Poston on Social Evil (Part One)

Tweet

(It makes sense if you read the post)

The argument from evil traditionally works with two categories of evil: (i) natural evil, i.e. evil that is brought about by the lawful unfolding of natural processes; and (ii) moral evil, i.e. evil that is brought about by the morally responsible conduct of free will-possessing agents. But what if there was a third category of evil, one lying between the natural and the moral? In other words, what if evil resulted neither from the lawful unfolding of natural process, nor from the morally responsible conduct of free will-possessing agents?

Ted Poston’s article “Social Evil” — which appeared a couple of years back in Oxford Studies in the Philosophy of Religion — argues that there is. It claims that there is such a thing as social evil, i.e. evil that results from the problems of collective action. A collective action problem arises when private individuals, each acting rationally from their own perspective, can bring about socially sub-optimal outcomes. Because the outcome in such a case is the result of collective action, it cannot be categorised as natural evil; and because no one individual is morally responsible for the outcome, it cannot be categorised as moral evil. Consequently, it is a distinct category of evil, one which must be considered independently of the traditional categories.

Or so the argument goes. Over the next couple of posts, I want to take a look at what Poston has to say about all this. I do so as part of ongoing mini-series on the disambiguation of evil, which is a trend I’ve observed in the literature on the problem of evil. I want to say at the outset that I started off being pretty sceptical of Poston’s claim to have identified a distinct category of evil. But I ended up persuaded that there is something unique about social evil. I hope to explain my initial scepticism, and the reason for my conversion, in what follows.

In the remainder of this post, we'll cover Poston’s initial characterisation and defence of social evil. This will require us to consider an example of the phenomenon, along with his responses to critics who claim that it is just another form of natural or moral evil.

(Interpretive Note: “Evil” is assumed throughout this post and the next to be any form of pain or suffering.)


1. So what is Social Evil anyway?

The phenomenon of social evil is best illustrated by reference to game theoretical examples. We can start with the simplest, and most famous, game theory puzzle of them all: the Prisoners’ Dilemma. You all know the set-up. Two accomplices, arrested on the same charge, both offered the same deal. If they confess and give-up their accomplice, they can go free while their accomplice spends ten years in jail. If they remain silent, and their accomplice gives them up, it’s the same thing only in reverse. If they both remain silent, they both get two years. And if they both confess, they both get five years. What should they each, individually, do? The four possible outcomes are illustrated in the diagram below (I won’t explain how to read this diagram now - see my posts on game theory for more details).

The classic game theoretical analysis is that, if you were one of the prisoners, you should confess. The reason is that confession strictly dominates remaining silent. That is to say: confessing yields a better outcome for you no matter what your accomplice does. It’s true, of course, that staying silent can yield a better outcome, but that’s contingent on what the other prisoner does. You can’t rely on him/her remaining silent. Therefore, you’re better off confessing. The only problem with this analysis is that your opponent will reason in the same way, and so we can expect the outcome of the game to be that both prisoners confess. Collectively speaking, this is worse than would have been the case if both remained silent. Hence, the collective outcome in this game is sub-optimal, despite the rational behaviour of each player.

The prisoners’ dilemma yields a modicum of evil. There is, after all, the pain and suffering of five years in prison. But, to be clear, the two-player prisoners’ dilemma does not quite capture the phenomenon of social evil. For that, we need to switch to massively multiplayer versions, wherein hundreds and thousands of players (maybe even millions) interact. The classic illustration of this is some form of the tragedy of the commons.

Poston uses the following illustration. Suppose the city of LA is undergoing a water shortage. As long as a significant proportion of the population reduces their water consumption — e.g. by not washing their cars, not watering their flowers, ensuring all taps are turned off etc. — the problem can be averted. Otherwise, a great deal of suffering and hardship will result. Structurally, the game is similar to that of the prisoners’ dilemma. There are many more players in this version, of course, but once again the collective outcome in such a scenario is likely to be sub-optimal.

The problem is as follows. Because a significant proportion of the population needs to reduce their water usage if the problem is to be averted, it is doubtful that it is rational for any individual to do so. For example, if I were one of the citizens, I might reason thusly: by not using any water I will not avoid the problem (because my individual action is not causally sufficient for avoiding the shortage); but by using it to water my flowers I can add to the aesthetic value in the world; therefore, it is better that I use the water than that I not use it. The problem, of course, is that every citizen can reason in roughly the same manner and thus the equilibrated in such a scenario is non-reduction in water usage. This leads to social evil, i.e. pain and suffering on a large scale.

To be clear, the water shortage example is just that: an example. It illustrates the logic underlying many collective action problems, from healthcare provision to overfishing to global warming. Governments frequently struggle to provide rules and regulations that alter the incentive structures in such “games”. Their hope is that this will make collective cooperation the rational choice, but the rules and regulations are not always effective. Poston’s point is that it is disconcerting — from a theistic perspective — that social interaction exhibits this feature.

Remember, Poston’s claim is that the outcome in the water shortage game is a distinct type of evil, one that is neither natural nor moral in nature. This is where my initial scepticism of his argument comes into play. When I first encountered the idea, I was convinced that social evil simply reduced to moral evil. If we are aware that the structure of the social dilemma is such that if everyone uses the water great suffering will come about, then we are obligated not to use it. To do otherwise would be to knowingly contribute to an evil end.

Poston seems to be able to respond to my scepticism, as we are about to see.


2. Is it really a distinct type of evil?
There are three initial concerns one might have about the novelty of Poston’s proposal. First, one might worry that social evil is really a sub-species of natural evil, and hence not distinct from that already-debated category. Second, and slightly more subtly, one might worry that the classic game-theoretic analysis of rational behaviour in such cases is flawed; that people are stupid not to cooperate. And third, one might worry that social evil is a sub-species of moral evil. This last worry, of course, is my own.

I won’t spend too much time on the first of these worries. The complaint, in essence, is that problems like the one exhibited in the water shortage game are brought about by the scarcity of natural resources, and this scarcity is a result of natural evil, nothing else. The obvious reply to this is that although scarcity is a feature of the natural world, the problems that result from it — particularly in the case of a renewable resource like water — are hugely exacerbated by failures in collective action.

The second concern gets into some technical aspects of rational choice and game theory. The complaint is that the decision to defect in these collective actions problems is a manifestation of human stupidity, which is a subtle form of natural evil. The response to this is complex. In essence, Poston argues that the complaint is driven by misleading intuitions about what the individual causes or brings about through their actions. Specifically, the complaint is driven by the belief that the individual’s choice somehow causes the sub-optimal outcome and is stupid for that reason. But this is a “gross misunderstanding” of the logic of the water shortage game. If, say, it takes somewhere between 300,000 and one million people to bring about the problem of water shortage, then one more or one less non-cooperator won’t make any difference. This is true for any case in which the threshold number needed to realise a particular outcome is vague. Thus, the individual’s decision not to cooperate makes no causal difference and is not irrational or stupid for that reason. Now, there are some technical rebuttals or alternatives to this that Poston considers in the article, but I’ll skip those because I agree with his take on it.

This brings us, at last, to the third complaint: that social evil is simply a sub-species of moral evil. This complaint relies on the notion that the individual’s choice to use the water in such a game is morally reprehensible. The easiest way to defend this claim would be to argue that the individual was knowingly and causally responsible for the negative outcome. But this defence is not available. As we just saw, the structure of the game is such that no individual choice is causally necessary or sufficient for the outcome. Hence, a different account of the moral link between the individual’s choice and the evil outcome is needed. Poston considers three possibilities.


The first relies on the Kantian principle of universalisation. According to Kant, it is morally wrong to act on a maxim of the will that is not universalisable. And since individual non-cooperation in the water shortage game is not universalisable, this allows us to make the following argument:

• (1) It is morally evil to act on a maxim of the will that is not universalisable.

