1. Introduction

1.1 The scenario

Recently, a dilemma has been shared on X and other places. Here’s the question:1

For simplicity, we may suppose that people cannot coordinate in advance, offer incentives/disincentives to each other, or reveal individual votes afterward. Indeed, we may suppose that you are right now tasked with pressing one of the buttons. What’s the rational choice?

I will also assume that the votes are statistically independent. Perhaps this isn’t exactly correct, but I will assume that any statistical dependence is sufficiently weak such that the independence assumption is admissible in this case. I will revisit this issue in §4.1.

I approach this scenario like any other decision problem. I want to determine what the expected outcome is if I vote blue, what the expected outcome is if I vote red, and then choose the option with the better expected outcome. Notably, the value of an outcome isn’t merely a function of how likely I am to survive. It may be worthwhile to take on some risk to myself to increase the likelihood that others will survive. Accordingly, it would be too quick to say that voting red is rational merely because there’s only risk to me if I vote blue.

1.2 Overview

I wanted to give this problem a careful analysis, since I’ve found that most of the discourse concerning it has been very poor. Most of the arguments I’ve seen, both for red and for blue, are not good arguments. As such, I think that at least some people might benefit from a well-thought-out argument, or at least find it interesting.

I will argue that voting red is the correct choice. The basic reason is that voting blue takes on a substantial risk to yourself and others who would survive you if you die, while creating a negligible difference in the likelihood that blue will win and everyone will survive. While there are other factors worth considering, the given consideration in favor of red is clearly decisive.

In §2, I will consider the risks to life that you create by voting red and voting blue. I will estimate the risks to yourself by voting blue in §2.1, and the risks to others by voting red in §2.2. In §3.1, I will explain why those expectations favor voting red. In §3.2-3.6, I will consider motivations aside from those risks for voting blue. In §4, I will discuss some of the modeling assumptions made in my analysis. I will conclude in §5.

2. Risks to life

2.1 Risk to myself

If I vote red, there is no risk to myself. If I vote blue, the risk to myself is that less than 50% of people will vote blue, and I will die. Accordingly, the chance that I will die if I vote blue is simply the probability that red wins if I vote blue.

Our expectation of this risk, therefore, will depend on what evidence we have about how people will likely vote. Polls on X and other websites indicate a moderate victory for blue. I suspect, however, that more people would vote red if faced with this problem, and for a few reasons. I will revisit this issue in §4.2. However, my analysis here does not require the expectation that red will win. I will assume, as I think is reasonable, that the chance that red will win if I vote blue are about 50%, and so the chance that I will die if I vote blue is about 50%. I will revisit this assumption in §4.2.

2.2 The risk to everyone else

Here, I want to consider how much worse off I expect everyone else to be if I vote red than if I vote blue. After all, if I vote red, there’s a greater chance that many people will die than if I vote blue. Sure, it’s only very slightly greater, but contributing even slightly to the chance of a very terrible outcome might be too much risk. Accordingly, we have to figure out how serious the risk is in order to determine whether voting red is sensible. I will argue that the risk is very tiny, but it will take some math to give a plausible estimate.

We will let p̄ stand for the average bias in the vote toward blue. That is, if voters are on average disposed with 55% likelihood to vote blue, then p̄ = 0.55. We will also let X = the number of blue votes out of the total population.2 By the linearity of expectation, E[X] = np̄, where n is the population size. Thus, E[X]/n gives us the expected fraction of blue votes, which equals p̄. Importantly, however, we don’t know ahead of time what the value of p̄ is. We can thus consider an expectation for p̄, which I’ll write as E[p̄].3 We then have E[X]/n = E[p̄].

We may also want to estimate the variance of X, of the total number of blue votes. While the mean total votes depends only on the average voter bias, the variance does not; it also depends on individual voter biases. However, for somewhat technical reasons that I won’t fully explain here, the variance will not ultimately matter for our calculations. Nevertheless, when p̄ is very close to 0.5, Var[X] ≈ 0.25n, scaled down a bit if we expect greater voter heterogeneity.

Because X is a sum of many independent random variables (n is quite large), the distribution for X can be modeled, for our purposes, as a Gaussian with mean E[X] and variance 0.25n.4 Before we proceed, we need one more thing: a specification of the prior distribution for p̄. The exact shape won’t matter very much; all that really matters is how much of the probability density is focused in a very tiny window around 0.5. I will let f(p̄) be our probability density function given our prior beliefs, and I will suppose that it’s a uniform distribution between 0.25 and 0.75. We may think that another distribution is more plausible. If it’s narrower or more Gaussian, more of the density will be focused around 0.5. However, if it’s skewed or bimodal, less will be.

Now, suppose that my initial expectation that blue will win is 0.5 and n = 8⋅10⁹.5 My expectation that blue will win should be slightly higher if I vote blue and slightly lower if I vote red. We are now equipped to estimate how much higher and how much lower that is. There are more complicated ways to calculate this, but the probability that blue will lose if I vote blue equals my prior probability that blue will lose, minus the probability that my vote will be pivotal.6 The probability that my vote will be pivotal is essentially the probability that the rest of the votes will be an exact tie. The corresponding distribution will be basically the same as for X, and so it suffices to determine P(X = n/2). This is very well approximated as f(0.5)/n, although I will forgo the tedious explanation for why this is the case. We then have:

Unsurprisingly, we find that the chance that blue loses if you vote blue is very slightly lower than the chance that blue loses if you vote red.7 We are then equipped to determine the expected number of deaths in the rest of the population conditional on you voting blue vs. voting red. Roughly speaking, the expected number of deaths to others if blue loses is approximately n⋅E[p̄|p̄ < 0.5], which is 8⋅10⁹⋅0.375 = 3⋅10⁹. However, this value is not quite the same if you vote blue vs. if you vote red. In fact, it turns out that:

I will forgo a derivation of these values.8 We are finally equipped to estimate the expected number of deaths to others, conditional on my voting blue and conditional on my voting red.

This result makes sense. Regardless of how we vote, we expect close to 20% of the rest of the population to die on average. If we vote red, the increased chance that blue loses translates to one extra expected death to others compared to voting blue. Of course, the estimation here required several assumptions. First, it assumes that individual votes are statistically independent from each other. Second, it assumes that the expected likelihood that blue wins is 0.5. Third, it assumes that our prior expectation on p̄ is a uniform distribution across [0.25,0.75] and 0 outside that range. These assumptions will be discussed further in §4. In the next section, I will compare the expected outcomes and determine the right course of action.

3. Values of outcomes

3.1 Risks of death

I will first weigh the risks to lives (of myself and others) as estimated in §2. To be clear, this isn’t the only factor relevant to the decision, although it is arguably the most significant. I will consider other factors in §3.2, §3.3, §3.4, §3.5, and §3.6.

Regardless, here’s what I consider the headline observation. If you vote blue, you take on a 50% chance that you’ll die to lower the expected number of deaths to others from 1,500,000,000 to 1,499,999,999. The exact expectations may differ somewhat, but this is representative of a reasonable expectation. The point is, you should think that your vote is almost certainly not going to make a difference to anyone else, but is likely to make a difference to your life. For the vast majority of people, the negligible increase in the likelihood that everyone survives from you voting blue is not worth the significant likelihood that you will die.

It’s even worse if you have family, friends, and people who care for you who might survive your death. The risk you take to your own life is thereby also a risk to them. How would you prefer them to vote? How would they prefer that you vote? I would hope that the people I care about voted red, since I don’t want them to die, and I hope that they’d feel the same for me. The negligible benefit of their voting blue is not even remotely worth the significant chance of death. Imagine you have a young child, and you could tell them what to do. You know that if they vote blue, there’s about a 50% chance that they’ll die, and about a 0% chance that they’ll save anyone else. If you told them to vote blue, I would think that you either didn’t fully understand the situation or that you’re some sort of moral monster. These considerations will be revisited in §3.5.

3.2 Easier to save everyone with blue

Many people commenting on this problem have observed that it’s much easier to save everyone if more people vote blue. After all, the only scenarios where everyone survives are if blue wins with >50% or if everyone votes red. However, it’s simply not going to happen that everyone votes red. Indeed, the number of people who vote blue will at least be in the hundreds of millions, if not billions. Given this, so the argument goes, we should try to save these people by helping blue to win.

It is true that among the plausible outcomes, the best are those in which blue wins. However, this fact was already assumed by the analysis in §3.1. Blue winning is a good outcome, and the fact that voting blue makes it more likely that blue wins is some reason to vote blue. My point is that the expected contribution to that outcome by voting blue is so negligible that it’s not worth taking a substantial risk to your life.

3.3 Contributing to death

Another relatively common remark is that, if you vote red and red wins, you’re contributing to the death of many people. Even if your contribution was negligible and they all would have died regardless of what you do, it’s still bad to have contributed to that outcome. Furthermore, even if blue wins and everyone survives, it’s bad that you were part of a collection of voters who, had more people voted along with you, would have led to the death of many people.

In support of this reply, we might point out that there are other cases where our action makes no or a negligible difference to the outcome, but that it’s arguably still bad that we act in that way. For example, imagine an election where one of the candidates is a murderous maniac. You might think, perhaps correctly, that your vote is almost certainly not going to make a difference to whether they win. Nevertheless, there’s arguably something bad about voting for them, even if your vote is fully anonymous. Furthermore, it’s still bad even if the maniac loses the election. Similar points may be made about, for example, our negative contribution to the environment or our negative contribution to animal welfare, even if individual inefficacy concerns are legitimate.9

While I think the general point is fair, this is not a good argument for voting blue. The difference is that, in the red/blue button case, the cost of voting blue is much higher. Consider the maniac candidate. Part of the reason why it’s reasonable to vote against him (or at least abstain) is that there’s basically no cost in doing so. If, on the other hand, there were a 50% chance of you dying unless you voted for him, the general badness of contributing even negligibly to his election is a much less significant concern. Or suppose that every time you wanted to make an eco-friendly choice, you had to flip a coin to decide whether you would die. The point is that you’re in a regrettable situation where the stakes are so high that you basically have to do an action that, without those stakes, would be worse for you to do. Accordingly, red remains the better option.

3.4 Character traits

It might be argued that voting blue is simply a more virtuous choice. In particular, voting blue exemplifies kindness, concern for others, altruism, self-sacrifice, and so on. On the other hand, voting red exemplifies selfishness, lack of caring, cold indifference, etc. Since blue is the more virtuous choice, we should vote blue.

There are two main problems with this argument. First, this does not fairly describe the relative virtuousness of voting blue and voting red. After all, voting blue is rather foolish and shortsighted, whereas voting red is appropriately sensitive to the cost that your death would cause to yourself and those around you. This is a kindness and concern for others that only voting red exemplifies. Additionally, while self-sacrifice is often commendable, it’s not good when done for poor reasons. Your sacrifice here is almost certainly not going to make any positive difference to the welfare of others. On the contrary, as discussed, it’s relatively likely to harm yourself and others.

Second, the argument overstates the importance of exemplifying certain virtues on one particular occasion. Even if voting blue were more virtuous in certain ways, the costs to voting blue clearly outweigh the good of cultivating and exemplifying those virtues on this one occasion. Consider, again, the maniac candidate from §3.3. Are there some virtues that are better cultivated/exemplified by refusing to vote for him, even if you’re likely to die? Perhaps, but not so much that it’s worth the terrible cost in this scenario.

Ultimately, I think that voting red is the more virtuous choice. However, even if this is wrong, it’s still not the case that this consideration outweighs the negative stakes of voting blue. At best, then, the considerations adduced in §3.3 and §3.4 provide some reason to vote blue, but not nearly enough to make blue the better choice.

3.5 Concern for particular individuals/groups

Probably one of the most common remarks made in support of voting blue is that we know that there will be many people who end up voting blue. This will include children, the elderly, people who don’t fully understand the problem, or who are disadvantaged in some way or another. It will also include family, friends, and others for whom we care directly. With this in mind, so the thought goes, it is clear that we should try to save them, and that requires voting blue.

There are two problems with this idea. First, the fact that there will be many people who vote blue was already built into the analysis in §3.1. The fact that there will be many people who vote blue, and that our voting blue contributes to the likelihood that they will survive, is some reason to vote blue. Nevertheless, the significant risk to us and others around us by voting blue is not worth the negligible contribution our vote would make to the chance that everyone will survive.

Second, as suggested in §3.1, this consideration actually cuts the other way. By voting blue, you’re creating a substantial risk to others who might survive you. Suppose that blue loses, and you vote blue. In that scenario, any family, friends, loved ones, etc., who voted red will have to deal with losing you. Had you voted red, although things as a whole would still be bad (many other people would still have died), they wouldn’t have to deal with losing you. Think about children losing a parent, or parents losing a child, or someone losing their spouse, and so on. The person died from voting blue when their vote made no positive difference to anyone else, but rather just made things clearly worse.

This is the key observation: if you vote blue, there’s basically a 50% chance that you’ll die and things will be significantly worse for yourself and others. If you vote red, there’s basically a 0% chance that things will be worse for anyone. Again, the risk you take on to yourself and others by voting blue is not at all worth the negligible contribution to the likelihood that everyone will survive. With this in mind, it is simply unavoidable that red is the rational and moral choice.

3.6 The world we live in

A few people have remarked that they’d rather not live in a world where red wins, perhaps because it would be such a terrible outcome (likely billions of people died), and it would mean that a majority of people didn’t vote in a virtuous manner. They would rather die with blue voters than live in a world like that.

There are a few things to say about this. If someone genuinely doesn’t care about their own life (or the welfare of those who would survive them), then they would discount the costs to voting blue that I’ve discussed. If, on reflection, you really would rather die than live in a world where red wins, then it’s in your interest to vote blue. However, I find the values required for that to be rather strange. Suppose you were the last person to vote, and you know that red is winning by billions of votes. Suppose you know that many of your family and friends had voted red. Would you really prefer to kill yourself by voting blue?

If your answer is “yes”, then I don’t have a lot to add. I do find that perspective rather insane, and I suspect few people will share it. For the vast majority of people, the considerations that support voting red will easily dominate. The large risk to yourself and others you incur by voting blue is not at all worth the entirely negligible chance that you’ll help others.

