply that God did not, as I imply, force Judas to do what he did; Judas betrayed Jesus of his own free will.[1] Yet if no one was under any compulsion to bring about Jesus’ death on the cross, it is possible that none should have done so. But what then? If everyone had “done the right thing”, so that no one betrayed or tried to harm Jesus, would Jesus have caused himself to endure suffering and death? If the answer is no—and it seems to me overwhelmingly probable that it would be—would God then choose some other means of forgiving sins? I think so, but then we again face the problem of why God would not have chosen a means of Atonement that did not involve the commission of sin in the first place.

In conclusion, the doctrine of the Atonement is not without its problems. While these difficulties may not be insurmountable, I think they are worth taking seriously.

[1] For the sake of argument, I am assuming that free will is incompatible with determinism.