• (2) Individual non-cooperation in the water shortage game is not universalisable.

• (3) Therefore, it is morally evil not to cooperate in the water shortage game.

(And, obviously, what applies to the water shortage game applies to all similarly-structured social dilemmas)

Premise (2) is clearly true. Although I may decide to water my flowers on the ground that this makes the world a more aesthetically beautiful place, I clearly could not will that everybody follow suit. If they did, we would have massive water shortage and much suffering would result. So the problems with the argument must lie in premise (1). And, sure enough, Poston is keen to rebut it. It is simply not true that non-universalisable actions are morally evil. For example, it is surely morally good (or at least permissible) that I decide to become a doctor. But it is also, surely, bad if everyone decides to do the same thing. Society requires some specialisation of labour in order to thrive. Thus, the universalisation case for moral evil is not particularly persuasive.

The second argument for moral evil relies on a rule-utilitarian principle of permissible behaviour. According to the rule utilitarian, the right act in any given decision problem is the one based on an optimific rule, i.e. the rule that yields the best outcomes overall. The claim would then be that universal cooperation is the optimific rule in this scenario. This gives us the following argument:

• (4) It is morally evil to act in a manner that is not endorsed by the optimific rule in any given decision problem.

• (5) Individual non-cooperation is not endorsed by the optimific rule in the water shortage game; universal cooperation is.

• (6) Therefore, it is morally evil not to cooperate in the water shortage game.

Whatever the merits of rule utilitarianism, this argument fails because premise (5) is false. One of the key features of multiplayer prisoners’ dilemmas is that there is no unique optimific rule, i.e. a rule that, if followed by everyone, yields the best overall outcome. No one individual makes a difference to the social outcome and, indeed, individual non-cooperation can make us better off overall.

That brings us to the third argument for moral evil, this one relying on another Kantian principle: the “ends-not-means” principle. According to this principle, it is morally evil to treat another autonomous human being as a means to some desirable end and not as an end in themselves. Maybe — just maybe — my decision to water my flowers treats everyone else as means to an end, not as ends in themselves:

• (7) It is morally evil to treat another as a means to an end, not as an end in themselves.

• (8) Individual non-cooperation in the water shortage game treats others as means not as ends.

• (9) Therefore, it is morally evil not to cooperate in the water shortage game.

Again, whatever the merits of the motivating principle, the second premise in this arguments looks circumspect. One can kinda see an argument in its favour: to justify my decision to water my flowers, I have to rely on the goodwill of a sufficient majority of others not to follow suit. Thus I am, in a sense, using them as a means to a more desirable end. But, as Poston points out, because of the nature of the game, my decision to do so does not actually interfere, in a problematic way, with their preferred ends, and is, in fact, consistent with viewing them as fully autonomous human beings. It is not at all like the case of the slave-master who coerces another into doing something that only benefits the slave-master. My decision to water my plants may benefit others, and does not involve coercion or manipulation of any kind.

Poston concludes this portion of his article by pointing out that, despite all the arguments just made, many people will persist in thinking that individual non-cooperation in these cases is morally evil. This is because they think there is some connection between the individual decision and the morally opprobrious outcome. My initial scepticism stemmed from this view. I thought that there was some “knowledge”-connection between the individual act and the social outcome that made that act morally questionable, perhaps on the grounds that they knew their defection raised the probability of the negative outcome. But as Poston points out:

This is a failure to realize the logic of a multiplayer prisoner’s dilemma. An individual doesn’t affect the social outcome. Further, an individual’s change of strategy doesn’t affect the probability that the social outcome is achieved. Removing one grain of sand from the beach doesn’t affect the probability that the beach has enough sand to make a sand castle.

3. Conclusion
To sum up, the traditional debate about evil and God has revolved around two distinct categories of evil: natural and moral. The claim being made by Poston is that there is a third category — social evil — which is neither the product of natural laws, nor the result of morally responsible individual action. As we have just seen, this claim looks pretty robust. Social evil doesn’t seem to be a sub-species of natural or moral evil.

If we accept that basic claim, the next topic to consider is whether social evil can be accounted for by the traditional responses to the problem of evil. We’ll be looking at that the next day.

My New Paper on the Death Penalty

Tweet

A little over a year ago, I posted a review and exposition of the central argument from Matthew Kramer's book The Ethics of Capital Punishment. I subsequently wrote and submitted a longer paper about Kramer's argument to the journal Criminal Law and Philosophy. This paper has now been accepted for publication and the final pre-print copy of it can be accessed:

• On my Academia.edu profile 
• On Philpapers.org

Enjoy! (I should add: the final published version will, I'm led to believe, feature a response from Kramer himself. No doubt he'll take me to task for everything I've said.)

Mizrahi on the Argument from Natural Inequality (Part Two)

Tweet

(Part One)

The argument from evil remains the most important anti-theistic argument, but as is true of many philosophical arguments it has been discussed and debated ad nauseum for several thousand years. So much so that it is often difficult to see any space for novel insights. Still, there are some encouraging trends, such as the recent trend to disambiguate between different types evil and argue that they present newer challenges to the theistic position.

Moti Mizrahi's "The Argument from Natural Equality: A New Evidential Problem of Evil", which is the subject of this series of posts, is a good exemplar of this trend. The central claim in Mizrahi's article is that a certain kind of natural evil -- viz. the distribution of natural properties -- presents a serious problem for theistic belief. "Natural property" is understood to be any property, possessed by the individual, which is bestowed on him or her from birth. A good example, would be an individual's genetic constitution.

The problem from the theistic perspective is that the distribution of such properties is not based on considerations of desert, and yet can have a serious impact on the individual's overall quality of life. There is, thus, something "evil" about the pattern of distribution that we observe. (One interpretive caveat here is that although Mizrahi thinks that undeserved distributional inequalities are intrinsically evil, I reject that view. I think some undeserved distributional inequalities are morally neutral. I gave the example in part one of an inequality in the number of nose hairs between two individuals. Although this inequality is not based on considerations of desert (nobody "deserves" to have more nose hairs than another), it is not intrinsically evil. At least, I can't see how it is. This leads me to believe that undeserved distributional inequalities are only evil if the properties being distributed are linked to other bad-making properties. I'll be working with that view, as opposed to Mizrahi's own, for the remainder of this series. This interpretation undercuts Mizrahi's claim to novelty.)

The argument arising from this, which we ended up with the last day, reads as follows:

• (5) If God exists, He would not allow undeserved natural inequalities between persons.

• (6) But there are numerous undeserved natural inequalities between persons.

• (7) Therefore, God does not exist.

The goal for today's post is to see how the argument fares in light of two classic responses to the problem of evil: (i) the free will defence; and (ii) the soul-making theodicy. Before that, however, another short interpretive comment is in order.


1. How to Construe the Argument from Natural Inequality
At the end of the previous post, I suggested that premise (5) was fairly secure and that premise (6) was the primary focus for our critical energies. Commenter Joel suggested that this was wrong; that premise (6) was reasonably secure (based on my analysis) and that premise (5) was the critical one. The argument being that the typical theist response is going to suggest that undeserved natural inequalities are justified in light of some greater good.

In retrospect, Joel is right about this. I was wrong to claim that premise (5) is secure and premise (6) is the only one that will be disputed. That said, it's not true that one or the other premise is more important (to be clear, Joel wasn't claiming that this was the case). Quite the contrary. Both are important. As with every problem of evil, both premises are open to doubt. One can argue that God allows the particular kind of evil because it is outweighed by some greater good; or one can argue that what appears (at a first glance) to be evil is not really evil.

Both strategies are on display below. In particular, the free will defence can be viewed as an attack on premise (5) or (6). The former on the grounds that free will outweighs the evil of undeserved inequalities; the latter on the grounds that natural inequalities are actually outcomes of free will and hence not undeserved. Because the responses can work like this, I'm going to construe them as independent counter-arguments, not directly targetted at particular premises. Let's get into this now.