4. Modeling assumptions

4.1 Statistical independence

The calculations in §2 assumed that individual votes are statistically independent. That is, if we knew how a particular person or group voted, that wouldn’t change our expectation about how another individual or disjoint group voted. In reality, this is certainly incorrect. There are all sorts of factors that would lead to correlations between votes. People with similar psychology, values, background, culture, education, and so on are at least somewhat more likely to vote in the same way.

It turns out that this introduces two effects on the expected outcome of our choice, but they pull in different directions. First, if there are relatively broad correlations, ties become less likely, and so the likelihood that my vote will be pivotal decreases. What we would have, then, is a distribution for E[p̄] that is more bimodal, and so the likelihood that p̄ falls in the tiny window around 0.5 is reduced. How much it is reduced will depend on how sharply bimodal it is. Realistically, though, it probably won’t scale it down by more than an order of magnitude.

Second, if how I vote is somewhat positively correlated with how a relevantly similar group of people votes, then I should expect the total number of blue votes conditional on my voting blue to be greater than the expected number of blue votes conditional on my voting red by more than one. And the chance that the corresponding voting bloc is pivotal may be orders of magnitude greater than the likelihood that my uncorrelated vote would have otherwise been.10

Combined, these two effects might raise the impact of my vote by a couple of orders of magnitude. While that’s a relatively substantial difference, the chance that my voting blue will make a positive difference is still negligible, something around 10^-8 or 10^-9. On the other hand, if I’m updating on expected correlations between myself and others, I should think that there are a lot more people who will reason similarly to me who will ultimately vote red than there are in the bloc that would correlate with me from before. If this is right, then updating on this broader correlative data will lead me to expect more total red voters conditional on my voting blue than I would have otherwise expected without that evidence as background.

Ultimately, I think that taking these correlations seriously will count slightly against my voting blue, not for it.11 Nevertheless, what exactly we say here isn’t so important. Maybe these considerations count slightly in favor of blue, maybe they count slightly against it. Either way, the contribution of my voting blue to the likelihood that blue wins remains negligible, and the motivations for voting red previously adduced remain decisive.

4.2 Likelihood of blue winning

For my analysis, I assumed a 0.5 probability that blue would win. However, this can be questioned. In particular, polls conducted on this scenario found that ~58% of people preferred blue, give or take. On the other hand, there are some reasons to think that these polls may not be highly representative of how people would behave if actually facing the scenario. In addition to the sample population likely not being very representative, I strongly suspect that a greater portion of people would vote red when actually put into a life-or-death scenario. If I had to guess what the final vote would be, I think it would be ~35-40% for blue.

In any case, my analysis will not change significantly. If we suppose that E[p̄] = 0.58 but otherwise keep f(p̄) as a uniform distribution over [0.33,0.83], we’ll find that our chance of dying by voting blue has gone down to 0.34, although the likelihood that our voting blue will save others is unchanged.12 However, while voting blue is less risky here, it’s still quite risky, and not worth the negligible contribution to the likelihood that everyone will survive. On the other hand, if E[p̄] = 0.42, the cost of voting blue is higher, since you should think that your chance of dying by voting blue is about 0.66, with the same negligible contribution to the likelihood that everyone will survive. All else equal, changing the expected average voter bias only affects your expected chance of death by voting blue. Either way, the cost of voting blue goes up or down a bit, but it remains a terrible choice. Now, this assumes that the distribution is uniform, which I covered briefly in §4.1.

5. Conclusion

The correct answer is red. You should vote red if you faced a scenario like this. You should hope that your family, loved ones, and people you care about would too. After all, you don’t want them to die, and you don’t want whoever survives them to have to deal with losing them. That would be a terrible outcome, and it’s not worth a substantial risk to each of their lives just to make a negligible difference to the likelihood that everyone lives.

Nevertheless, I would hope that enough people vote blue, since that would ensure the best of the feasible outcomes. But hope is not a plan. If I could ensure that enough people would vote blue, perhaps by running a global campaign, then I would do so. In the actual stipulated scenario, I only have my own vote, and I have to weigh the expected outcomes conditional on my voting red and conditional on my voting blue. Again, there are some reasons to vote blue. It slightly increases the likelihood that everyone will survive. Other reasons include the factors discussed in §3.3 and 3.4. However, red is nevertheless the far better option. It’s not worth the large risk to yourself and others to make a negligible difference to the likelihood that everyone will survive. When facing the problem, you should think that if you vote blue, there’s about a 50% chance that you will die, leaving those who survive you to mourn your loss, and about a 0% chance that you’ll save anyone from death. That’s a horrifically bad trade for you to make, and I hope that you would recognize that were you to ever have to face such a terrible situation as the one under consideration.

If you enjoy posts/content like this, please consider supporting by becoming a paid subscriber on Substack! Also, consider checking out my YouTube channel. All of my links can be found here. Anyway, thanks for reading, and I hope you got something out of it!

1.1 Veritasium

Recently, the YouTube channel Veritasium published a video on Newcomb’s problem. There, they explore the problem, consider arguments for the possible responses, and discuss some related issues. Since this problem (and the surrounding issues in decision theory) is one of my favorite philosophical issues, I thought I would review their video and offer my approach. If you know someone connected with Veritasium, I’d very much appreciate it if you could show them this article! Also, spoiler: I am a very committed one-boxer.

1.2 The Problem

Newcomb’s problem was originally published by Robert Nozick,1 although he attributes the basic thought experiment to William Newcomb. He reportedly devised it in 1960, while working as a theoretical physicist at the University of California's Lawrence Livermore Laboratory. The problem gained mainstream popularity when Martin Gardner featured it in his “Mathematical Games” column in Scientific American in 1973. Here’s how Veritasium introduces the problem:

You walk into a room and there’s a supercomputer and two boxes on the table. One box is open and it’s got $1,000 in it. There’s no trick. You know it’s $1,000. The other box is a mystery box you can’t see inside. You also know that this supercomputer is very good at predicting people. It has correctly predicted the choices of thousands of people in the exact problem you’re about to face.

Now, you don’t know what that problem is yet, but you do know that it has been correct almost every time. Now the supercomputer says you can either take both boxes, that is the mystery box and the $1,000, or you can just take the mystery box. So what’s in that mystery box? Well, the supercomputer tells you that before you walked into the room, it made a prediction about your choice.

If the supercomputer predicted you would just take the mystery box and you’d leave the $1,000 on the table. Well, then it put $1 million into the mystery box. But if the supercomputer predicted that you would take both boxes, then it put nothing in the mystery box. The supercomputer made its prediction before you knew about the problem, and it has already set up the boxes.

It’s not trying to trick you. It’s not trying to deprive you of any money. Its only goal is to make the correct prediction. So what do you do? Do you take both boxes? Or do you just take the mystery box? Don’t worry about how the supercomputer is making its prediction. Instead of a computer, you could think of it as a super intelligent alien, a cunning demon, or even a team of the world’s best psychologists. It really doesn’t matter who or what is making the prediction. All you need to know is that they are extremely accurate, and that they made their prediction before you walked into the room. [00:26-2:14]

The relevant facts are that you are now deciding between taking only the mystery box (one-boxing) and taking both boxes (two-boxing), and you get to keep the monetary contents of the box or boxes that you take. The first box is transparent, contains one thousand dollars (hereafter, $K), and this is known to you. The second box, the mystery box, is opaque, and the contents are not known to you. Prior to you facing this problem, a predictor (supercomputer or otherwise) made a prediction about your choice, and it very reliably predicts choices like this, and you don’t take yourself to be an exception. If it predicted that you’d one-box, it put one million dollars (hereafter, $M) in the opaque box. If it predicted that you’d two-box, it puts $0 in the opaque box. All of this is known to you when you face the problem, but you do not know what prediction was made, and you do not know the contents of the opaque box. What decision would you make, and which, if either, is the rational choice?

1.3 Overview

I will explain the motivations for one-boxing that Veritasium discusses in §2 and critique them in §4.1 and §4.2. I will explain the motivations for two-boxing that Veritasium discusses in §3 and critique them in §4.3 and §4.4. In §5, I will cover some of the group rationality problems that they explore. In §6, I will analyze some remaining issues. I will conclude in §7.

2 Motivations for One-Boxing

2.1 Expected Utility

The following motivation for one-boxing is presented:

Look, I’m a reasonable guy and I like money, so I’m going to do whatever gets me the most money. So let’s go weigh the outcomes of both of these decisions. First, I’m going to say that the probability that the computer predicted my decision correctly is going to be c. And because of that the probability that it got it wrong is going to be one minus c.

So let’s look at what happens if I tried to two-box. There is a c chance of me getting $1,000 and a one minus c chance of me getting $1,001,000. If I add these two together, I get a weighted sum, which is going to tell me how much I can expect to get if I tried to two-box.

This is also known as Expected Utility or the EU of two-boxing. And I can just simplify this expression a tiny bit. So let’s look at what happens if I try to one-box. Now there’s a c chance of me getting $1 million, and there’s a one minus c chance of me getting nothing. So we can cancel this out.

Simplify this to just million dollars times c if I equate these two expressions, I’m going to get the c at which these two expected utilities are equal. And it turns out that the c at which this happens is 0.5005 or 50.05%, which means if the computer is better at predicting than what is basically random, then the expected utility of one-box is going to be higher. [03:32-04:53]

The basic idea is that we can calculate the expected utility of one-boxing and the expected utility of two-boxing as a function of c, and use that to determine which option is preferable if the predictor is reliable (that is, c is close to 1). The expected utilities are:

Filling in the relevant values for $K and $ M and solving so that EU(one-boxing) = EU(two-boxing), we get:

That is, one-boxing and two-boxing have the same expected utility when c = 0.5005, or 50.05%. Notably, the expected utility of one-boxing is greater for higher c. Since the predictor is presumed to be much more reliable than 50.05%, one-boxing is expected to earn more money, and so is the preferable option. Here, they show the expected utility as a function of c:

While I agree with the ultimate conclusion, there are some issues with this argument, which I will discuss in §4.1.

2.2 Why Ain’cha Rich?

They also consider the ‘why ain’cha rich?’ argument, as discussed by David Lewis:2

This is known as the why ain’cha rich argument, which boils down to one super annoying question. If you so smart, then why aren’t you rich? You know, if winning is getting more money, then of course the one-boxers are going to end up better off than the two-boxers. [13:52-14:07]

The point here, although not explored much by Veritasium, is that since one-boxers fare much better on average than two-boxers, it’s more rational to one-box so that you’ll be among those who typically fare much better.

3 Motivations for Two-Boxing

3.1 Causal Dominance

Veritasium presents an argument for two-boxing as follows:

You know that the supercomputer has already set up the boxes. So whatever I decide to do now, it doesn’t change whether there are 0 or $1 million in that mystery box.

And that gives us four possible options that I’ve written down here. If there is $0 in the mystery box, then I could one-box and get $0, or I could two-box and get $1,000. But there could also be $1 million in a mystery box. And in that case, I would get $1 million if I won box, or I would get $1,001,000 if I two-box.

So I’m always better off by picking both boxes. This is known as strategic dominance, where I always pick the dominant strategy, which in this case is to two-box. So give me those boxes. [05:29-6:12]

Either there is $M in the opaque box, or there is 0$ in the opaque box, and whatever it is, your action cannot change it. If there is $M, then you get $1000 more by two-boxing than by one-boxing. If there is $K, then you get $1000 more by two-boxing than by one-boxing. Either way, you get $1000 more by two-boxing than by one-boxing, and so you should take both boxes.

3.2 Expected Utility

They go on to make another argument:

I make my decision based off something else, something a little more rational, because I believe that whatever I do now can influence and change the past. I only take into account things that I can actually influence. And clearly whatever I do now, whatever I think now, is not going to change whether that million dollars is going to be in a mystery box or not, because it was already set up before I learned about the problem.

This is known as causal decision theory, where you only take into account things that you can actually cause. And so with this, your expected utility calculation changes. And that’s because you need to use a different probability, one where you could actually cause that $1 million to be in the mystery box or not.

So right before the supercomputer made its prediction, there was some probability that it thought I was going to one-box. So let’s say that probability is p. Then that’s the probability that I’m going to use in my expected utility calculation. And the expected utility to one-box is just going to be zero plus $1 million times P.

That’s pretty good. But the expected utility for two-boxing is going to be $1,000 plus $1 million times p. But that’s just the same as the expected utility for one-boxing plus an extra thousand dollars. So no matter what the computer predicted, my expected utility is always higher by picking both boxes. So of course you’re going to two-box. [08:42-10:10]

Here, the idea is that since the predictor thought that you would one-box with some probability p, and you can’t now affect that probability, we can perform the expected utility calculations with this probability. Notably, this probability is not a function of anything you think or do now, including the choice you ultimately make. We then have:

Since 1001000p is strictly greater than 1000000p for any probability p, the expected utility of two-boxing is strictly greater than the expected utility of one-boxing, and so we should one-box. Here, they show the expected utility as a function of p:

Indeed, these expected utilities reflect the fact that you’ll get an extra thousand by two-boxing than by one-boxing.

4. Criticism and Analysis

4.1 Expected Utility and One-Boxing

There are a couple mistakes in the argument here. First, the assumptions that Veritasium makes about c are not a consequence of the problem as given. I will let:

• H₁ = you are predicted to one-box

• H₂ = you are predicted to two-box

• A₁ = you one-box

• A₂ = you two-box

To say that the predictor is reliable is to say that the following probability is high:

We could also express this probability as follows:

We may suppose that P(A₁|H₁) and P(A₂|H₂) are both high, although that doesn’t strictly follow. Regardless, this is also the probability that “the computer predicted my decision correctly”, which is what Veritasium labels ‘c’. However, when they then say that,

So let’s look at what happens if I tried to two-box. There is a c chance of me getting $1,000 and a one minus c chance of me getting $1,001,000. If I add these two together, I get a weighted sum, which is going to tell me how much I can expect to get if I tried to two-box. [03:54-04:10]

This is wrong. The expected value of two-boxing, in the relevant sense, is:

The calculation performed by Veritasium assumes that P(H₂|A₂) = c and P(H₁|A₂) = 1-c, but this does not follow. Recall, c = P(A₁|H₁)P(H₁) + P(A₂|H₂)P(H₂). Even if we suppose that P(A₁|H₁) = P(A₂|H₂) = c, note that those are not the same conditional probabilities required for the expected utility calculation above. Indeed, it could be that P(A₁|H₁) and P(A₂|H₂) are both high, but P(H₁|A₁), P(H₂|A₁), P(H₁|A₂), and P(H₂|A₂) are such that the relevant sort of expected utility calculations favor two-boxing.3

Nevertheless, most discussions about Newcomb’s problem assume that P(H₁|A₁) and P(\H₂|A₂) are both high. However, note that if some assumption like this is not specified (or otherwise warranted), then the decision rules might not disagree, since the details could be filled in so that Evidential Decision Theory (hereafter, EDT) favors two-boxing.45 For sake of analysis, hereafter, I will assume that P(H₁|A₁) and P(H₂|A₂) are both equal to c as given.