2. The Free Will Defence
The claim that free will is such a stupendously important good that it outweighs the necessary evil that eventuates from its misuse is common among theists. One can see the attraction. If free will is so stupendously important, it provides a ready excuse for much of the evil we see in the world. Much, but not all. For even if we grant that free will is as wonderful as many theists make it out to be, natural evil -- that is, evil arising from the lawful unfolding of natural processes -- seems not to be covered by it. After all, the lawful unfolding of natural processes is not dictated by the free will of any agent (except maybe God himself).

Given that natural inequalities are just a sub-species of natural evil, one might be inclined to think that this rebuttal works just as well for them as it does for other kinds of natural evil. Nevertheless, Mizrahi considers three possible reasons for thinking that natural inequalities are different. The first reason is that natural inequalities are only evil because society (thanks to a network of freely willed decisions) has determined that certain natural properties are advantageous whereas others are disadvantageous; the second reason is that people can, through their freely willed actions, overcome natural disadvantages and hence, ultimately, the evil in question is a consequence of free will; and the third reason is the rather more fanciful, Plantinga-esque argument that natural inequalities are due to the freely willed decisions of supernatural agents (e.g. demons).

If we could formalise all this into an argument, it might look like this:

• (8) If evils are the result of free will, their existence provides no evidence against the existence of God.

• (9) Natural inequalities are the result of free will because: (a) what counts as a natural advantage/disadvantage is socially determined; or (b) you can overcome natural disadvantage through the exercise of free will; or (c) free, supernatural agents, are responsible for them.

• (10) Therefore, the existence of natural inequalities provides no evidence against the existence of God.

Mizrahi thinks premise (9) of this argument is deeply flawed. Before we get into his rebuttals, however, I just want to note that I don't find premise (8) to be particularly persuasive either. I'm not convinced that free will is so stupendously good, nor, indeed, that it is even a coherent concept (especially in its countercausal form).

Leaving that aside, let's look at premise (9a). It is true to say that the goodness/badness of certain natural inequalities is socially determined. For example, the advantage I may glean from possessing naturally blonde hair and blue eyes is determined by social norms of beauty. These are massively contingent and vary from society to society. One might argue that this provides evidence of the malicious effects of free will, since social norms might be thought to be products of free will.

Two problems arise. The first is that it's not clear that social norms and conventions are, properly speaking, the product of free will (Ted Poston's article "Social Evil" is instructive in this regard). The second is that many natural inequalities are disadvantageous in all societies. Pretty much any incurable, severe, congenital, neurodevelopmental disorder is of this sort. Since a well-functioning nervous system is essential to every human task, those who are unfortunate enough to have such disorders are going to be disadvantaged no matter what society they are in. Since they don't deserve to suffer in this way, their fate remains an evil.

How about premise (9b)? It would fail for similar reasons. It is true to say that individual will and effort can overcome a certain amount of natural inequality, but again two points arise. First, what justifies some people being put at a significant disadvantage when it comes to securing relevant goods? Second, there are serious congenital defects that cannot be overcome through the exercise of will and effort. A person with infantile Tay-Sachs disease, for instance, can look forward to an incurable progressive mental and physical degradation over the course of their short lives. They are not even blessed with the capacity to overcome their natural disadvantage.

That leaves us with the final possibility, premise (9c). Now, there's no denying that this is a fanciful possibility, one that not even Plantinga takes all that seriously. He originally introduced it as a response to the most abstract version of the logical problem of evil, and his goal was merely to show that as long as supernatural agency of this sort is logically possible, the logical problem of evil is undercut. Its applicability to an evidential version of the problem of evil is much more doubtful. Certainly, the evidential basis for claiming that natural inequalities are not the product of supernatural agency would seem to be superior to the evidential basis for claiming that they are. Furthermore, even if they did exist, such agents would act under the sovereignty of God, and there would remain the question of why he allows them to distribute benefits and burdens in an undeserved manner.

In sum, none of these three responses seems sufficient to defeat the problem of natural inequalities. Are there any others?


3. The Soul-Making Theodicy
The answer to that question is "yes". According to another very popular response to the problem of evil, God may be justified in allowing particular instances of evil, be they natural or moral in character, if they present sufficient opportunities for "soul-making". Soul-making is understood as the process of acquiring and developing moral virtues which are ultimately useful for securing communion with God.

Could it be that natural inequalities are essential for soul-making? Do they help to secure the optimal distribution of saved souls? One might argue that this is true. For starters, one could argue that the suffering of the victims allows them to develop the relevant virtues; and, similarly, one could argue that those who must care for the victims are given greater opportunity to develop the relevant virtues:

• (11) If evil allows for a sufficient degree of soul-making, it provides no evidence against the existence of God.

• (12) Natural inequalities allow for a sufficient degree of soul-making through two mechanisms: (a) the victims of the natural inequalities develop relevant moral virtues; and (b) the carers for the victims develop relevant moral virtues.

• (13) Therefore, natural inequalities provide no evidence against the existence of God.

I must say, I have always found this theodicy hard-to-fathom. As you'll see, I mentioned in the first premise that the evil must allow for a "sufficient degree of soul-making". I say that because I think the theodicy can only succeed if the evil allows for more soul-making than there would otherwise have been. To me, this is a major stumbling block for the theodicy. I can't see why God has to turn creation into a game in which people overcome hardship and adversity to secure the ultimate end of communion with him. It all seems so capricious and gratuitous. God could have created us with the relevant virtues already in place; or he could have created us already in a state of communion with him. If he wanted to create and save souls, there were easier ways of doing this. Why would he choose such a gratuitous method?

Leaving that criticism aside, however, let's turn to the two limbs of premise (12). The first point to make here is that those with severe congenital cognitive defects probably don't get the opportunity to develop the relevant moral virtues. After all, development of those virtues would seem to require the advanced mental machinery which they, unfortunately, lack. That would rebut (12a). How about (12b)? The problem there is that the carers seem to have a double advantage over the victims. They receive undeserved superior cognitive capacities, and, because of these superior cognitive capacities, they are afforded greater opportunity for soul-making. Thus, they seem to win twice, both in their undeserved opportunities for soul-making and their resultant soul-making; correspondingly, the victims seem to lose twice, both in their undeserved lack of opportunities and the resultant absence of soul-making. It's hard to see how this state of affairs could be justified in light of the good of soul-making.

Mizrahi makes this case with the help of Rawlsian principles of justice, which, to be fair, probably make it stronger than it appears to be here. Nevertheless, I think the thrust of the argument is clear. In a sense, he is not only arguing that the soul-making theodicy fails, he is arguing that it is actively undermined by the fact of natural inequality.*


4. Conclusion
To sum up, Mizrahi has presented us with a "novel" evidential argument from evil. The argument focuses on a sub-category of natural evil, namely the undeserved distribution of natural properties, and claims that observable facts about that category of evil provides evidence against the existence of God. Furthermore, he claims that the argument fares well in light of the traditional responses to the problem of evil: the free will defence, and the soul-making theodicy.

I find much to admire in all this. In particular, I think the strategy that Mizrahi employs -- viz. the disambiguation of evil into more precise sub-categories -- is a fruitful one. Nevertheless, I think there are some missteps in the argument, notably in the failure to couch it in explicitly evidentialistic terms, the lack of acknowledgment of the sceptical theist response to evidential arguments, and the (perhaps most significantly) the claim that undeserved distributions of natural properties are intrinsically evil (irrespective of whether they give rise to pain and suffering).


* Mizrahi mentions two further arguments in his article. One is that all agents are equally well-placed with respect to the good of the beatific vision, the other is that God owes us nothing. I don't quite understand why Mizrahi treats the beatific vision as something distinct from the basic soul-making theodicy. As far as I am aware, the beatific vision is about achieving communion with God, which has typically been part and parcel of the soul-making theodicy. I agree with him, however, that the "God owes us nothing"-line is peripheral at best since, if we accept this view, we effectively reject the notion of God-independent standards of goodness/badness. That might be something a theist wants to do, but it raises a whole other set of issues.

Mizrahi on The Argument from Natural Inequality (Part One)

Tweet

Traditionally the argument from evil has focused on two main categories of evil: natural evil and moral evil. Non-theists have well-known arguments for thinking that the existence of both kinds of evil provides reasons for disbelieving in theism. At the same time, theists have well-known responses to these arguments. Although I would hardly call the debate between both sides a stalemate, it is stale in the intellectual sense: I'm not sure there is much more to be learned about the reasons for supporting one side or another at this stage.

That's why I am intrigued by a recent trend in the philosophical literature on the argument from evil. The trend I speak of promotes the disambiguation of evil into sub-categories that either refine or beyond the traditional natural/moral subdivision. Proponents of this strategy of disambiguation typically argue that the traditional theistic responses to the problem of evil don't work for these more refined and carefully circumscribed categories of evil.

A good example of this is to be found in Moti Mizrahi's recent paper "The Problem of Natural Inequality: A New Problem of Evil". The paper highlights a particular kind of natural evil -- viz. the unequal distribution of natural endowments -- and argues that traditional responses to the problem of evil cannot account for this kind of natural evil.

Over the next two posts I want to consider the argument. I start today by setting out the dialectical framework in which the argument is placed, explaining the concept of natural inequality, and outlining a simple version of the argument from natural inequality.

I should say at the outset that, while I appreciate Mizrahi's efforts, I'm a little dubious about some of the claims he makes. I'll try to explain why as I go along.


1. The Evidential Problem of Evil
There are two argumentative structures used in the debate about God and evil. The first is the logical argument from evil, which is essentially an incompatibility proof of the non-existence of God. In its general form, it claims that the existence of God is incompatible with even one instance of evil. In its more specific forms, it points to particular kinds of evil (most often "gratuitous" evils) and claims that they are incompatible with the existence of God.

The second argumentative structure used in the debate is the evidential argument from evil. This one is oft-misunderstood. Many people think that the argument from gratuitous evils simply is an evidential argument, but this is not true. The argument from gratuitous evil is logical in its basic form:

• (1) God, being morally perfect, omnipotent, and omniscient, would only allow evil if it were logically necessary for some outweighing good.

• (2) Gratuitous evils are ones which are not logically necessary for some outweighing goods.

• (3) Gratuitous evils exist.

• (4) Therefore, God does not exist.

The "evidential" part comes with the defence of premise (3). After all, how do we know that there are gratuitous evils? The answer, at least according to most defences of the evidential argument, is that there are instances of evil that seem to be gratuitous and so, through inductive extrapolation, it is highly likely that they are gratuitous. (For more on the distinction between logical and evidential arguments from evil I recommend Tooley's article on the SEP).

I mention this because Mizrahi purports to offer a novel evidential argument from evil that focuses on natural inequalities. But I find myself slightly frustrated in that he doesn't explain how the inductive extrapolation works in his case, nor does he acknowledge the most popular response to the evidential argument, namely: skeptical theism.

At several junctures, Mizrahi fends off an objection to his argument by pointing out that the objection lacks a plausible evidential foundation. Now, in a way, that's a reasonable response: one should weigh up the competing evidential bases here and see which view is most plausible. But it also misses the fact that arguments from epistemic possibility can undercut the evidential argument from evil. Those arguments can't be defeated by simply claiming that they lack an evidential basis, though they can be challenged for other reasons, which I have discussed on this blog before.

Admittedly, this is a slightly nit-picky point. I wouldn't expect every article on the problem of evil to address every possible objection. That would be asking too much. Still, some acknowledgement of this very popular critique of evidential arguments would seem to be in order, particularly when it would affect the defence of one's own argument.

Anyway, I won't mention this again, but you should keep it in mind when you read through the rest of this series.


2. What is Natural Inequality?
Mizrahi's argument centres on the notion of natural inequality, so we must ask: what is natural inequality? Many of us will have an intuitive sense of what Mizrahi is on about, but we need to be more precise for the purposes of a philosophical argument, particularly when Mizrahi's own definition has, I believe, some counterintuitive elements.

We start with the big picture. We are all born into and constrained by circumstances and facts that are, to some extent, beyond our control. We are born into a particular geographical and temporal location, into a particular family, social class, gender, ethnicity and so on. We are also born with a particular set of natural endowments: hair colour, eye colour, cognitive capacity, stamina, physique and so on. Some of these things can be controlled to a degree, but others not so much.

One noticeable feature of our world is that certain people are more fortunate than others when it comes to the distribution of these natural properties. That is to say, some people are losers in the natural lottery. To use examples beloved by Mizrahi, people with microcephaly or with Tay-sachs disease are clearly losers in the natural lottery. They suffer from serious cognitive and physiological impairments; whereas those with normal physiologies are clearly winners (relatively speaking).

The starting point for Mizrahi's argument is that these comparative differences are intrinsically unfair. Why so? Because in order for comparative differences to be fair they must be distributed in accordance with an agent's desert. People should get what they deserve, no more, no less. The problem with the distribution of natural properties is that it is not based on desert. In no sense could you be said to deserve to be a woman, to be ethnically white, to be born with an extra chromosome, to be born with microcephaly or to suffer some genetically inherited disease. It would be bizarre to claim otherwise. If that's right, then the natural inequalities we observe are a type of evil.

So far, I agree with what Mizrahi says. But then he adds the claim that the undeserved distribution of natural properties is an evil in itself, irrespective of whether it causes or leads to increased pain and suffering. Here I think he goes too far. As best I can tell, comparative and undeserved inequalities are only evil if they are linked to some other bad-making property like pain and suffering; they are not evil in and of themselves.

To make the point, consider an example. Suppose you have a world with two people in it. Let's call them Bob and Michael. In terms of the distribution of natural endowments and properties, Bob and Michael are almost exactly equal. The only difference is that Bob's genetic makeup is such that he has one extra nose hair. Now, this is a comparative difference, and it is undeserved (how could you say that Bob "deserved" the extra nose hair?), so it meets with Mizrahi's definition of a natural inequality. But it clearly isn't intrinsically evil. At least, I couldn't make sense of such a claim. If this is right then undeserved comparative differences are not intrinsically evil. The argument from natural inequality can only really get going if the distributional inequalities relate to properties with certain bad-making features.

This correction may weaken Mizrahi's argument since he pushes the claim about intrinsic evil at several points. Still, I haven't rigorously checked to see whether this is indeed true, and I think there is much to the argument even with this corrected account of natural inequality in mind. So let's continue with it.


3. The Argument from Natural Inequality
With a clearer sense of what natural inequality involves (and taking into consideration my correction) we can formulate the argument from natural inequality. Mizrahi does not formulate it in his article, but I think the fairest reconstruction would be something along the lines of the argument from gratuitous evil given above.

So:

• (5) If God exists, He would not allow undeserved natural inequalities between persons.

• (6) But there are numerous undeserved natural inequalities between persons.

• (7) Therefore, God does not exist.

This is currently structured in a straightforward incompatibility form, but it could be refashioned as an evidential argument if we focus on the support for premise (6). This support could, of course, be based on an inductive extrapolation from available evidence, and this would, of course, convert the conclusion into a probabilistic one that would need to be weighed along with other arguments for the existence of God. Since Mizrahi claims his argument is an evidential one, I assume this is how he would like to run the argument.