There is a second problem with the given utility calculation, although a less serious one. In decision theory, standardly, expected value is not a function of monetary value per se, but our preferences over those outcomes. Strictly speaking, the expected utility calculation above requires an unwarranted assumption, that preference of monetary gain varies linearly with monetary value. Not only is this an unstated assumption, it’s a psychologically unrealistic one.6 For most people, there is diminishing marginal utility of monetary value.

Nevertheless, most discussions of Newcomb’s problem model monetary preference as linear. This is a fair assumption, since we could just stipulate that there is a person facing the problem with linear preference for monetary value and consider what is the rational choice for them. Additionally, even if we don’t assume that monetary preference is linear, the true preference function is unlikely to be so extreme so that the decision rules would agree. In any case, the monetary values and probabilities could be made more extreme to ensure that the decision rules disagree.

With all of this in mind, assuming that P(H₁|A₁) and P(H₂|A₂) are both high and that monetary preference is linear, what are we to make of the argument for one-boxing? In short, it’s correct. I expect to have more money if I one-box than if I two-box, and that is a strict probabilistic consequence of the problem as stipulated. Since I care about having more money, I’m going to act in a way given which I’m likely to have more money. The calculations in §2.1 are mathematically correct, and they do represent the amount of money you expect to have if you one-box vs. the amount of money you expect to have if you two-box. Since I care about having more money, I’m going to perform the action conditional on which I expect to have more money. And that is, quite clearly, one-boxing.7

4.2 Why Ain’cha Rich?

Taking for granted the probabilistic assumption discussed in §4.1, it is a consequence of the problem that one-boxers will get close to $M on average, and two-boxers will get close to $K on average.8 However, while mathematically correct, this is really just another expression of the fact that the expected monetary return of one-boxing is greater than the expected monetary return of two-boxing, and so is essentially another way to frame the argument discussed in §2.1 and §4.1.

Informed two-boxers will recognize this fact, but maintain that two-boxing is rational. Veritasium notes,

But maybe it’s not about who wins, but about what’s rational. In their 1978 paper, philosophers Gibbard and Harper argue that the rational choice is to pick both boxes, although they do admit that two-boxers will fare worse. They instead say that the game is rigged, and if someone is very good at predicting behavior and rewards predicted irrationality richly, then irrational party will be richly rewarded. But I think that’s a bit of a cop-out, because really, Newcomb’s paradox reveals something surprising that sometimes, in order to be a rational person, you must act irrationally. [14:08-14:45]

It is obviously true that irrational behavior can be rewarded. For example, I could make a bad bet (an irrational act) but get lucky and win. Similarly, I could make a good bet (a rational act) but get unlucky and lose. However, if one-boxing in Newcomb’s problem is irrational, then the rewarded irrationality in Newcomb’s problem is of a special sort, since it was expected that you would get rewarded. The subject facing the Newcomb scenario can rationally expect that they’ll be rewarded for one-boxing. Thus, on the two-boxer’s understanding of ‘rationality’, it must be possible for an action to be uniquely rational even though you expect to be worse off if you perform that action compared to some alternative.

On how I understand ‘rational action’, that is straightforwardly incoherent. It is simply not possible for the rational action to be to take the worse bet, but that is exactly what two-boxers require.9 David Lewis (a two-boxer) recognized this approach:

For it is impossible, on their conception of rationality, to be sure at the time of choice that the irrational choice will, and the rational choice will not, be richly pre-rewarded. V-irrationality cannot be richly pre-rewarded, unless by surprise. (And we did not plead surprise. We knew what to expect.) The expectation that only one choice will be richly pre-rewarded—richly enough to outweigh other considerations—is enough to make that choice V-rational.10

Here, “V-rationality” and such is the notion of rationality according to EDT. I agree with this notion of rationality. Or, more accurately, it is this notion of rationality that I care about when deciding how to act. Someone may consider other features relevant, so that what they count as ‘rational’ is sometimes about certain causal chains, non-backtracking counterfactuals, or something else that allows the ‘rational action’ to be one given which they expect a worse outcome. That’s fine with me: they can use the phrase ‘rational action’ to capture what they have in mind, and act ‘rationally’ in their intended sense. I’ll return to this in §4.4 and §7.

Veritasium also said, as I quoted, that “Newcomb’s paradox reveals something surprising that sometimes, in order to be a rational person, you must act irrationally.” Depending on exactly how “acting irrationally” is understood, I might agree with this, but I do not think that Newcomb’s problem reveals this. I will revisit this in §5.2.

4.3 Causal Dominance

In the video, Veritasium calls their dominance argument “strategic dominance”. However, I prefer to call this sort of argument a causal dominance argument. After all, there are different sorts of dominance arguments, some of which I would accept.

The problem with the causal dominance argument, in short, is that there is what’s called ‘act-state dependence’. To help illustrate the problem, consider an uncontroversially illicit application of dominance-style reasoning. Suppose that you’re considering whether to get a particular vaccine. The vaccine is quite effective at preventing some disease, and most people who don’t get the vaccine contract the disease. While getting the vaccine incurs some small cost to you, getting the disease incurs a significant cost. However, you might reason, you should not get the vaccine, since not getting the vaccine dominates getting the vaccine. After all, if you don’t get the disease, then you’re better off not having incurred the cost of getting the vaccine, and if you do get the disease, then you’re still better off not having incurred the cost of getting the vaccine. Either way, you’re better off not getting the vaccine, and so you should not get the vaccine.

This conclusion is wrong, of course; you should get the vaccine. You may be quick to point out that in the vaccine scenario, whether you get the vaccine is causally relevant to whether you get the vaccine, and dominance arguments only applies in general when the relevant state is not causally dependent on how you act.

I think this is close, but doesn’t capture exactly what’s wrong with the given simple dominance argument. Rather, the problem is that whether you get the vaccine is not probabilistically independent from whether you get the disease. In other words, it’s more likely that you get the disease if you get the vaccine than if you don’t. The dominance argument against getting the vaccine is illegitimate because there is probabilistic dependence of the relevant states on the act that you perform.

Consider a similar case. In this version, we might suppose that the vaccine is very unusual in that while it’s in a sense very “effective”, it is causally irrelevant to whether you get the disease. Nevertheless, the vast majority of people who get the vaccine avoid the disease, and the vast majority who do not get the vaccine contract the disease. Although unusual, the scenario is at least coherent. We might suppose that all of our expectations regarding what will happen in this modified vaccine scenario are exactly the same as our expectations regarding what will happen in the original vaccine scenario except that, of course, the connection between our getting the vaccine and our getting the disease does not count as causal. The point is, we have just as much confidence we’ll avoid the disease if we get the vaccine (and so on) in both versions.

To me, it is quite plain that the decision-theoretically relevant facts are exactly the same in both vaccine scenarios. In both cases, you should get the vaccine precisely because it’s much more likely that you’ll get the disease if you do not, and you care most about not getting the disease. Accordingly, in both cases, the simple dominance argument is fallacious. Note that the reason it is fallacious has nothing to do with causation (since that is absent in the second vaccine case), but because they both involve act-state dependence.

This is why causal dominance arguments can go wrong, and do go wrong when applied to Newcomb’s problem. Valid applications of dominance require act-state independence, but causal dominance arguments do not require that. In Newcomb’s problem, there is act-state dependence, and so the given causal dominance argument is illegitimate.11

4.4 Expected Utility and Two-Boxing

Veritasium spends some time noting that our thinking or action now does not causally influences the predictor, and it does not alter the contents of the opaque box. This is correct, of course, but this shouldn’t motivate calculating expected utilities in some other way.

Let’s suppose that you initially think that there’s a probability p that you were predicted to one-box. It would be false to say that the expected monetary return of one-boxing is p⋅$M and the expected monetary return of two-boxing is p($M + $K) + (1-p)($K). Those expressions would be correct only if p is probabilistically independent from your act, which is not satisfied here. The correct calculations for expected monetary value are the same as the expected utility calculations given in §2.1 and §4.1.

As an illustration, imagine you were facing Newcomb’s problem, and many smart investors were watching you make your choice. They observe that you two-box, but they don’t know what’s in the opaque box. Then, without revealing the contents of the opaque box, you offer them a chance to pay you to get all of the money for themselves. What do you think they would bid, and how much do you think they would bid had you one-boxed instead? Of course, they would bid significantly more if you one-box, since they recognize that it’s much more likely that the opaque box contains $M if you do.12

A proponent of two-boxing might grant this, pointing out that they aren’t intending to calculate expected monetary value, but expected utility in some sense that is distinct from evidential expected utility. Two-boxers are trying to maximize this other sense of expected utility (which we might call ‘causal expected utility’). Note what I said toward the end of §4.2. It might be that they have some other notion of ‘rational action’ that is concerned with maximizing this other notion of expected utility. Someone can use ‘rational action’ in that sense and use it to guide their actions accordingly.

However, I find it utterly mysterious. In Newcomb’s problem, I’m concerned with having more money, and so I want my decision rule to track the evidential expected utilities. In other words, it should be that the rational action is the one conditional on which I expect the most preferred result. The two-boxer’s notion of ‘rational action’, and the corresponding decision rule, does not guarantee this. By their own admission, that is violated in Newcomb’s problem. Accordingly, they are free to act in a way that maximizes some other utility function, whereas I will act in the way that maximizes how much money I rationally expect to have. If that’s what you’re concerned with too, congratulations: you’re a one-boxer!

5. Group Rationality

5.1 The Prisoner’s Dilemma

Veritasium also introduces the prisoner’s dilemma, saying

In the prisoner’s dilemma, you and another player compete for money by either cooperating or defecting. If you both cooperate, then you get three coins each. But if you defect and your opponent cooperates, then you get five coins and they get nothing. And if you both defect, you get one coin each. So no matter what your opponent does, you are always better off by defecting.

But if you play this game, not once but repeatedly, then everything changes. All of a sudden, you’re better off by cooperating. [15:02-15:33]

I agree with this, unless you expect your opponent’s actions sufficiently correlate with yours. In other words, perhaps it’s more likely that they’ll cooperate if I cooperate, and more likely that they’ll defect if I defect. In that case, the expected monetary returns for cooperating may exceed the expected monetary returns for defecting, and so I should cooperate even in the one-shot prisoner’s dilemma.1314

5.2 Mutually-Assured Destruction

Veritasium continues,

But there are some realistic scenarios where staying true to a worse option could have deadly consequences. On the 29th of August 1949, the Soviet Union detonated the one bomb as part of their first nuclear weapons test. This sent the US and the USSR into a furious arms race. By the mid 1960s, the US had over 30,000 nuclear warheads and the USSR had just over 6000.

Both sides were more than capable of destroying the other. The US Secretary of Defense at the time, Robert McNamara, didn’t advocate for disarmament. Instead, he recommended a strategy of assured destruction where the US should be able to deter a deliberate nuclear attack by maintaining a highly reliable ability to inflict an unacceptable degree of damage upon any single aggressor.

This strategy eventually became known as mutually assured destruction, or MAD. If either country attacked first, the other would surely retaliate and lead to total annihilation of both sides. So having that commitment to retaliate is beneficial. It stops the attack from happening in the first place. [16:50-17:59]

This is a rather interesting sort of decision problem where what you rationally do at one time might incline you to do something at a later time which, narrowly considered, is irrational. As a host on Veritasium points out, perhaps the best approach is to appear that you would follow through with the counter-attack, but not actually do it if prompted.

In a realistic scenario, this may suffice, but we could modify the details so that it’s actually not the best strategy. Suppose that the opponent is very good at determining whether we would retaliate. And if they determine that we will likely not retaliate, they will likely strike first, and otherwise they will not strike first. In this case, keeping up appearances is not enough unless we are actually inclined to retaliate. Accordingly, the rational approach is to develop our psychology (and/or the relevant infrastructure) so that we actually would be inclined to retaliate. If we succeed in developing our psychology (and/or the relevant infrastructure) in this way, we would retaliate.

Considered on its own, that retaliation is technically irrational, but it’s admissible that we act irrationally on that occasion because our doing so (if that circumstance arises) was a consequence of the best overall strategy for dealing with the threat of nuclear war. Put one way, this is the best strategy because although it does create a chance of maximum destruction (worst outcome), by creating that chance we make it much less likely that there are any nuclear attacks, which is the best outcome. A speaker on Veritasium makes a good point along these lines, saying,

There’s this other game theory interaction, the game they call chicken. You’re both driving your cars at each other. The worst thing is if neither of you swerve because then you both die. But you win if the other person swerves and you don’t. The best strategy in this game is to visibly take the steering wheel out of your car and throw it out the window so that the opponent can see that you’ve done that. [19:10-19:30]

In the nuclear case, the analogous strategy would be to take the control of retaliation out of our hands so that we would retaliate automatically, and convince nuclear powers that we’ve set up our infrastructure in this way. This idea was explored, as Veritasium points out, in the movie “Dr. Strangelove”.15 The point of these cases is that it can be rational to do something that will convince our opponent that they’ll be worse off if they strike (or stay the course, etc.) even if us convincing them of that risks the worst possible outcome.