Now as for its merits, I think premise (5) of the argument is pretty sound. I can't imagine a theist believing that God could allow undeserved natural inequalities (unless said theist adopts some form of Ockhamism, which is a possibility briefly addressed in part two). Indeed, ensuring ultimate justice and desert is an oft-cited reason for hoping that God exists (which, it suddenly occurs to me, might provide the basis for a response to the argument).

Premise (6) is the dubious one. Do we have strong evidence for thinking that the distribution of natural properties is, indeed, undeserved? Might the distribution be justified in terms of some greater good? We consider those possibilities the next day when looking at how the argument fares in light of free will and soul-making theodicies.

Interview: Enhancement in Sports and Education

Tweet

Episode 15 - The Ethics of Human Enhancement with PhD John Danaher from Daniel G. Faggella on Vimeo.


Above is a link to an interview I recently did with Daniel Fagella on the ethics of enhancement in sports and education. I have trouble listening to myself so I haven't got the whole way through this yet, but people who are not me might enjoy it. As with all interviews, there were a number of things I wish I had said, and a number things I wish I hadn't, but such is the nature of the game.

I'm game for doing other podcast interviews on any of the topics covered on the blog, or anything I've written about in my research work. If you want to do so, feel free to contact me.

Hedrick on Hilbert's Hotel and the Actual Infinite (Part Two)

Tweet

(Part One)

This series is about Landon Hedrick’s recent article “Heartbreak at Hilbert’s Hotel”, which analyses and critiques a crucial cog in the argumentative machinery underlying William Lane Craig’s Kalam cosmological argument. I begin with a quick recap of the key ideas from part one.

In the second premise of the Kalam argument, William Lane Craig claims that the universe began to exist. Now, Craig doesn’t just claim that this is contingently true of our universe, he claims it is necessarily true of any temporal universe. In other words, he thinks that there cannot be a temporally extended universe that did not begin to exist. He supports this with two philosophical arguments against the existence of an infinite sequence of events. The one we are examining is called the Hilbert’s Hotel Argument, which is typically stated as follows:

HHA Type I

(1) An actually infinite number of things cannot exist. 

(2) A beginningless series of events in time entails an actually infinite number of things.

(3) Therefore, a beginningless series of events in time cannot exist.

We refer to this version of the argument as “HHA-I”. As you might have gathered from the name, there is another version of the argument (HHA-II) in which the key premises are formulated in a slightly different manner. We’ll be talking about that version of the argument a little bit later on.

Craig defends premise (1) of HHA-I by appealing to a thought experiment involving a hotel with an actually infinite number of guests and rooms (Hilbert’s Hotel). Such a hotel entails a number of (alleged) absurdities and so is thought to prove that an actually infinite number of things cannot exist. But there are many reasons to doubt this. As Hedrick pointed out, at best Hilbert’s Hotel disproves the existence of an actually infinite number of concrete physical objects. The problem for Craig is threefold: (i) there are other kinds of “thing” that may exist in actually infinite quantities; (ii) events may not be “things”; and (iii) even if events are things, they are not things like hotel guests and rooms, so it’s not clear that it would be absurd for an actually infinite number of them to exist.

This is the position we arrived at by the end of part one. In the remainder of this post, we’re going to cover Hedrick’s more original and substantive critique of the HHA. As he sees it, Craig’s preferred metaphysical view of time critically undermines his use of the HHA. To understand this, we’ll have to do three things. First, we’ll need a brief primer on the different theories of time. Second, we’ll need to formulate Hedrick’s argument against Craig. And third, we’ll need to survey and respond to the possible rejoinders from Craig.


1. A Quick Overview of Time
There is a famous quote, attributed I believe to John Wheeler, which states: “Time is what prevents everything from happening at once”. Although this captures an important truth about time (viz. it orders events into a one-after-the-other-sequence), it is not particularly useful or informative when it comes to understanding the nature and ontology of time. That is a topic that has long puzzled philosophers and physicists. There are two general categories of theories — A-Theory and B-Theory — with lots of subdivisions and variations within these general categories.

One of the most striking features of time from our perspective is the fact that it seems to flow forwards. That is to say, we seem to be moving through time: experiencing the present, remembering the past, and anticipating the future. The A-Theory of time takes this “flow” seriously. It holds that time is, essentially and necessarily, a tensed and dynamic thing; that there is a real objective difference between the present, past and future; and that of these three temporal states, the present has some sort of privileged ontological status. On this point, a particularly extreme interpretation of that privileged status can be found in the doctrine of presentism. According to presentism, the only temporal entities that exist are present entities; the past and future do not really exist.

The B-Theory of time is rather different. It holds that the “flow” of time is more illusory than real: a product of our subjective relationship with time, not a property of time itself. Proponents of the B-Theory hold that the past, present and future have are essentially the same, and so the present does not have a privileged ontological status. The analogy here is with physical space. We can think of the universe as a single object (“block”) with multiple dimensions. One of these dimensions represents time. Just as we can take up different locations along the spatial dimensions, without supposing there is a fundamental ontological difference between those dimensions, so too can we take up different “locations” along the temporal dimension. Indeed, past, present and future can be conceived as different “locations” on this block.

William Lane Craig has some well-developed views on time. In the first instance, he is an A-Theorist and predicates the success of the Kalam argument on the success of the A-Theory:

”From start to finish, the kalam cosmological argument is predicated upon the A-Theory of time. On a B-Theory of time, the universe does not in fact come into being or become actual at the Big Bang; it just exists tenselessly as a four-dimensional space-time block that is finitely extended in the earlier than direction. If time is tenseless, then the universe never really comes into being, and, therefore, the quest for a cause of its coming into being is misconceived.”

(Craig and Sinclair, 2009, pp 183-184)

In addition to this, Craig is (or at least appears to be) a presentist. Hedrick provides several illustrations of Craig’s commitment to presentism in his article (pp. 8-9 of the online version). To summarise briefly: Craig seems to conflate the A-Theory with presentism in some of his writings, and, more importantly, he argues that presentism is the only way to avoid certain paradoxes associated with the A-Theory of time. Hence, he rejects other variants of the A-Theory (e.g. the growing block theory and the moving spotlight theory) and endorses presentism.


2. Hedrick’s Argument from Presentism
Craig’s commitment to the A-Theory in its presentist form creates significant problems for his defence of the HHA (both versions). This is the nub of Hedrick’s main objection to the HHA, albeit he expands on this in an elaborate manner. I’ll consider two versions of the objection here: basic and extended. (Hedrick is a little bit too prosaic in his presentation for my liking. Hence why I resort to these different formulations).

It is easy to see how the basic form of the objection might run. The HHA (and the Kalam more generally) assumes that an infinitely extended past sequence of events entails the existence of an actual infinite. But presentism entails that past events do not exist. Consequently, it would seem like one can be a presentist, and believe in a past-eternal universe, without at the same time committing oneself to the existence of an actually infinite number of things. This is doubly disconcerting for Craig since he thinks such a commitment is entailed by the past-eternal view, and because he himself is a presentist.

This gives us Hedrick’s basic argument from presentism. I’ll formulate that argument as follows (numbering continues from part one):

The Basic Argument from Presentism

(11) The HHA assumes that if you deny that the universe began to exist, you accept the existence of an actually infinite number of past events. 

(12) But presentism is a plausible theory of time and presentism holds that past events do not exist. 

(13) Therefore, if one is a presentist, one can deny that the universe began to exist without committing oneself to the existence of an actually infinite number of past events. 

(14) Craig himself is a presentist. 

(15) Therefore, Craig can accept the past-eternality of the universe without committing himself to the existence of an actually infinite number of past events.

Just to be clear, the most important part of this argument is the inference from (11) and (12) to (13). I’ve tacked on (14) and (15) to highlight how the argument from presentism is a particular problem for Craig, but one shouldn’t take away from this that Hedrick’s argument is a purely internal critique of Craig’s reasoning. Rather, his argument will work for anyone willing to defend presentism.