6. Other Issues

6.1 Free Will

Veritasium says,

For example, the only way you’re going to win this game is to already be the kind of person to one-box, but then two-box at the last second anyways, that’s the only way you’re going to get the million and a thousand dollars. [11:44-11:57]

This is not correct. It’s not merely that the predictor is reliable at tracking some general disposition, or “what kind of person you are”. It’s not even required that the predictor knows any of that. Rather, the predictor is reliable at tracking what act you actually perform, be that one-boxing or two-boxing. Thus, you should expect that if you are the “kind of person to one-box” but two-box at the last second, the predictor likely will have predicted that you would two-box, and you will leave with $K only, not $M + $K.16

They continue,

If the predictor is so good, let’s say it’s 100% accurate, then that’s not even possible. Would you say that’s true? Yeah. Then a follow up question is, if such a perfect predictor would exist, does that mean that free will doesn’t exist because you’re saying there’s nothing you can do in between walking into that room and making your decision that ends up changing what was predetermined?

That’s right. And maybe this reveals where I’m coming from. And I think where I’m coming from is maybe free will doesn’t exist. I come down on this point of like, free will is an illusion, but our world operates in a way that is indistinguishable from free will being real. And therefore you have to act as though it’s real, as though it’s 100% real.

If we think that free will is not real and it’s an illusion, and then you have someone who’s committing crimes, and then you want to say, well, that’s not his fault. Therefore, instead of putting, you know, murderers in jail for 25 years, we’re just going to, give them some gardening classes or something like that, the problem is that then changes the environment where everyone knows you can kill someone and you can go to like, do the gardening.

So you can’t change the system based on the knowledge that it’s an illusion. Whether we do or don’t have free will, you have to live as though it exists. [12:00-13:20]

It would’ve been interesting if they had discussed the perfect predictor case further. How should we analyze the case where the predictor is inerrant (never in fact makes a false prediction) or infallible (could not make a false prediction)? In particular, if we think that one-boxing is rational in the perfect predictor case (for at least one version), but two-box in the imperfect predictor case, that suggests a rather strangely discontinuous strategy. After all, it doesn’t seem that there should be a decision-theoretically relevant difference between the case where the predictor is 99% reliable and the case where the predictor is 100% reliable.17

Of course, I say the same thing in the limit case as in the standard case. If P(H₁|A₁) = P(H₂|A₂) = 1, then I should view my choice as between a certain $M and a certain $K, and so should one-box accordingly.

However, it might be objected that the limit case undermines free will, and perhaps isn’t even coherent.18 I reject both conclusions. In particular, I reject that freedom (and rational choice) requires that there be what Fischer calls “accessible” worlds where I perform at least two distinct actions. However, since the main subject of this post is not free will, I will not explore this further here.19

6.2 Pre-Commitment

Veritasium ends by considering how we might act as if we had a precommitment, saying,

The question isn’t how to act. The question is what rules are one to follow? Or how does one even decide what rules to follow? Sometimes it’s put in the form of if you knew that you were a robot with programing that you could set, and you could rewire yourself to make yourself obey, one set of rules rather than another, the question is, what sort of rules would you wire yourself to obey?

And what you would do is you would make yourself into the kind of creature that sort of always acts in line with the commitments that would have been good to form had you even known about the problem. When you’re in a situation like the Newcomb case, you would end up finding yourself think, if I had been able to make a pre-commitment, what pre-commitment would have been the good one to make? The good pre-commitment to make would have been to be a one-boxer.

And since I’ve already wired myself up to be the kind of person that lives up to all the pre-commitment, I would have made, then I’m already in effect, committed to one-boxing, even though I didn’t realize it. [20:46-21:50]

If I could rewire myself so that I was sure to follow some decision rule, it would be that given by EDT. Presumably, there’s some rule or rules that I think correctly capture which actions are rational, and so if I could decide to make myself follow some rule, it would be that. However, I would think that someone who favors Causal Decision Theory (CDT20, or some other decision rule) would answer with their preferred decision rule instead. As such, frankly, I’m not sure what the point here is supposed to be.21

7. Conclusion

In this post, I’ve explored Veritasium’s presentation of Newcomb’s problem, and some of the common issues related to that problem. While there were several problems with their video, I still found it pretty good overall. The problem and main arguments they consider were discussed in §1, §2, and §3. In §4, I provided my analysis, revealing my approach. I’m a very committed one-boxer and proponent of EDT.22

In Newcomb’s problem, all I’m concerned with is having money, and I prefer more money to less. It straightforwardly follows from the statement of the problem (given the qualification in §4.1), that I expect to have more money if I one-box than if I two-box. Accordingly, I one-box. As discussed in §4, I just understand the phrase ‘rational action’ in a way such that it’s incoherent to suppose that the rational action is the one given which I expect to be worse off. My notion of rationality is, after all, what Lewis calls V-rationality.23

I do not suppose that I have shown that this is the ‘correct’ sense of the term or that two-boxers are wrong. Two-boxers are, after all, free to tie their notion of rational action to things other than having what they want. On their notion of rationality, there are cases (like Newcomb’s problem) where the “rational action” is one given which they expect to be worse off. I find that quite absurd, but have not here offered much to persuade them apart from explaining my approach.

It may seem that the prospects for breaking the stalemate are bleak, and we’ll be left with groups of people following consistent but divergent decision rules, proclaiming their actions ‘rational’ in their respective sense. Perhaps, although the relevant philosophical literature continues anyway. There is much discussion on other decision problems, some of which many people find that certain decision rules give unintuitive recommendations.24 It’s also possible to explore other principles/features sometimes associated with rationality, like ratifiability, dynamic consistency, reflection, and resistance to Dutch books. Additionally, it may be that exploring broader philosophical issues, like modality and counterfactuals, probability, free action, and so on, will move people one way or another.25 Regardless, I am confident in my decision to one-box, and I hope you are too!26

If you enjoy posts/content like this, please consider supporting by becoming a paid subscriber on Substack! Also, consider checking out my YouTube channel. All of my links can be found here. Anyway, thanks for reading, and I hope you got something out of it!

1.1 A Kalamity

The Kalam Cosmological Argument (hereafter, KCA) is an argument often used as part of a broader case in support of theism, the view that God exists. The basic argument, as popularized by William Lane Craig, is this:

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. Therefore, the universe has a cause.

From there, proponents of this argument will typically offer reasons to think that the cause of the universe is God.1

1.2 The Non-Being Argument

The plausibility of these further inferences, and of the KCA itself, is not my concern for today. Rather, I will be critiquing an argument made in support of the KCA’s first premise, sometimes called the “causal principle”. The argument is given by Andrew Loke, and appeals to the concept of “non-being”. He explains the argument as follows:

Now, the concept of non-being is the absence of anything: no matter, no energy, not even the potential for anything. Therefore it is metaphysically impossible that anything—whether the Universe itself or anything in the phenomenal or noumenal world—could begin to exist from non-being.2

In a video, Alex Malpass discusses his concerns with this “argument”. First, he points out that the conclusion that it’s impossible that something begins to exist from non-being is not itself the causal principle, and so more work would need to be done to show that Loke’s point supports the causal principle. Second, Malpass worries that Loke is treating ‘non-being’ as a sort of thing/state, or as a sort of ‘empty container’, but this is an illicit reification of non-being.

In response, Loke made a video to address these concerns. Against Malpass’s first concern, Loke says that the causal principle does follow. He says,

The conclusion is that, therefore, it is metaphysically impossible that anything, whether the universe or anything else, could have began to exist from non-being. So what that means is that whatever begins to exist would have to come from some being. Which means that whatever being to exist would have to come from something, and that something would have been the cause for whatever begins to exist. And, therefore, whatever begins to exist has a cause.

Against Malpass’s second concern, Loke denies that he is reifying non-being, saying,

What I mean by “nothing” is the absence of anything, regardless of whether there is or isn’t a container. […] I’m just saying, when somebody says that something comes from nothing, he is assuming that something begins to exist in the absence of any causally necessary condition. I am not referring to a thing called ‘nothing’.

Loke adds,

What he says does not answer my argument at all. Recall that my argument is saying that in the absence of any causal conditions prior to the beginning of the universe, there would be no potential, not even the potential for anything, for the universe to begin. […] In the absence of any potential for the universe to begin to exist, the universe wouldn’t begin to exist at all.

2. Response

2.1 Reconstructing the Argument

To start, I must say that I find Loke’s original argument, and subsequent defense, to be grossly unclear. Indeed, given the initial passage, I don’t think that Malpass’s interpretation is implausible. Nevertheless, I will try to reconstruct an argument from Loke’s sloppy exposition.

He does not mean to treat “non-being” as a thing, but is using it as a quantifier phrase. That is to say, if something “came from non-being”, that means that it did not come from anything.3 Furthermore, when he says that “in the absence of any potential for the universe to begin to exist, the universe wouldn’t begin to exist at all”, I take him to be suggesting that the universe (or anything else) beginning to exist requires the potential for the universe to begin to exist, and there would not be that potential if the universe (or whatever) did not come from something. Given this, we can express the argument as follows:

4. For all x, if x began to exist, then there was the potential for x to begin to exist.

5. For all x, if x did not come from something, then there was not the potential for x to begin to exist.

6. Hence, for all x, if x began to exist, then x did come from something.

For a more formal statement of the argument, let:

We then have:

The argument is valid as expressed. What remains of our analysis is to (a) interpret some of the key terms (in particular, ‘potential’), (b) assess the plausibility of the premises as then understood, and (c) determine the consequences of this for the causal principle and the KCA.

2.2 Interpreting Key Terms

There are two key terms in this argument: ‘potential’, and ‘comes from’. The term ‘potential’ is sometimes used in different ways. Sometimes it’s used to refer to features of things, in particular, that they might do something or change in a certain way. For example, I have the potential to continue writing this post. In this sense of ‘potential’, potentials are attributes of things that exist. However, sometimes we use ‘potential’ to speak about possibilities.4

How are we to understand the “potential to begin to exist”? Is it saying something about the power of something to cause the universe (or whatever) to begin to exist, or is it saying that there is a possibility that the universe (or whatever) begins to exist? If the former, then (4) is the claim that if x begins to exist, then there is something with the power to cause x to begin to exist. On this interpretation, (4) is rather close to the causal principle itself, and so is unlikely to be compelling to anyone who does not already accept the causal principle (or something near enough).

Alternatively, we might understand “potential to begin to exist” as merely saying that it’s metaphysically possible that the universe (or whatever) begins to exist. However, on this interpretation, it’s a further question whether it’s possible that there is something that begins to exist and did not come from anything. The mere fact that it’s possible that it begins to exist does not evidently require that it came from something else. On this understanding of “potential to begin to exist”, (5) is basically a restatement of the causal principle,5 and so shouldn’t be compelling to anyone who does not already accept the causal principle.6

Notably, on either interpretation of “potential to begin to exist”, the plausibility of the argument seems to rest on the plausibility of the causal principle itself (or something near enough). As support for the causal principle, then, Loke’s argument as understood is a bad argument. Indeed, if I think that it’s possible that something begins to exist without a cause (as I do), it’s hard to imagine that anything like Loke’s argument, or anything based on the concept of non-being, will undermine my position.

The other key relation is “comes from”. What does it mean for something to “come from” something else, and how is that relevant to causation? We might think of “coming from” as efficient causation such that “x came from y” is merely another way of saying that “y caused x”. On this interpretation, the connection between (4)-(6) and the causal principle as given in (1) is clear, since (6) is simply another way to state the causal principle. However, if “comes from” expresses a relation other than (efficient) causation, then more work would be needed to infer the causal principle from (6). In the video, Loke says that,

Whatever begins to exist would have to come from something, and that something would be the cause for whatever begins to exist.

This suggests that if x comes from y, then y causes x, but this is true only if “comes from” is (efficient) causation, or otherwise some other relation that is a subrelation of the converse of (efficient) causation. I think it’s probably best to interpret Loke as using “comes from” and “caused by” interchangeably, but it would be helpful if he were more clear in his presentation.

3 Conclusion

The central problem with Loke’s argument is that its plausibility rests on the plausibility of the causal principle (or something like it), as explained in §2.2. If the “potential to begin to exist” is understood as the power to cause that thing to begin to exist, then (4) is unlikely to be compelling to anyone who does not already accept the causal principle (or something near enough). Alternatively, if “potential to begin to exist” is understood as the possibility that that thing begins to exist, then (5) should not be compelling to anyone who does not already accept the causal principle. Either way, the argument (4)-(6) in support of the causal principle is unlikely to be compelling to anyone who does not already accept the causal principle (or something near enough).

It is possible, of course, that Loke has in mind something else by “potential to begin to exist”, or otherwise a somewhat different argument than my construction in (4)-(6). I do think that my construction and interpretations are reasonable (and quite charitable), but I do leave open the possibility that I didn’t entirely capture his true intentions. Regardless, I think I did the best that I could from his remarks given how sloppy and unclear they were, and it doesn’t appear to me that his argument enables any meaningful progress in the ongoing debate over the causal principle or the KCA.

If you enjoy posts/content like this, please consider supporting by becoming a paid subscriber on Substack! Also, consider checking out my YouTube channel. All of my links can be found here. Anyway, thanks for reading, and I hope you got something out of it!

1.1 Introduction

“Causal finitism” is the thesis that the causal history of any effect is necessarily finite. That is, if we had a causal sequence leading up to some effect, there must have been a finite number of things in that sequence. It could be a very large number, just not infinitely many. Various philosophers have argued for finitist theses like this (causal and/or temporal finitism).1

In this post, I’m going to explore another argument for causal finitism introduced by Ibrahim Dagher.2 In §1.2, I will introduce the standard Grim Reaper scenario. In §1.3, I will explain the “prefixed” version of the Grim Reaper scenario. In §1.4, I will explain Dagher’s argument. In §2, I will critique that argument, and conclude in §3.

1.2 Grim Reaper Scenarios

Dagher’s argument involves a variant of the Grim Reaper Argument (GRA) introduced by Koons (2014). I will not fully explain Koons’ argument here, but I will need to explain the scenario described in that article. We are to imagine that there exist these Grim Reapers who are able and disposed to carry out a particular task: for any particular time they are given, they kill a particular person (Fred) if he is alive at that time.3 We suppose that there are infinitely many Grim Reapers, who we might label R₁, R₂, R₃…, for each natural number ℕ. Then, suppose that R₁ is assigned 12:30pm, R₂, is assigned 12:15pm, R₃, is assigned 12:07:30pm, and so on. In general, R_n is assigned the time 2^-n hours past noon. Accordingly, each of the Grim Reapers are assigned a time strictly after noon, although there is no first one in the sequence.