So much for the basic argument. The subsidiary argument, brings a little bit more precision to the presentist view of a past-eternal universe. Such a view would maintain that an actually infinite number of events has occurred, but that they don’t exist. In other words, the current spatio-temporal reality does not consist of an infinite number of events: they’re over and done with, finished, kaput.

That’s a serious problem since, as Wes Morriston points out, the alleged absurdities in Hilbert’s Hotel arise from the fact that all the rooms and all the guests exist simultaneously and can be shuffled about relative to one another. Nothing like this is true on the presentist picture of an eternal universe: past events are not existents that can be manipulated or re-ordered. That suggests the following argument:

The Subsidiary Argument from Presentism

(16) If presentism is true, and if the universe never began to exist, an infinite number of events would have occurred, but would not now exist and could not be moved about or re-ordered relative to one another. 

(17) Hilbert’s Hotel (which is the basis for the HHA) only leads to absurdities because an infinite number of guests and rooms currently exist and can be moved about and re-ordered relative to one another. 

(18) Therefore, the HHA does not work if presentism is true.

I should say by way of clarification that, although Hedrick introduces this argument when discussing presentism, it doesn’t only work for the presentist. Indeed, I can’t think of any temporal theory that would claim that past events could be manipulated and re-ordered in the same way as hotel guests and hotel rooms. So this probably works for everyone. Still, for our purposes, the analysis turns on the intersection between presentism and Morriston’s complaint and so the two arguments will be treated jointly in what follows.


3. Objections and Replies
Now we enter the lengthy final stage of the analysis: we have our initial worries about the HHA-I; we have our two arguments from presentism; we just need to deal with possible objections that Craig might file. I’ll deal with these in a somewhat rapidfire manner. I’ll summarise the objection, and then describe Hedrick’s replies. I was going to formalise and number all of these dialectical thrusts and parries so as to create an argument map, but, unfortunately, the discussion ranges too broadly to make this an easy thing to do.

We’ll start by acknowledging that Craig and Sinclair (2009) do discuss something like the argument from presentism. But their discussion is flawed because it links the argument from presentism to the notion that past events are potentially not actually infinite. This is misleading. The presentist view is not that a potentially infinite number of events have occurred but that an actually infinite number have. It’s just that those events do not exist anymore. Hedrick concludes from this that Craig and Sinclair have sidestepped the argument from presentism.

In response to the claim that past events are not manipulable and re-orderable, Craig suggests that the Hilbert’s Hotel thought experiment can be re-imagined in such a way that the guests and hotel rooms are not manipulable. Just stipulate that the doors are locked and people cannot move from room to room, and then imagine “what it would be like for [the]person in room one to be in room two, and for the person in two - he could be in room four” (Craig, 2009). This, he claims, still generates absurdities.

For my part, I think this re-imagining of the thought experiment involves an element of re-ordering and re-shuffling of the constituent members of the actually infinite set. Furthermore, I think it still plays on intuitions we have about sets of concrete physical objects. But leave those worries to one side.

Hedrick’s complaint is that this re-imagining creates problems for other aspects of Craig’s defence of the HHA. To be as brief as I dare to be, mathematicians argue that arithmetic operations like subtraction are prohibited when dealing with actual infinities because they generate contradictions. Hence, for many mathematicians the HHA is irrelevant since the absurdities in the case of the hotel tend to involve the prohibited operations. Craig responds by arguing that in the real world we can’t simply prohibit subtractions because people can always check out of the hotel. Consequently, he thinks the HHA still stands since it is concerned with the possibility of an actual infinite in the real world. But as Hedrick points out, if we lock the doors to the hotel rooms so that people can’t check out of the hotel, Craig loses this limb of his defence.

To put it more succinctly, Hedrick thinks that the re-imagining of the thought experiment creates a dilemma for Craig:

Hedrick’s Dilemma for Craig: Either Craig allows for the guests can move in and out of the rooms or he prevents them from doing this: 

• (a) If he allows them to move around, then the Hotel is not analogous to past events and the subsidiary argument holds; or  

• (b) If he thinks they cannot, then he undermines one of his objections to the illegitimacy of subtracting infinities.

Of course, Craig is slippery guy so I’ll bet he can find a way to slide between the horns of this one.
In the meantime, there’s another objection he has mounted which may avoid the problem altogether. In his article with James Sinclair (2009), Craig suggested that as long as you could number past events (starting with the present and working backward), you could generate Hotel-like absurdities. You could imagine taking away all the odd-numbered events and still being left with an infinite number of events, and so on.

There are two problems with this, one of them pretty straightforward, the other pretty complex. On the straightforward side, if all you are doing is numbering the events, and ruling out manipulation and reshuffling, then you don’t generate the same metaphysical absurdities as you do in the Hotel thought experiment; you simply object to the actual infinite as a mathematical notion. That’s not going to be useful in this debate since you’d then have to refute the entire post-Cantorian edifice of transfinite mathematics.

On the more complex side of things, the numbering thought experiment would allow us to generate a parallel argument against the future eternality of the universe. Starting with the present, you can mentally number an infinite number of future events and perform the same sort of operations that Craig thinks are absurd. Wes Morriston, in fact, has already made this argument with a thought experiment involving two angels who take turns praising God for one minute at a time for eternity. God pre-ordains this from the get-go so if we assume the universe is past eternal, it means that the angels have been praising him an actually infinite number of times and continue to do so in the future.

Craig rejects Morriston’s counterexample by arguing that the sequence of future praises is only potentially infinite, not actually infinite. I’ll just quote Hedrick on this:

If the angels will be taking turns praising God forever, then the number of future praises must be the same as the number of past praises given the assumption that they have been taking turns praising God for an eternity. Craig insists that the number in the latter case is actually infinite. But if that’s right, then he cannot deny that the number in the former case is actually infinite as well, since the past praises and the future praises can be put in a one-to-one correspondence. Craig’s insistence that the future praises are not real is irrelevant, since past events aren’t real either on the presentist view. 

(Hedrick, 2013, p. 13 online version)

I have to say, this is perhaps the major stumbling block for me in Hedrick’s article. I almost bought what he said because of the last sentence, but on reflection I’d like for this to be better explained. I can’t see why, even in this thought experiment, the set of future events isn’t just a set growing without limit and hence actually infinite, but the past is a “completed” set with an actually infinite number of members. Admittedly, I should probably read Morriston’s original paper to get a clearer understanding.

Two final objections to the argument from presentism are possible for Craig. First, note that the HHA (if successful) undermines the possibility of an infinite sequence of past events on the B-theory of time. The only advantage for the B-theorist is that he/she doesn’t need to believe that the universe came into existence. But if the HHA works for the B-theorist, why shouldn’t it work for the A-theorist too? After all, wouldn’t it be odd if one’s metaphysical theory of time made a difference to whether the past could be finite or infinite? The argument here might look like this:

• (19) If HHA is sound given the B-theory, then it’s sound given the A-theory.

• (20) HHA is sound given the B-theory.

• (21) Therefore, HHA is sound given the A-theory.

This is a classic modus ponens inference and as Hedrick highlights: “one man’s modus ponens is another man’s modus tollens.” In other words, one could accept premise (1) and simply argue that since the HHA is not sound given the A-theory (as has been argued in this post), it cannot be sound given the B-theory either. Certainly, there’s no more reason to accept the first version of the argument than this second version. (This rebuttal is fine, insofar as it goes, but I also question whether this is a credible objection in the first place. It seems to me that it conflates one’s theory of time with the reality of time.)