It turns out that this scenario is not possible. Fred can’t survive past 12:30pm, since R₁ would kill him at that time if he’s alive at that time. However, for any Reaper n, R_n cannot kill Fred, since for them to kill Fred at 2^-n hours past noon, he must be alive at that time, and so was also alive at 2^-(n+1) hours past noon, and so R_n+1 would have killed Fred at that time. In other words, no individual Grim Reaper can kill Fred, since he would have been alive for earlier Reapers to kill him. Consequently, Fred cannot be killed by any Reaper, but he also cannot survive all of the Reapers, which is a paradox.

This sort of scenario was introduced first by José Benardete, and is called a “Benardete paradox”.4 See Shackel (2005) for an explanation of the form of the paradox and a demonstration of its impossibility. I will not explain the details here, but suffice it to say, the described Grim Reaper scenario (and Benardete paradoxes more generally) require an inconsistent structure, and so are impossible.

1.3 Prefixed Case

Dagher considers a variation of the Grim Reaper scenario which is exactly like the original scenario, but there’s an additional Grim Reaper set to carry out the task at an earlier time. We can suppose that its time is noon exactly. In this case, we don’t get the paradox of the original Grim Reaper scenario, since the newly-added first Reaper would kill Fred, and the rest would do nothing. This variation of the Grim Reaper scenario was introduced by Pruss (2018), pp. 47-49. There, Pruss suggests the following sort of argument. Dagher expresses it as follows:

1. If causal finitism is false, then the prefixed story is possible.

2. If the prefixed story is possible, then the standard Grim Reaper scenario is possible.

3. The standard Grim Reaper scenario is not possible.

4. Hence, causal finitism is true.

(1) seems plausible, since in the prefixed case, the scenario does not have the contradictory structure required by the standard Grim Reaper scenario. If causal finitism is false, then it doesn’t seem that there’d be anything about the prefixed scenario that’s impossible. (2) also seems plausible, since if the first scenario is possible, it seems that we could set the additional Reaper’s time to a later time (or remove it altogether), which would result in the standard Grim Reaper scenario. Since (3) is true (as discussed in §1.2), it seems to follow that both the standard Grim Reaper scenario and the Prefixed Reaper story are impossible, and so causal finitism is true (4).

1.4 The Argument

Against the argument Pruss suggests, Dagher notes that opponents of causal finitism might reject (2), or perhaps (1). Notably, he says:

“The opponent of causal finitism is by no means committed to the metaphysical possibility of the Prefixed Reaper story just because it is consistent.”

Dagher develops a different argument involving the Prefixed Reaper story that he thinks will avoid some of the concerns for Pruss’s version. Suppose that someone, Rachel, can turn a dial to set the time for the additional Reaper. Initially, the dial is set to noon, which would result in the Prefixed scenario.5 We then have the following circumstance:6

• Rachel attempts to turn the dial to set the additional Reaper’s time to a time after noon, and all of the Reapers will carry out their task at their respective assigned times.

Dagher argues, generalizing from a proposal from Loewenstein (2022), that Rachel’s inevitable failure in this circumstance to set the dial is an inexplicable failure. He summarizes his approach to inexplicability here as follows:

“So, more broadly, when a circumstance C is held fixed, and an agent is being foiled in their attempts to ϕ at all the worlds with C, this is explicable if (and only if) C builds in a causal mechanism which explains why each token attempt is foiled. Whenever an agent is being foiled in their attempts to ϕ at all C-worlds, C ought to provide an explanation of the satisfaction of the description that this class of worlds all have a foiling mechanism. If C provides no such explanation, then we have problematic inexplicability.”

However, “building in” or “providing an explanation” does not necessarily require explicitly describing any particular mechanism. He adds,

“when I claim “it will be that I remain seated,” I am claiming (fundamentally) something about the world. I’m claiming that the world is such that it (causally) ensures I remain seated. It’s thus not surprising, or problematic, that every world at which it will be that I remain seated, and I attempt to stand up, there is always a foiling mechanism in place to stop me. The circumstances build in this foiling mechanism. It’s not as though we held fixed some circumstance wholly unrelated to my standing up, and then it was true that at all the worlds at which I attempt to stand up, I was foiled in my attempt. That would be problematically inexplicable.”

The scenario with Rachel and the Reapers, Dagher contends, is of the problematically inexplicable sort. He says,

“The fact that there are many other reapers, set for later times and awaiting far away from Rachel, is not the kind of fact that builds in a causal mechanism. It says nothing about the world—beyond that we have a certain spatial arrangement of odd machines.”

Thus, the fact that this circumstance is problematically inexplicable is evidence for causal finitism. After all, if causal finitism were true, then the given circumstance would be impossible, and so there’d be nothing that is problematically inexplicable.

2. Critique

2.1 Is it Possible?

One potential response to Dagher is that the Prefixed Reaper story isn’t possible even if causal finitism is false. Strangely, he recognizes this response with respect to Pruss’s suggested finitist argument, but appears not to consider it as a response to his inexplicability argument.

That said, he might say that even if that is an option, absent strong reason to think that it’s impossible for some other reason, we have some reason to think that causal finitism is true. However, that response renders Dagher’s argument more modest than initially presented.7

Moreover, there may be reason to think that the Prefixed Reaper case is not possible. If we require that the Reapers are such that they will each carry out the Reaper task for whatever times are set, this suggests a modal property that’s impossible even in the Prefixed Reaper scenario. After all, it’s not possible that they carry out the task if the dial is turned. Thus, in the Prefixed Reaper case, even if we suppose that the dial isn’t turned, the situation is impossible because it requires that the Reapers collectively have an impossible modal profile.

2.2 In Favor of Impossibility

It may be responded that the inference to the impossibility of the modal profile merely assumes that it is possible that the dial is turned. After all, if it’s not possible, then the given modal property is vacuously satisfied by the Reapers.

Strictly speaking, this is logically correct, but it’s at best not obvious that the right analysis is that the Reapers could have that modal profile and so Rachel could not turn the dial. If we think that Rachel (or something else) could turn the dial even with Reapers nearby, then the circumstance Dagher describes isn’t possible.

Moreover, Dagher’s analysis of the Machine case may also support this reply. In that case, Dagher invites us to imagine a machine that makes true any proposition uttered to it. Now, suppose that Rachel attempts to say to the machine that “my shirt is both red and not red”. Since the machine’s definition requires the statement to become true, but logic forbids a contradiction, the agent is necessarily prevented from completing the sentence. This could be by slipping on a peel, choking, or being stung by a bee, or something else. Dagher argues that Rachel’s failure is problematically inexplicable because the mere presence of the machine (a physical box) offers no causal mechanism for her failure. From this, he concludes that a machine of that sort isn’t possible. Put another way, it’s not possible that something have the modal profile attributed to the machine. But this line of reasoning seems equally available in the Reaper case; we could similarly conclude that Reapers with that modal profile are not possible even if causal finitism is false.

2.3 Objection

In response, it may be alleged that the cases are relevantly dissimilar because the possibility of the Reapers conditional on the falsity of causal finitism seems more plausible than the possibility of the machine. In other words, the more plausible culprit in the Reaper case is the falsity of causal finitism, not the Reapers, even if the culprit in the Machine case is the machine itself (or its stipulated modal profile). I do not share this assessment.

To see why, consider another case. Suppose that Alice is a bridge-crosser who, walking normally, crosses over every bridge in some area without doubling over her path. She has this property essentially such that whatever bridges there are, she will carry out the task. Suppose that in the relevant area near Alice, there are initially six bridges, and Rachel is considering whether to construct another bridge that would result in the arrangement characteristic of the Bridges of Königsberg. If we suppose that this scenario is possible, then it follows that it’s not possible that Rachel succeed in constructing the seventh bridge. This circumstance is relevantly quite similar to the Machine case. If we are similarly moved by concerns of inexplicability to reject the bridge-crosser circumstance as impossible, the most plausible candidate would be Alice herself (or her stipulated modal profile). However, if we now compare the three cases, it seems that the possibility of Reapers with their given modal profile isn’t any more plausible than the possibility of Alice with her given modal profile. Consequently, if we accept that Alice with her given modal profile isn’t possible, the more plausible analysis of the Reaper case is to reject the possibility of the Reapers with their given modal profile than to adopt causal finitism.

More can be said on this, of course. For now, I’ll conclude that it seems to me that if we accept Dagher’s approach to problematic inexplicability generally, we should think that the right analysis is that Reapers with the described modal profile are not possible, and this blocks his inference to causal finitism.

2.4 Inexplicability

Let’s suppose that the objection raised in §2.1 is wrong, and that the Prefixed Reaper scenario is possible if causal finitism is false. I contend that even with this assumption, Dagher’s argument is unsound. Indeed, I will argue that none of the cases he considers are inexplicable, and so provide no good reason to think that they are impossible.

To see why, consider again the “Standing up” case I mentioned in §1.4. While that circumstance didn’t explicitly mention any foiling mechanism, Dagher considers the failure explicable because the circumstance involves a claim about the world, that the world is such that the causal history is such that the person will remain seated. It seems that we can say much the same about the bridge-crosser case: the circumstance likewise involves a claim about the world, that the causal history is such that the bridges will admit an Eulerian path. The Machine case similarly involves a claim about the world, that the causal history is such that inconsistent propositions will not be expressed to the machine. Finally, the Prefixed Reaper circumstance involves a claim about the world, that the causal history is such that the Reapers will form a well-founded ordering.8

Indeed, it seems to me that any stipulated outcome is “a claim about the world” that necessitates a compatible causal history. But insofar as failure is guaranteed by the circumstance, any circumstance with built in failure involves a claim about the world that renders that failure explicable. This then rules out that we could even construct a scenario that is problematically inexplicable in the way that Dagher describes. Put another way: either the circumstance builds in failure, which is the sort of claim about the world that renders failure in that circumstance explicable (as in the Standing up case), or it does not build in failure, in which case the worry of inexplicable failure doesn’t even arise. Either way, the failure is not inexplicable, and so there cannot be any circumstance that involves inexplicable failure in the way that Dagher discusses. So, a fortiori, the Prefixed Reaper circumstance does not involve it. However, since his inference to causal finitism requires that the failure in the Prefixed Reaper circumstance is problematically inexplicable, his argument for causal finitism is unsound.

2.5 Objection

In response, Dagher might claim that not just any claim about the world will do. In particular, it can’t be claims about the world wholly unrelated to the failure in question. In the Standing up case, that Bob will remain seated is a fact related to his failure to stand up, whereas that there is a machine nearby is not a fact related to Rachel’s failure to express an inconsistent proposition. And so on for the other cases.

However, in the Machine case, it is built into the circumstance that no inconsistent propositions are expressed to the machine, just as it is built into the bridge-crosser circumstance the bridges will admit an Eulerian path, and so on. Surely those built-in facts are related to Rachel’s failure to express an inconsistent proposition, or to build a seventh bridge in a certain way, and so on. I find it no different than the way in which the failure is built into Standing up.

Still, it may be that Dagher has in mind (or could develop) some sense of “related to” on which the details of Standing up are related to the failure and the details in the cases he considers problematic are not related to their respective failures in the relevant way. In order to save the argument from my critique, Dagher would have to clarify an understanding of “related to” that satisfies this, and argue that it rightly separates the explicable failures from the inexplicable ones.

3. Conclusion

In this post, I explored Ibrahim Dagher’s fascinating argument for causal finitism, but found it unconvincing. I covered two main concerns. First, as discussed in §2.1-2.3, there is reason to think that the Prefixed Reaper story is impossible even if causal finitism is false, and so Dagher’s argument is unsound. Second, as discussed in §2.4-2.5, the Prefixed Reaper story arguably does not involve any inexplicable failure even if we suppose that it’s possible, and so Dagher’s argument is unsound. While I leave it open that the argument could be modified to avoid these concerns, as it stands, they seem rather decisive, and so I conclude that this argument for causal finitism is unsound.

In any case, I hope that you’ve found this post interesting as a discussion of another argument for causal finitism. Feel free to leave a comment! If you enjoy this content and want to support more of it, you can become a patron at patreon.com/Friction, or make a one-time donation at paypal.com/paypalme/frictionphilo. Many thanks to my current patrons. You can find my other links at linktr.ee/frictionphilosophy.

1.1 Introduction

What is ‘nothing’? Can something come from nothing? Perhaps intuitively, the answer is no. There is a Latin expression, ex nihilo nihil fit, which means “out of nothing, nothing comes”. However, it turns out that the answer is not so straightforward, in part because the question is potentially ambiguous between different senses of ‘nothing’. Are we talking about a thing called ‘nothing’? Or are we just saying that there weren’t any things at all? And what’s the difference?

In this post, I will explore this ambiguity and attempt to answer the question, ‘can something come from nothing?’ The first sense, as we will see, understands ‘nothing’ as a noun, whereas the latter understands ‘nothing’ as a quantifier. While some authors have suggested hybrid or alternative views, I will not explore them much in this post. In §1.2, I will discuss the noun understanding. In §1.3, I will discuss the quantifier understanding. In §2, I will cover other potential mistakes and draw general conclusions. In §3, I will explore consequences for physics/cosmology. I will conclude in §4.

1.2 Noun Understanding

A noun is, broadly, a term used to refer to things, to denote stuff of some sort or another. When we use ‘nothing’ as a noun, we are referring (or at least attempting to refer) to a particular sort of thing, that is, nothingness itself. For example, we might think that the universe was initially in a state of nothingness prior to the Big Bang. However, there is an obvious issue with ‘nothing’ in this sense: we’re treating nothingness as if it’s a thing that might exist and to which we might refer. That makes no sense! Surely, nothingness cannot be a thing. Accordingly, using ‘nothing’ as a noun appears to involve a sort of category mistake: it treats nothingness as a thing even though ‘it’ could not be a thing.