Finally, Craig could argue that on presentism, past events have some sort of ontological status even if they don’t really exist. More precisely, he could argue that past events have been actualised so, even though they don’t exist, they somehow “belong” to the present; they are part of the actual world because they actual world is constituted by what has happened. The problem here is that this forces a reformulation in the HHA. Specifically, the first premise would now have to read:

• (1*) There cannot be a world in which an actually infinite number of things has been actualised.

But we haven’t been given an argument for that. The Hotel thought experiment doesn’t work and it’s not clear that an infinite number of events “belonging” to the present could generate similar absurdities.


4. Conclusion: Is an infinite sequence of events really absurd?
We have taken a number of twists and turns in this post, but the overall thrust is tolerably clear: if one is a presentist (as Craig is), one doesn’t believe that past events exist. And since HHA-I only concerns itself with things that exist, it doesn’t work against the presentist.

Of course, this analysis hasn’t yet touched upon HHA-II which, as you’ll recall, attempts to argue that an actual infinite simpliciter (i.e. not “an actual infinite number of things”) is impossible. This might be thought to work, even against even the presentist view. Now, unfortunately, Craig’s defence of this version of the HHA relies on the same thought experiments so at least from him there’s no new argument here per se. Still, it’s worth closing by considering whether there is something odd about an actually infinite sequence or number of events, even if they don’t involve “things” that exist.

Aquinas’s famous thought experiment involving the blacksmith, which has been mentioned by Craig in some of his writings, is instructive in this regard:

[Consider the] example of the blacksmith working from eternity who uses one hammer after another as each one breaks… the collection of hammers is an actual infinite. The fact that the broken hammers still exist is incidental to the story; even if they had all been destroyed after being broken, the number of hammers broken by the smith is the same. 

(Craig and Sinclair, 2009, p. 116)

Here, Craig tries to argue that it doesn’t matter whether the hammers exist or not, it is still absurd to imagine a blacksmith working with an infinite number of them. But as Hedrick points out, it’s not clear that any metaphysical absurdities are generated here. Suppose the blacksmith wasn’t working with an infinite number of new hammers here, but, instead, renewing or reforging the hammer using existing material. That way the “destruction” of the old hammer would be built into the thought experiment, and you’d get something more analogous to the notion of finite universe with an infinite sequence of events.

This doesn’t seem absurd. It is hard to fathom, for sure, but hard-to-fathomness isn’t a good criterion in this dialectic since, as Craig himself acknowledges, when it comes to the origins and nature of the universe, all the possibilities are hard to fathom. Where is the logical or metaphysical inconsistency in this example? If we can’t find one, the possibility of an actually infinite sequence of events lives to fight another day.

Hedrick on Hilbert's Hotel and the Actual Infinite (Part One)

Tweet

The second premise of William Lane Craig's Kalam Cosmological Argument reads:

• The universe began to exist.

Typically, Craig presents four arguments in support of this premise: two scientific, two philosophical. Though the scientific arguments raise many interesting points, I think many would agree that the philosophical arguments do the heavy lifting. This is for the simple reason that current physical theories of the origin of the universe are incomplete and hence provide, at best, weak and defeasible support for the premise. The philosophical arguments are much stronger than this, purporting to provide an "in principle" argument for the truth of the premise.

One of the philosophical arguments relies heavily on a thought experiment from the mathematician David Hilbert. The thought experiment describes a hotel with an actually infinite number of rooms and guests. Serious reflection on this thought experiment is alleged (by Craig) to show that an actual infinite cannot exist. This is significant in that if the universe never began to exist, the set of events prior to this moment in time must be actually infinite.

This argument -- which will be formalised more precisely in a moment -- can be called the Hilbert's Hotel Argument (HHA) in honour of its motivating thought experiment. In a recent article entitled "Heartbreak at Hilbert's Hotel" Landon Hedrick has offered an interesting critique of the HHA. Over the next couple of posts, I want to look at what he has to say.

Hedrick's article is interesting for at least three reasons. First, it has a curious, and I think praiseworthy, rhetorical structure. Although Hedrick does not shy away from general and robust criticisms of the HHA, he nevertheless concedes a lot of ground to Craig, repeatedly granting certain premises arguendo, saving most of his argumentative muscle for a subtle internal critique of Craig's argument. The net result is a disarming, yet deceptively comprehensive dismissal of the HHA.

Second, the internal critique that Hedrick offers claims that Craig's commitment to a presentist A-Theory of time undercuts the forcefulness of the HHA. As many will know, Craig has repeatedly emphasised that the Kalam argument "from start to finish" relies on the A-Theory of time. This has led many to rebut the argument on the grounds that the A-Theory is flawed. But if Hedrick is right, these rebuttals are unnecessary, maybe even flawed.

Third, and this is slightly more personal in its interest, Hedrick first entered my consciousness through his blogging several years back. Though never a prolific blogger, he wrote some good pieces on his role in organising the Craig-Carrier debate on the resurrection, and he always struck me as a thoughtful, self-effacing guy. As someone who blogs, while at the same time trying to launch a scholarly career, it's always nice to see someone else making the transition.

Anyway, let's get down to business. In the remainder of this post, I will set out the HHA in more detail, and cover some of Hedrick's initial criticisms of it. I'll leave the argument from presentism for the next day.


1. The Hilbert's Hotel Argument
The HHA comes in two forms. The first of which reads like this (my numbering doesn't follow Hedrick's, he adds letters to code different arguments, but since I won't be going into all those different arguments in my series, I've chosen to ignore them):

HHA Type I

(1) An actually infinite number of things cannot exist. 

(2) A beginningless series of events in time entails an actually infinite number of things. 

(3) Therefore, a beginningless series of events in time cannot exist.

Some further argumentation is required to seal the gap between (3) and the second premise of the Kalam argument, but it's pretty easy to see how that might go. You just add: if the universe did not begin to exist, there must be a beginningless series of events prior to the present moment. We'll come back to the link between the HHA and the Kalam a little later on anyway.

As you'll have noticed, HHA-I focuses specifically on the existence of an actually infinite number of things. The second version of the argument, which has been mooted by Craig in some of his work, tries to broaden its scope by dropping the reference to "things":

HHA Type II

(1*) An actual infinite cannot exist. 

(2*) A beginningless series of equal past intervals of time is an actual infinite. 

(3*) Therefore, a beginningless series of equal past intervals of time cannot exist.

We won't be dealing with this version of the argument for a while, so keep it filed away in your brain for the time being. For the foreseeable future our main focus will be on HHA-I.

Before proceeding, a quick word about "actual" and "potential" infinities. Those who are familiar with the mathematical history will know that there is an important difference between the two concepts. This can be defined as follows:

Actual Infinite: "Is a collection of definite and discrete members whose number is greater than any natural number." (Craig, 2008). In other words, it is a set with an infinite number of members.

Potential Infinite: "Is a collection that is increasing toward infinity but never actually gets there." (Craig, 2008). In other words, it is a collection which ceaselessly grows in size, but never actually contains an infinite number of members.

The distinction is significant insofar as Craig only objects to the existence of an actual infinite. He's quite comfortable with the existence of potential infinite. Indeed, he thinks the future is a potentially infinite sequence of events. Thus, a classic move for Craig in these debates is to reject an opponent's counterexample by arguing that it appeals to a potential, not an actual infinite.

So why does Craig reject the existence of an actual infinite? The answer lies in his analysis of a set of thought experiments, of which the most famous and prominent is the Hilbert's Hotel thought experiment. In it, we are asked to imagine a hotel with an actually infinite number of guests and an actually infinite number of rooms. Such an entity would entail the existence of an actual infinite number of things. But could it really exist? No; a series of absurdities is thought to follow. Consider:

If one new customer checks to the hotel he/she can be accommodated even though the hotel is full. Simply move every guest in the hotel up one room (i.e. the guest in room 1 moves to room 2, the guest in room 2 moves to room 3, and so on). This way room 1 becomes available.

If an infinite number of guests arrives, they too can be accommodated. Simply move every guest to the room that's twice their current number (i.e. the guest in room 1 moves to room 2, the guest in room 2 moves to room 4, and so on). This empties out all the odd numbered rooms. Indeed, an infinite number of guests can keep checking into the hotel.

Odd things happen when people check out. If one guest checks out, thereby emptying one room, an infinite number remain (infinity minus one is still infinity). If all the guests in odd numbered rooms check out, an infinite number of guests will have left, but they will still leave behind an infinite number of guests. Nevertheless, if every guest in a room number greater than 3 checks out, only three are left.

Mathematicians use these examples to illustrate the fact that certain arithmetic operations are improperly applied to an actual infinite, but Craig uses them to argue that an actual infinite number of things cannot exist in the real world. If they did, absurdities such as those present in Hilbert's Hotel would arise. This suggests, to me at any rate, that Craig defends something like the following argument in order to defend premise (1) of HHA-I:

• (4) If an actual infinite number of things existed, Hilbert's Hotel would be possible.

• (5) But Hilbert's Hotel is not possible; it is absurd.

• (2) Therefore, an actual infinite number of things cannot exist.

(Note: as an aside, one thing that slightly annoys me about Hedrick's article is how he names the different arguments. To my mind, this argument would be more properly called the "Hilbert's Hotel Argument" since it is actually about Hilbert's Hotel, and the argument that he calls the "Hilbert's Hotel Argument" would not since it is really just a general argument against the existence of an actual infinite. I toyed with the idea of re-naming them in this series of posts, but decided against it. It would create too great a chasm between my series and Hedrick's article, which might be confusing for those who wanted to read both.)

In the remainder of this post we'll consider how plausible Craig's defence of the HHA-I is.


2. Does Hilbert's Hotel rule out the existence of an actual infinite?
The first thing we need to do is see whether premise (1) of the HHA-I is properly defended. Craig thinks that the thought experiment does the job but is he right? In answering this question we begin to appreciate Hedrick's concessionary and disarming style.

Hedrick says we can grant that Hilbert's Hotel would be absurd. And since Craig uses very similar thought experiments with other concrete physical objects (e.g. the infinite library), we can grant that this conclusion holds for all concrete physical objects. The problem is that this doesn't rule out the existence of an actual infinite number of things.

Three counterexamples suggest themselves. First, what about the set of natural numbers? According to certain metaphysical views (Platonism), numbers are real objects, and there is an actual infinity of them. Second, what about other abstract objects such as propositions or properties? Surely there are an infinite number of them as well? For example, possible worlds can be understood as sets of propositions, and the notion that there is an actual infinite number of possible has found favour among some religious philosophers (e.g. Plantinga) and some not-so-religious philosophers (e.g. David Lewis). Third, some have even argued that physical space is made up of an actual infinite number of discrete points.

Now, Craig, of course, will reject these counterexamples. He will argue that Platonism is false because numbers aren't things, or there isn't an actual infinite number of them; He will argue that modal realism and cognate views are deeply implausible; or that the notion that space consists of an infinite number of points is unproven. But these counterarguments miss the point. If the alternative metaphysical theses listed above are true, then Hilbert's Hotel doesn't disprove the existence of an actual infinite number of things. The thought experiment only appeals to intuitions we have about concrete physical objects. It does not deal with abstract, non-physical objects, where arguably our intuitions are going to be much less reliable. Sure, the alternative metaphysical theses could be wrong, but to show this one must engage in some pretty abstruse and technical metaphysical arguments. There is no straightforward, intuitively appealing pathway from the thought experiment to premise (1), contrary to what Craig seems to think. To summarise this informally:

• (6) An actual infinite number of things can (and indeed does) exist: there is an actual infinity of natural numbers; an actual infinity of propositions and properties; and an actual infinity of possible worlds.

• (7) The metaphysical theories that support these examples are controversial, implausible or unproven.

• (8) Fair enough, but you have the engage with the arguments for an against these metaphysical theories to support that conclusion; Hilbert's Hotel can't do all the work as it only deals with an actual infinite number of concrete physical objects.

This is a modest dialectic, with a modest conclusion, but it does undercut the force of Craig's use of Hilbert's Hotel.


3. Are past events "things"?
So much for premise (1) of HHA-I. In some ways, premise (2) is even more problematic and, indeed, oft-neglected in debates about the Kalam. The big difficulty is that premise (2) assumes that past events are things, much like rooms in an infinite hotel or books on the shelf of an infinite library. But is this remotely plausible?

For starters, it is worth noting that several leading philosophers have denied that events are things. Terence Horgan, for instance, writing on the topic back in 1978 said:

[I]t is a mistake to posit events at all...despite their initial appearances, there is no real theoretical need to posit events. So, since their elimination yields an important simplification of ontology, we should banish them from existence. 

(Horgan, 1978, 28)

More recently, Peter van Inwagen has taken a similar view:

There are, I would say, no events. That is to say, all statements that appear to involve quantification over events can be paraphrased as statements that involve quantification over objects, properties and times - and the paraphrase leaves nothing out. 

(Van Inwagen, 2009, 14)

Bizarrely enough, Craig agrees that this is a plausible view. Indeed, he seems to think that whatever it is that events are, they aren't "things" like books and hotel rooms. As he says himself:

"These things [i.e. events] are real in the sense that they are not illusory, but they are not, properly speaking, existents. 

(Craig, 2011, 220)

But if events aren't existents this creates significant problems for his defence of HHA-I. For if events are not objects like rooms and books, then the support that the Hilbert's Hotel thought experiment provides for premise (2) evaporates. The thought experiment only covered concrete physical things. Note, it doesn't get any better if we switch to HHA-II and its talk of "intervals of time" rather than "events". The problem there is that, unlike ordinary things, intervals of time don't come into and pass out of existence. They merely pass.

Leaving all this aside, problems remain when we consider premise (2) in light of Craig's stated views about the nature of events. In his lengthiest, most recent defence of the Kalam argument (Craig and Sinclair, 2009) he says that an event is simply any change. A change, as Hedrick notes, presumably involves something gaining or losing one or more properties. If that's right, a counter-thought experiment suggests itself:

Sphereworld: Imagine a past and future eternal world consisting of one sphere that alternates between green and red perpetually.

This world consists of one object, but an actual infinite number of events (the colour changes). On the face of it, this seems like a possible world. It involves no outright contradictions or apparent absurdities. Craig could perhaps deny its plausibility by arguing that it consists of an actual infinite number of things, much like Hilbert's Hotel. But, as Hedrick notes, this is an extremely counterintuitive interpretation of the thought experiment. At a stretch, you might say the world consists of three things: the sphere, and the two colours (which might be abstract objects). But you wouldn't say it consists of an infinite number. Counting the events as actual things feels bizarre. Furthermore, Sphereworld arguably comes pretty close to being a plausible view of reality: a finite number of things passing through an infinite number of changes. Indeed, Spinoza argued for something like this. He thought reality consisted of a single indivisible substance existing in an infinite number of modes.

To summarise this line of reasoning:

• (9) One can plausibly argue that events are not "things", or that if they are "things" then they are very different from concrete physical objects like hotel rooms.

• (10) Sphereworld seems like a non-absurd possible world: it consists of a finite number of things and an infinite number of events.

4. Interim Conclusion
Remember, this is just the warm-up. All Hedrick has done so far is suggest that support for premises (1) and (2) of HHA-I (and premise (2*) of HHA-II) is somewhat lacking. This is because the Hilbert's Hotel thought experiment doesn't apply to abstract objects like numbers or propositions; and because events are probably not "things" in the ordinary sense of the term. But Hedrick is still willing to grant these premises to Craig. That's because he thinks bigger problems are lurking when we combine the defence of the HHA with Craig's views about the ontology of time. We'll get to those problems the next day.