It may be objected that ‘nothing’ in the noun sense does make sense, because there are non-existent objects.1 For example, we might say that “nothing is a unicorn”, since there aren’t any unicorns? On the contrary, this sort of expression should normally be understood with the quantifier reading of ‘nothing’ (to be discussed in §1.3), not the noun reading. After all, we wouldn’t say that a unicorn is this thing, ‘nothingness’. Rather, we mean to say that there aren’t any unicorns, or that the number of unicorns is zero. To help disambiguate, going forward I will use the word ‘nothingness’ to express the noun sense of ‘nothing’.

Perhaps the most notable use of ‘nothing’ in the noun sense is by Martin Heidegger. Heidegger said, among other things, that “the nothing nothings”. I cannot hope to give Heidegger’s approach a full treatment here.2 Nevertheless, on my understanding, Heidegger discusses how feelings of angst/emptiness can involve a sort of “pushing away” of the world, of things, in thought and significance. As a description of what certain experiences feel like, this may be fine. However, Heidegger seems to make the move from the psychological to the metaphysical, saying that the phenomenology helps to reveal the fundamental nature of Reality/Being. Insofar as this fundamental nature involves nothingness, as I take him to be suggesting, Heidegger’s view falls into incoherence. While some other authors attempt to make sense of non-quantificational uses of nothing,3 I am inclined to agree with Carnap (1932) that the only coherent sense of ‘nothing’ is as a quantifier.

1.3 Quantifier Understanding

A much more common use of the term ‘nothing’ is as a quantifier. When we use ‘nothing’ as a quantifier, we are saying that there are not any things, or are not any things of a particular sort. As before, if I say ‘nothing is a unicorn’, I’m not saying that nothingness is a horned horse. Rather, I’m saying that there are not any unicorns. Of all of the things that exist, none of them are unicorns. Importantly, when we employ nothing in the quantifier sense, we often have a relevant domain in mind. For example, if someone says ‘there’s nothing in the fridge’, the relevant domain is something like ‘food items that might reasonably be used for a meal or snack’. If there are not any such things in the fridge, then our statement is true even though, of course, there are some things inside the fridge (shelves, air, etc.). The claim is true because the fridge doesn’t contain anything in the more restricted domain.

It’s not always obvious when we’re using ‘nothing’ as a quantifier rather than as a noun. For example, if I say ‘I’m afraid of nothing’, it might appear to be the same sort of statement as ‘I’m afraid of spiders’, since I’ve merely changed what it is that I’m afraid of. However, that would be a mistake.4 Those sentences merely bear a surface grammatical similarity, when in fact there is a crucial difference in meaning. The use of ‘nothing’ in the first sentence is not as a noun, but as a quantifier, unlike the use of ‘spider’ in the second sentence. For the first sentence, you wouldn’t infer that there is something (nothingness) of which I’m afraid. Rather, you’d conclude that there are not any things of which I’m afraid.

It may be objected that the noun and quantifier sense of ‘nothing’ aren’t all that different. In particular, isn’t a state of ‘nothingness’ just the same as a state of ‘not any things’? On the contrary, this suggestion requires nounifying the quantifier sense of ‘nothing’. When I say that I’m afraid of nothing, I’m not saying that I’m afraid of the state of ‘not any things’. That would be to misinterpret my statement as employing the noun sense of ‘nothing’. Accordingly, the given suggestion is in error.

2. Something from Nothing?

With this distinction between noun and quantifier uses of ‘nothing’ in mind, how should we answer the question, ‘can something come from nothing?’ To represent the different senses of the statement a bit more formally, letting C(x, y) mean ‘x came from y’,5 we can express the two senses of “something came from nothing” as follows:

Noun sense:

• In more natural language: ‘there is some x such that x came from nothingness’.

Quantifier sense:

• In more natural language: ‘there is some x for which there is not a thing y such that x came from y’.

On the noun reading, the statement doesn’t make sense, and for the same reason mentioned in §1.2. It doesn’t make sense to say that there is nothingness, let alone that it stands in the given relation to anything. The problem is not the further relation per se, but the notion of nothingness itself. Since it’s incoherent to suppose that nothingness exists, it’s likewise incoherent to suppose that something came from it.

However, on the quantifier reading, there are not any obvious issues with the statement. After all, for all we know, maybe there are things that did not come from anything. For example, on common views about God, God did not come from anything. It’s not that God came from nothingness, but that there isn’t any thing such that God came from that thing. This is a perfectly coherent sense in which we might think that something came from nothing. Whether there is anything like this, God or otherwise, is not the subject of this post.

3. A Universe from Nothing?

What significance does this have for the universe, and whether it could have come from nothing? In 2012, physicist Lawrence Krauss published a book titled “A Universe from Nothing: Why There Is Something Rather than Nothing”.6 However well Krauss expresses the physics, it’s broadly agreed that he overstated his case.7 Krauss’s “nothing” is really a quantum vacuum which, while void of particles, is still something. Perhaps it is ‘nothing’ in some other sense, but it is not nothingness in the sense under consideration.

Even if Krauss (and others) err in this way, it might still be thought that the Big Bang theory suggests that the universe began in a state of nothingness, and then expanded outward. However, this is entirely incorrect. Indeed, the Big Bang theory does not strictly entail that the universe began from nothingness, or even that it had an absolute beginning at all.8

Finally, it is often assumed that we face a trichotomy. People often assume that the universe fits into one of three categories:

1. Eternal toward the past (no beginning),

2. Caused by something else (e.g., God), or

3. Came from nothingness (noun sense).

However, this trichotomy leaves out relevant alternatives. For our purposes here, it leaves out the alternative that the universe:

4. Came from nothing (quantifier sense).

That is to say, it might be that the universe had a beginning, but did not come from anything at all. As we saw in §2, there is nothing incoherent about this view. (4) is coherent even if (3) is not. Of course, we may have reason to think that the universe in particular did come from something, but it is important to recognize and take seriously this alternative option.

4. Conclusion

So, can something come from nothing? That depends on what we mean by ‘nothing’. On the noun reading, where nothingness is treated as a kind of thing, the idea is incoherent. Nothingness, by definition, can’t be a thing, let alone a thing that might produce things. But on the quantifier reading, where nothing simply means ‘not anything’, the idea becomes far more plausible. There’s no contradiction in supposing that something might exist without having come from anything else. Whether anything actually fits that description (e.g., the universe, God) is a further question that I’ll leave for another time.

In any case, I hope that you’ve found this post helpful for thinking about ‘nothing’ both in everyday discourse and in more philosophical contexts. Feel free to leave a comment! If you enjoy this content and want to support more of it, you can become a patron at patreon.com/Friction, or make a one-time donation at paypal.com/paypalme/frictionphilo. Many thanks to my current patrons. You can find my other links at linktr.ee/frictionphilosophy.

1.1 The Problem

If God knows ahead of time what you’ll choose, is your choice still free?1 Linda Zagzebski (1985) frames the worry this way:

If God knows everything, he must know the future, and if he knows the future, he must know the future acts of his creatures. But then his creatures must act as he knows they will act. How then can they be free?

The view that God’s knowledge of the future is compatible with our free will is called theological compatibilism, whereas the view that they are incompatible is called theological incompatibilism. This is not to be confused with compatibilism/incompatibilism generally, which concerns whether free will is compatible with determinism.

In §1.2, I will introduce an argument for theological incompatibilism, that is, for the view that God’s foreknowledge is incompatible with human freedom. In §2, I will explore the various ways in which the premises of that argument might be rejected. In §3, I will explore some other responses to the argument, and conclude in §4.

1.2 Argument for Theological Incompatibilism

In this section, I will lay out in more precise terms the concern for theological compatibilism, consider the various ways in which that inference could be resisted, and assess the plausibility of the different options. A good expression of the worry is given by Pike (1965) and by Fischer and Tognazzini (2014). I will present Fischer and Tognazzini’s version here, which is given as an argument:

1. For any true proposition describing a human action, God believed that proposition even before the relevant human was born.

2. If Eva is able to do otherwise, then (given the entailment relation between God’s past belief and her action) that means she is able to do something such that, were she to do it, either: (1) God would have believed something false before she was born, (2) God would have had a different belief before she was born, or (3) God wouldn’t have existed before she was born.

3. Eva is not able to do something such that, were she to do it, God would have believed something false before she was born.

4. Eva is not able to do something such that, were she to do it, God would have held a different belief before she was born.

5. Eva is not able to do something such that, were she to do it, God would not have existed before she was born.

6. So, Eva is not able to do otherwise than what God actually believed, before she was born, that she would do.

The idea is that since Eva is not able to do otherwise whenever she acts, then she never acts freely. And what is true for Eva is true for everyone, and so nobody acts freely.

2. Possible Responses

We can now go through the argument and consider the various ways in which the conclusion could be resisted, starting with premise (1).

2.1 Premise 1

Recall, according to (1),

1. For any true proposition describing a human action, God believed that proposition even before the relevant human was born.

There are a few ways in which this premise might be denied. First, we might think that God’s knowledge is not temporally prior in this way, probably because it does not occur in time at all. For a development of this view, see, e.g., Stump and Kretzmann (1981).2 However, there are several worries here. For example, Plantinga (1986) and Zagzebski (1993) argue that we’d have just as little control over God’s timeless beliefs as God’s past beliefs.

Second, we could deny (1) by denying future contingents, at least including those concerning our free choices. The idea is that all future-tensed (contingent) propositions are false (or that they are neither true nor false, or that there are no future contingent propositions), and so God would have no beliefs about future free actions in the sense described. For example, suppose you chose to eat a sandwich today. On the given view, it wasn’t true yesterday that you will eat a sandwich today, and so not something that God then knew. While this view preserves God’s omniscience, it involves rejecting God’s foreknowledge of our free choices. For more on the view that all future contingents are false (or neither true nor false), see, e.g., Todd (2016), Todd and Rabern (2019) and Hasker (1990).

Third, we could deny (1) by denying that if it’s true at some time that you will choose a sandwich that you at that later time in fact choose a sandwich. On this rather strange view, the truth values of propositions change over time. For example, on this view, it could be that the proposition that “you will eat a sandwich tomorrow” is true today, but nevertheless when tomorrow comes around, you don’t eat a sandwich. For more on this view of truth, see Geach (1977). While this view is technically a way to deny (1), I do not consider it very plausible.

2.2 Premise 2

Recall, according to (2),

2. If Eva is able to do otherwise, then (given the entailment relation between God’s past belief and her action) that means she is able to do something such that, were she to do it, either: (1) God would have believed something false before she was born, (2) God would have had a different belief before she was born, or (3) God wouldn’t have existed before she was born.

Are there any possible alternatives to the three options given in the consequent of (2)? If we’re understanding “God” as a title rather than a proper name, there is the option that something else would have been God. I will not explore this rather strange view here.

2.3 Premise 3

Recall, according to (3),

3. Eva is not able to do something such that, were she to do it, God would have believed something false before she was born.

Denying (3) requires thinking that Eva is able to act in ways that make some of God’s beliefs false. Although God actually believes all true propositions (and believes no false ones), he could have been wrong, and he would have been wrong had anyone acted other than how they actually freely acted. This option may be unappealing for various reasons, but it is nevertheless a view according to which alternate possibilities are consistent with divine omniscience. For an article exploring the idea that God may not be essentially omniscient (or even essentially God), see Sennett (1994).

2.4 Premise 4

Recall, according to (4),

4. Eva is not able to do something such that, were she to do it, God would have held a different belief before she was born.

Denying (4) requires thinking that what God believed is counterfactually dependent on what Eva chooses. For example, suppose Eva chooses to eat a sandwich and God knew that. However, she could have refrained, and had she refrained, God would have known that she will not eat a sandwich.

In the literature, this has become an increasingly considered option in recent years. It tends to go along with something called “Origen’s suggestion”, the basic idea being that God knows some future free action because that action is taken, or that his knowledge of that future free action depends on the action itself. In some sense, what God believed depends on what we choose when we act.

A general argument against this goes something like this: so-called “hard” past facts are past facts over which we now have no control, God’s beliefs are hard facts about the past, and so we don’t have control over God’s beliefs. The distinction between hard and soft facts can be tricky to spell out very precisely, but the rough idea is that “hard” facts about the past are facts only about the past, only about things intrinsic to the past, whereas “soft” facts about the past are at least partly about things in the present or future.3

Those wanting to take this option, then, have three options:

1. Affirm that we at least sometimes have control over hard facts about the past.

2. Deny that God’s beliefs are hard facts about the past.

3. Affirm that we could have acted such that God would have had a different belief, but that what God believed is not something we control.4

For articles exploring Ockhamist and dependence-type response, see, for example, Plantinga (1986), Merricks (2011), Westphal (2011), McCall (2011), Swenson (2016), Cyr and Law (2020), and Cyr (2022). Further analysis of hard/soft facts, fixity principles, and so on, will be explored in future posts.

2.5 Premise 5

Recall, according to (5),

5. Eva is not able to do something such that, were she to do it, God would not have existed before she was born.

This requires thinking that Eva in some sense has control over whether God existed. This approach does face several difficulties. Most notably, it makes God’s existence highly contingent, since for any given free action, had someone chosen otherwise, God would not have existed. As well, it becomes a bit mysterious that God exists despite it being seemingly far more probable that we’d be in one of those worlds in which someone at least once acted differently, and so God did not exist. For more on this, see the previously mentioned article from James Sennett.

3 Other replies

3.1 Compatibilism

We might think that although Eva could not do otherwise than what God actually believed, before she was born, that she would do, she still acts freely. This is the view that we can act freely even if, when we act, we could not have acted otherwise. This requires denying the principle of alternative possibilities (PAP), and often takes the form of compatibilism, according to which free will is compatible with determinism. For more on compatibilism, see, e.g., McKenna and Coates (2024).

3.2 Molinism

Molinists hold that, in addition to knowing all necessary truths and all contingent truths about the actual world, God has middle knowledge of what any free creature would do in any possible circumstances.5 Given God’s creative acts, God can know (a) what circumstance Eva will be in, and (b) how she would freely choose to act in that circumstance. Thus, God can know how she will freely choose to act.

First, we should determine in what way Molinism constitutes a response to Fischer and Tognazzini’s argument. Fischer has argued that Molinism doesn’t itself offer a response to the argument.6 It seems to me that Molinists must either:

1. Deny (4), by maintaining that had Eva acted differently, a different counterfactual of creaturely freedom would have been true, and God would have believed that instead. Importantly, it’s not that Eva has “control” over God’s beliefs, but that there is nevertheless this counterfactual dependence of what God believed on what Eva freely chooses.

2. Affirm that even if Eva could not have chosen otherwise, she acted freely. This involves denying the PAP, and perhaps accepting either compatibilism or a sourcehood view about free will.7

Since the denial of (4) and the rejection of the PAP has been discussed already (in §2.4 and §3.1, respectively), I will not say much more on the Molinist approach here. That said, I do not find Molinism workable, at least given a leeway formulation.8

3.3 Moorean Shift

Another sort of reply is to say that, although it’s not clear where the argument goes wrong, it is clear that it does go wrong, and so we are warranted in rejecting the conclusion. For example, someone might just remark that they are much more strongly convinced of the falsehood of the conclusion than they are of the collective truth of the premises, even if they aren’t sure which premise to deny. For example, Craig (2000) and Hunt (1993) have suggested something like this. See also Hunt (2016) for a related concern. As well, Todd (2022) raises the concern that theological incompatibilist arguments like Fischer and Tognazzini’s require that there can be non-causal constraints on freedom, which may seem strange.

4. Conclusion

What’s the right approach, then? I can’t hope to fully resolve that here, although I find compatibilism broadly to be rather plausible, and find theological compatibilism plausible for similar reasons.9 Regardless, I suggest you think through it for yourself: how plausible do you find the incompatibilist argument and the various ways in which it might be resisted?

I’m interested to see how people feel about this case and what I’ve written here. Feel free to leave a comment! If you enjoy this content and want to support more of it, you can become a patron at patreon.com/Friction, or make a one-time donation at paypal.com/paypalme/frictionphilo. Many thanks to my current patrons. You can find my other links at linktr.ee/frictionphilosophy.

1.1 Vultures and Wultures

Imagine yourself on a safari tour, seeing for the first time all sorts of wildlife and scenery. In the distance, a vulture with unusually white feathers lands on a dry log, looking toward the group. Someone else on the tour leans over to you and says, “look! a true contradiction!”1 Taken aback, you consider asking him to clarify, since that is quite a strange thing to say. However, you conclude that this is probably some crazy person speaking nonsense, and think better of it.

Perhaps the remark is crazy, but it turns out that it’s not at all obvious that it is. The strange man on the safari had in mind a new term, ‘wulture’, such that the white vulture both is a wulture and is not a wulture. Here’s how the term functions, according to the following meaning-constituting inferential rules:2

1. All vultures are ‘wultures’.

2. All white things are not ‘wultures’.

The man had noticed that the observed bird was a vulture, and so a ‘wulture’ per rule (1), but also that it is white, and so not a ‘wulture’ per rule (2). Hence, it both is a wulture and is not a wulture, and this is exactly the “true contradiction” that he had in mind. This construction was introduced by Kane Baker in this video, although the basic structure is shared by earlier examples discussed by Graham Priest.3 Indeed, if any stipulation of this sort is legitimate, and forces true contradictions, it seems that there are endlessly many that deliver the same result. The consequences cannot be restricted merely to white vultures; mutatis mutandis we can run the same trick with other base predicates.

1.2 Possible Reactions

It would be far too quick, of course, to conclude that the man on the safari is right, and that there are true contradictions of the sort described. Apart from granting the true contradiction, what are the other candidate responses to this sort of case? I will consider the options as follows:

1. The rules for the stipulated concept are being misreported. That is, it’s not that all vultures are ‘wultures’ and that all white things are not ‘wultures’, but rather that all non-white vultures are ‘wultures’. On this more accurate understanding of the concept, so the objection goes, no contradiction follows; any white vulture is merely not a wulture (and not also a wulture). This will be explored further in §2.1.

2. The given stipulation treats the given inferential rules as sufficiency conditions (on being a wulture and on not being a wulture), but that what’s given cannot be sufficiency conditions, and so the stipulation is malformed. This will be explored further in §2.2.

3. The stipulated rules are inconsistent, and so the stipulation is malformed. This will be explored further in §2.3.

4. The stipulated rules require a false presupposition, that is, that there are no white vultures (and perhaps that there aren’t even possibly any white vultures), and so the stipulation is malformed. This will be explored further in §2.4.

5. Certain logical principles constrain what can count as a legitimate stipulation such that any legitimate stipulation must simultaneously cohere with (a) certain logical principles/inference rules, and (b) non-negotiable worldly facts. In other words, the stipulation must not clash with certain non-negotiable worldly facts when combined with whatever core inferential principles we’re currently treating as fixed. This response is perhaps not independent from some of the others, but I think that this reply (or, at least, this sort of reply), constitutes the most sensible objection. I will discuss this approach in §3.

1.3 Upshot

In this article, I will ultimately argue that wulture-style stipulations lie on the edge of what we treat as legitimate. In §2, I will expand on and discuss the first four reactions from §1.2, finding them largely unpersuasive. In §3, I cover the fifth reaction. In §3.1, I explore an illustrative case that’s been discussed already by philosophers. In §3.2, I consider how that example might be relevant to the wulture case. In §3.3, I offer some responses. In §3.4, I construct a hypothetical to motivate the view that there isn’t a relevant set of background norms/commitments that is “correct” in a substantive sense. In §3.5, I consider how our actual linguistic practice and commitments bear on the dispute, offering some considerations in favor and some considerations against the legitimacy of wulture-style stipulations. It is, to some extent, a matter of presently unfixed convention whether we allow such stipulations or rule them out. While I lean toward their legitimacy, I conclude that actual linguistic practice and commitments do not seem decisive either way. I draw general conclusions in §4.

2 Analysis of Reactions 1-4

In this section, I look more closely at the first four reactions to the ‘wulture’ case. With each reaction, I’ll ask: (i) what motivates it, (ii) what exactly it commits us to, and (iii) whether it really undercuts the original stipulation.

2.1 Reaction 1: The Concept is Misreported

According to the first reaction, the safari-man’s stipulation has simply been mis-described. The idea is that he actually meant something different, such as “all non-white vultures are wultures”, or he’s describing two different concepts expressed by the same word, such that ‘Wulture₁’ applies to all vultures, and ‘Wulture₂’ does not apply to white things, but there is not a single concept for which both rules apply. Perhaps there are other options, although I will not explore them here.

Either way, no contradiction arises. If ‘wulture’ merely requires that “all non-white vultures are wultures”, then a given white vulture is simply not a wulture, since it is not a non-white vulture. On wulture₁ and wulture₂, while we can infer that a given white vulture is a wulture₁ and is not a wulture₂, we cannot infer that it is both a wulture and not a wulture in the same sense, and so the situation is perfectly consistent.

I think there is a natural temptation to tidy the case up in this way. We often repair people’s stipulations or informal definitions by charitably reading them as giving necessary and sufficient conditions, or as implicitly containing qualifications they forgot to mention. And the suggestions above are surely much closer to something someone might intend in ordinary discourse.

However, this reaction doesn’t seem to address the real issue. Maybe in everyday discourse, the contradiction-avoiding characterizations are more plausible, but that’s not to say the original characterization is impossible. I just am stipulating a term that functions in the described way. You might object that the stipulation is malformed in some way, but it’s not because I meant something else or had different conditions in mind. These are the conditions I have in mind. Sure, there may be nearby stipulations that are considered unproblematic, but those simply aren’t what’s currently being considered. The rules are given; we are asking whether the given stipulation is well-formed and, if so, what are the factual consequences?

With this in mind, I think we can safely dismiss the first reaction. The interesting question is not whether we can domesticate ‘wulture’ into a more familiar, contradiction-free notion, but whether the stipulation as originally given is illegitimate. We will explore other reactions relevant to that question in §2.2-2.4 and §3.

2.2 Reaction 2: Misuse of Sufficiency Conditions

One way to read the stipulated rules is as providing sufficiency conditions. That is to say, being a vulture is sufficient for being a wulture, and being white is sufficient for not being a wulture. Alternatively (or additionally), we might understand condition (2) as supplying a necessary condition for being a wulture (being non-white). However, given condition (2), being a vulture can’t be sufficient for being a wulture, since if it were a white vulture, it would not count as a wulture. If something could fail to be a wulture while meeting conditions “sufficient” for being a wulture, then the given conditions are not actually sufficiency conditions for being a wulture. Since the stipulation requires that the conditions are sufficiency conditions, but that they fail to fill that role, the stipulation is therefore malformed.

There are three main steps to this reaction. First, it is claimed that the given stipulation requires treating the rules as supplying sufficiency (and perhaps necessary) conditions on being a wulture and not being a wulture. Second, it is claimed that the given conditions cannot satisfy those roles. Third, it is concluded that therefore the stipulation is malformed.

Regarding the first step, it is at best unclear why we would have to think of the stipulated conditions as sufficiency conditions and such. Depending on how we understand what it means for something to be a sufficient condition, either the stipulated conditions qualify, or they do not. Either way, it seems that the wulture stipulation is no worse for wear. Thus, it seems wrong to suppose that the given stipulation requires that the rules supply sufficiency conditions (and such).

Regarding the second step, we might think of a “sufficient condition” as one which by itself guarantees some result.4 For example, “being an unmarried man” is sufficient for “being a bachelor” since the former guarantees the latter. Put another way, the term “bachelor” involves the following meaning-constituting inferential rule:

• All unmarried men are ‘bachelors’.

We can define “Ux” to mean ‘x is an unmarried man’ and “Bx” to mean ‘x is a bachelor’ and rewrite the inferential rule as follows:

• ∀x(Ux→Bx)

If it follows from this inferential rule that being an unmarried man is a “sufficient condition” for being a bachelor, then in exactly the same way, being a vulture is a “sufficient condition” for being a wulture (and so on). If we instead understand sufficient conditions in some other way, then the given condition may or may not qualify. I could explore other candidates,5 but it is inconsequential. Regardless of whether the stipulated conditions qualify on some understanding of “sufficient condition”, it’s not a requirement of the stipulation that they so qualify, and so this question is irrelevant to the well-formedness of the stipulation.

We might also contest the third step. That is, perhaps a stipulated term can be adequately well-formed even if it requires a false presupposition. However, since we have already adequately dealt with the second reaction, I will not explore that issue further.

2.3 Reaction 3: Rules are Inconsistent

It might instead be suggested that the stipulated rules aren’t even consistent, and so the concept is malformed. Let’s first express the rules more formally, letting “Px” mean ‘x is a wulture’, “Vx” mean ‘x is a vulture’, and “Wx” mean ‘x is white’.

1. ∀x(Vx→Px)

2. ∀x(Wx→¬Px)

Narrowly speaking, these two statements are logically consistent. A contradiction does arise given these stipulations if there is in fact a white vulture, but that’s not a consequence of the rules themselves being inconsistent.6

It may be objected that we can infer the following from (2) by contraposition:

• ∀x(Px→¬Wx)

We can then infer that for any white vulture, it is a vulture, and so it is a wulture, and so it is non-white. But then it would be white and non-white, and surely that’s a contradiction, right? There are two issues here. First, while the scenario involving a white and non-white vulture is contradictory, the overall statement is not contradictory. We could express it as follows:

• ∀x((((Wx∧Vx)→Vx)→Px)→¬Wx)

This entails the following formula:

• ∀x((Wx∧Vx)→¬Wx)

As before, this statement is logically consistent; a contradiction arises only given the further claim that there is a white vulture. Second, the derivation of this statement involves logical assumptions that may be rejected. We will revisit this in §2.4 and more thoroughly in §3. Either way, it appears that the given rules are logically consistent. It may be that something else is intended by this reaction, although I will not explore the possibilities here.

Here’s another way in which someone might allege that the rules are contradictory. We might say that, per rule (1), each member in the set containing all white vultures is a wulture. However, per rule (2), each member in the set containing all white vultures is not a wulture. And since the very set in question does contain white vultures, it follows from the stipulation alone that the rules entail a contradiction, that there exists something that is and is not a wulture.

This reply should seem mistaken on its face, since it surely can’t be a consequence of the rules alone that there are white vultures, but that’s what this reply requires. The problem is that, since we are here interested in conceptual consequences (that is, what follows from the stipulated rules alone), the relevant consequence relation is intensional: we may not build in further extensional information about the actual occupants of a set unless this is itself guaranteed by the rules. The move from ‘the set containing all white vultures’ to ‘the non-empty set containing all white vultures’ thus commits an intensional fallacy. Consider an analogous case. Suppose I stipulate that “the masked man” denotes the man standing over there in the corner. Suppose also that the man in question has brown hair. Was it a consequence of my stipulation that that man has brown hair? Of course not; that is a fact about the extension of the term introduced by my stipulation, not a consequence of the stipulation alone. In exactly the same way, the fact that the set of white vultures is non-empty is a fact about the extension of the relevant predicates, not a consequence of the wulture stipulation alone.

If someone were to say, “but every member of the set of white vultures both is and is not a wulture”, that statement is ambiguous between an intensional and an extensional reading. On the intensional reading, it is a conceptual consequence of the wulture stipulation, but no contradiction follows.7 On the extensional reading, a contradiction follows (since there are in fact white vultures), but it is not a conceptual consequence of the wulture stipulation alone. Either way, no contradiction follows from the wulture stipulation alone. Again, we could trivially construct relevantly equivalent examples that err in the same way, although I will not do that here.

It’s also not obvious (at least to me) that if the rules were inconsistent, that therefore the stipulation would be malformed. Regardless, we can dismiss reaction 3.

2.4 Reaction 4: False Presupposition

Another reason why we might think that the wulture stipulation is malformed is that it requires a false presupposition, that is, that there are no white vultures. As before, there are two main steps to this inference. First, it is claimed that the stipulation requires a false presupposition, and second, that its requiring that false presupposition renders it illegitimate.

In support of the first step, we might present the following derivation:

1. ∀x(Vx→Px) (rule (1))

2. ∀x(Wx→¬Px) (rule (2))

3. ∀x(Px→¬Wx) (2, contraposition)

4. ∀x(Vx→¬Wx) (1,3, hypothetical syllogism)

The rules require a false presupposition because they entail (4), and (4) is inconsistent with the fact that there are white vultures (and not also not any white vultures). And because they require this false presupposition, so the objection goes, the stipulation is malformed.

It is true that it is a (classical) logical consequence of the rules as universal generalizations that there are no white vultures. In response, the proponent of the wulture stipulation may say that what’s at fault here are those logical consequence relations, not the stipulation itself. There are white vultures, and the given rules are not meant to suggest that there are none; that result follows only given inference rules that they might reject. Indeed, contraposition is generally not validated by paraconsistent logics. If we accept the wulture stipulation as legitimate, concluding that white vultures both are and are not wultures, then certain logical principles/consequence relations would have to be rejected. If, on the other hand, we are to maintain those logical principles/consequence relations, then the wulture stipulation cannot be accepted as legitimate. However, this was already evident from the outset; we haven’t made any progress on the dispute with this reaction and the given inference (1)-(4). These issues will be revisited in §3.

Regarding the second step, it’s not clear (at least to me) that requiring a false presupposition renders the stipulation malformed, but I will not explore that further here.

3 Analysis of Reaction 5

I’ve separated reaction 5 from reactions 1-4 because, while the first four involve clear mistakes, reaction 5 does not. We may ultimately reject this reaction as well, but it will take some work.

3.1 Tonk

To introduce reaction 5, I want to first start with a point made by Arthur Prior.8 There was an idea that the meaning of a logical connective (like “and”, “or”, etc.) can be completely given by its introduction and elimination rules. Challenging this, Prior stipulated a connective that seemed inadmissible, called “tonk”. The rules regarding tonk are given as follows:

• tonk-introduction: from P, infer P tonk Q

• tonk-elimination: from P tonk Q, infer Q

The problem with this logical connective is that it would render logic trivial. That is, given any premise P, we can infer anything whatsoever. This is inadmissible since not everything is true (of course). Prior concluded that if we allow any intro/elim rules to fix meaning, we get triviality.

The subsequent literature on this topic is quite substantial, and I will only touch on a few points.9 The approaches broadly centered around figuring out what exactly makes tonk-style connectives illegitimate, and what general principles could be motivated regarding legitimate inferential definitions.

One of the key developments was made by Nuel Belnap, who argued that a key constraint of that sort was conservativeness.10 According to Belnap, a genuine logical term must extend a given consequence relation conservatively. With a conservative new connective, if you add a new connective with rules, you must not thereby make any new derivations purely in the old vocabulary possible. In other words, no new theorems purely in the old language (without this connective) are then licensed. ‘Tonk’ is decidedly not conservative.

Another key development was made by Michael Dummett. According to Dummett, there must be a sort of ‘harmony’ between the introduction and elimination rules for a legitimate connective. Roughly speaking, for a connective to be meaningful, the elimination rules shouldn’t let you get more out of the connective than the introduction rules put in.11 This is also similar to Prawitz’s inversion principle, according to which the elimination rules should be, in a sense, the mirror image of the introduction rules. Dummett later gave a much more rigorous treatment of harmony.12

There has been extensive analysis of conservativeness, harmony, the connection between them, and other principles (such as generality) to constrain legitimate inferential definitions of logical connectives. I will not cover the developments further here.13 In any case, it’s generally agreed that ‘tonk’ is a malformed connective, and it’s malformed because it violates something like conservativity and/or harmony.

3.2 Relevance

I hope you found this brief detour interesting in its own right, but you may wonder what connection it has to our wulture case. After all, ‘wulture’ isn’t a logical connective, but a non-logical predicate. However, on reflection, we can see why concerns related to conservativity/harmony can apply elsewhere. After all, if the stipulated rules regarding ‘wulture’ entailed that there were no white vultures, then there’s a sense in which the term is non-conservative and disharmonious in an analogous sense. It does make new derivations purely in the old vocabulary possible, for example.

However, as discussed in §2.4, that derivation assumes certain logical inference rules that proponents of the ‘wulture’ stipulation may deny. Does it make sense to assume those rules in order to show that ‘wulture’ violates conservativity (or some other constraints on inferential definitions), in turn showing that the wulture stipulation is malformed? More generally, can logical principles/consequence relations themselves constrain what counts as a legitimate definition?

To Belnap and Dummett, at least, the answer would arguably be yes. Belnap treats classical logical assumptions as background, and so ‘wulture’ arguably violates conservativity.14 Similarly, Dummett treats intuitionistic logical assumptions as background, validating non-contradiction, and so ‘wulture’ arguably violates harmony.15 If something like these principles are constraints on meaning-constituting stipulations, then wulture-style stipulations would be illegitimate.

3.3 Response

On some level, the move suggested in §3.2 is simply a more convoluted way of making the point in §2.4: given certain classical logical assumptions, the wulture stipulation licenses inadmissible inferences, and so is illegitimate. If we aren’t treating non-contradiction as background (among other things, like contraposition), then the corresponding conservativity/harmony-style constraints plausibly would not rule out wulture-style stipulations.

There is an important difference here between ‘wulture’ and ‘tonk’, which is that ‘tonk’ is non-conservative by itself given the falsity of trivialism, where nothing similar is true for ‘wulture’. We might weaken our logical assumptions in a plausibly non-catastrophic way to allow for wulture-style stipulations. In other words, the Belnap/Dummett-style move gives us, at best, a conditional: if we hold fixed certain background logical assumptions, then wulture-style stipulations are illegitimate.

Someone might respond that we should maintain the relevant background logical commitments (at least absent compelling motivation to reject them), and so we should lean against the legitimacy of wulture-style stipulations. But I ask, “why?” If it’s merely a matter of strong prior commitment and/or conventional choice, then I may report that I do not share those commitments or those conventions. If it’s because those logical assumptions are “true”, I may ask what makes them true independently of conventions about which inferential stipulations are admissible. Put differently: if the truth of those logical laws is itself partly a matter of which inferential practices we are prepared to countenance, then it’s not clear that we can simply assume them in order to rule out wulture-style concepts from the start.

3.4 Another Detour

Those very familiar with my view may know that I think that the correct analysis of vagueness is non-classical. That is, there are propositions that are neither true nor false, and this is a result of vagueness. There are vague terms (such as bald, heap, noonish, etc.) such that when asserted of certain things, it is indeterminate whether that term correctly applies. By “indeterminate”, I do not mean merely to suggest that we do not know whether it applies. Rather, there simply is no fact of the matter whether it applies. This post is not concerned with exploring or defending that further. I invite you to suppose, for sake of exposition, that I’m right.16 Suppose also that our background commitments strictly rule out as well-formed all wulture-style constructions, or anything else that might result in true contradictions.17

Imagine our distant descendants travel the galaxy, eventually encountering an intelligent alien species.18 While they are relatively friendly, we find learning to communicate with them challenging. After many years, we come to understand their language which, in some ways, is not too unlike ours. We do notice two critical differences, however. First, they are conceptually opposed to vagueness; each term introduced into their language is perfectly precise. That is to say, it’s never indeterminate whether a particular term applies. Second, their language is rife with wulture-like terms; it’s as inextricable from their language as vague terms are from ours. However strange and unrealistic this might be, it is surely not inconceivable. Additionally, the aliens have well-developed logics, and while they are strongly committed to the law of excluded middle, they have no issues with permitting contradictions, and they employ a paraconsistent consequence relation that blocks triviality.19

What might we say to the aliens? We may try to communicate that on our logical and conceptual commitments, vagueness is permitted (and excluded middle may be violated), but contradictions are not. If it turns out that they take the opposite approach and are unconcerned with our peculiar linguistic practices, what then?

The issue here is not merely that we might not be able to convince the aliens, but that it’s not clear in what sense we would be “right” and the aliens “wrong”. Both sides can impose systematic constraints on meaning-constituting rules. We rule out certain inferential stipulations, such as ones that permit contradictions, but tolerate vague predicates that sometimes yield neither truth nor falsity. They rule out vague predicates, insisting that every admissible term have perfectly sharp application conditions, but tolerate wulture-style predicates whose correct application sometimes yields both truth and falsity. We and the aliens can both formulate versions of conservativity and harmony to exclude “bad” stipulations by our respective lights.

Once we see how rational, logically sophisticated agents might adopt alien but nevertheless coherent background norms, it becomes much less compelling to insist that our own background logic and harmony constraints are beyond question. It appears to me that the admissibility of wulture-style predicates is partly a function of background norms and commitments, which themselves are not “correct” in some substantive sense.

It may be replied that we should simply build the relevant constraints into our notion of “meaning”. On this view, to count as genuinely meaningful, by definition an expression must be governed by rules that respect, for example, non-contradiction and certain harmony requirements. Since the aliens reject those constraints, much of their language is not, strictly speaking, “meaningful” in the sense that interests us. However, the aliens might do exactly the same thing. They can stipulate a notion of “meaning” that requires sharp boundaries and permits gluts, and then announce that much of our language fails to be “meaningful” in their sense. At that point, we simply have different notions of “meaning”, each tailored to the background norms of the respective linguistic communities. It is not clear that any genuine progress has been made. We have not shown that our constraints are correct and theirs mistaken; we have only arranged our terminology so that “meaning” favors our conceptual practices over the aliens’.

Perhaps it could be motivated that there is some way in which there’s a correct approach here, and that we have it right, although I’m very skeptical.

3.5 Actual Practice

It could be replied that, while there is no substantive, framework-independent sense in which we are “right” and the aliens wrong, it remains that our actual practices and background commitments rule out wulture-like stipulations. In that sense, even if the choice of background norms is not uniquely correct in some deeper way, it remains that relative to our framework, wulture-style predicates are illegitimate. Perhaps we do treat as background certain classical constraints on meaning-constituting rules, as suggested by Belnap, Dummett, and so on.

I take this as largely an empirical matter: which relevant background commitments, heuristics and such do we have, do we take as given? What sort of constructions would we treat as legitimate, and which not? I can’t hope to draw very definitive conclusions without doing the empirical work. Nevertheless, it does seem to me that there are some considerations that support the legitimacy of wulture-style stipulations, and others that weigh against it.

I will first cover a few considerations that support the legitimacy of wulture-style stipulations. First, we tend to be rather permissive regarding what stipulations are admissible. So long as the rules are intelligible, and we can understand how the term gets applied, we tend to admit it into our language. Second, it’s plausible that wulture-style constructions are, or could be, admitted into our language. For example, Graham Priest has argued there are (or at least could be) legal stipulations that lead to true contradictions in the law.20 Third, wulture-style stipulations are not radically different from other meaning-constituting inferential rules that we would consider legitimate. Suppose I stipulate a new term, with the following meaning-constituting inferential rules:

1. All bachelors are ‘wachelors’.

2. All married people are not ‘wachelors’.

Structurally, the rules here are the same as those in the wulture case. The difference is that there are background rules regarding ‘bachelor’ that rule out married bachelors, thus ruling out that something could be both a wachelor and not a wachelor. However, that seems like a relatively small difference between the legitimate wachelor stipulation and wulture stipulation. If the two cases differ only in this way, the thought goes, then the wulture stipulation should likewise be regarded as legitimate.

There are also considerations that count against the legitimacy of wulture-style stipulations. First, admitting wulture-like stipulations requires weakening or rejecting certain logical assumptions that we often take for granted, such as non-contradiction, contraposition, and so on.21 Second, wulture-style stipulations arguably do not satisfy certain norms concerning assertibility/deniability.22 Third, wulture-style stipulations are not radically different from other meaning-constituting inferential rules that we would consider illegitimate. Suppose I stipulate a new term, with the following meaning-constituting inferential rules:

1. All true sentences are ‘wrue’.

2. All ‘wrue’ sentences are false.

While not structurally the same as the wulture stipulation, the inferential rules here are somewhat similar. However, the ‘wrue’ stipulation is clearly illegitimate, since it would entail that every true sentence is also false, which is inadmissible.23 But since the ‘wrue’ stipulation is relevantly similar to the ‘wulture’ stipulation, the thought goes, the wulture stipulation should likewise be regarded as illegitimate. Or, consider another stipulation:

1. All humans are ‘wumans’.

2. All humans are not ‘wumans’.

The ‘wuman’ version is structurally basically the same as the wulture case, but plausibly is illegitimate. After all, it’d just be a term that applies and doesn’t apply to all humans, such that each human both is and is not a wuman. As before, if this stipulation is considered illegitimate, so too should the wulture stipulation. However, it may be objected that resistance to ‘wuman’-style stipulations is more a pragmatic concern, not a general constraint on what counts as well-formed.24

There may be other relevant points that I haven’t covered. Nevertheless, I report that I do not find either argument decisive. Our somewhat imprecise conventions regarding what gets counted as legitimate constructions do not, it seems to me, count decisively either for or against wulture-style stipulations.25 That said, I find the considerations in support of their legitimacy more compelling. If we found that our language were already rife with wulture-like terms, while that may be surprising, it would seem wrong to rule that part of our language as malformed or meaningless. On the other hand, it may be that I’m not taking seriously enough the logical commitments people broadly make, at least implicitly, that are relevant to constraining legitimate linguistic constructions.

4 A Bird’s Eye View

These issues are probably of little relevance outside of philosophy seminars. There are not many people like the strange man on the safari, pushing the boundary of legitimate linguistic constructions. Maybe if this were more prevalent, the linguistic community more broadly may be pushed to make more explicit or precisify the rules regarding what stipulations are acceptable. I do not know how that would go, or whether there would even be general consensus.

For those who do find this interesting to think about (and if you’re still reading, that’s probably you), here are my general takeaways. First, it’s implausible that there’s a framework-independent sense in which wulture-style stipulations are illegitimate (or legitimate). Second, it’s not obvious that such stipulations are illegitimate relative to our actual linguistic practice and commitments, and those things may even count more toward their legitimacy. Third, we could decide to make it clear that they are legitimate (or illegitimate), but that clarity would be the result of future development of the relevant conventions, not wholly a function of present practice and commitments. Whether that will happen, and how it is likely to go, I have little idea.

I’m interested to see how people feel about this case and what I’ve written here. Feel free to leave a comment! If you enjoy this content and want to support more of it, you can become a patron at patreon.com/Friction, or make a one-time donation at paypal.com/paypalme/frictionphilo. Many thanks to my current patrons. You can find my other links at linktr.ee/frictionphilosophy.

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