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Epistemic status: Something I thought about a lot, but have not talked to many people about. I would not be very surprised if I will be convinced that this argument is flawed.

In this post, I am going to make the argument that moral realism is not compatible with time discounting. I am going to use special relativity in the process, but you don't need to be familiar with physics to follow along. This post is based on an essay I wrote for university, and I will use it for my master's application. So if any of you (especially with an understanding of metaethics) have any critique or feedback, I would be happy to receive it. 

Relevance for EAs

Whether you use time discounting in your decision-making or not has huge practical implications. If you use time discounting, Longtermism is hard to defend. If you don’t use time discounting, Deontic strong Longtermism seems plausible.

As this is an argument against the compatibility of moral realism and time discounting, it is most useful for EAs, who have some confidence in both. If you don’t fall into that category, I hope you find it interesting too, but I don’t expect you will update your moral views by a lot. 


I am first going to explain key features of time discounting, moral realism, and special relativity. Feel free the skip any of those explanations, if you have a solid grasp of these topics. If you want to get straight to the argument, just read from “Thought experiment” onward.

Time discounting

In the context of economics, time discounting describes the relative valuation of receiving a good or service on an earlier date, compared to a later date. This means that according to models that include time discounting, people would prefer, all else equal, to receive a pleasurable good or service rather today than tomorrow. This must not be confused with inflation, which leads to goods and services being higher priced at a later time, or the opportunity cost of having, let’s say, a factory working one day earlier and making a profit for one more day. Time discounting means that given the choice to receive the same benefits for the same price with the same consequences today or tomorrow, people prefer having them today, over tomorrow.

Some ethical theories also have time discounting. Jeremy Bantham names "propinquity or remoteness" as one of the categories, whereby "pleasure and pain [is to be] considered [...] more or less"(Bantham,1780,30).

This must not be confused with caring less about the future because one can have more influence or more certainty about events that occur sooner rather than later. According to moral theories with time discounting, just because an event is further in the future, it is less important, even if one could influence it just as easily or just as confidently.

Moral realism

Moral realism is the position that moral claims (for example "Anna should not sell Christoph`s car") can be true or false, like regular claims about the world (like "Elsa is taller than Anna").

One implication of moral realism is that there is some correct moral theory. With "correct moral theory", I mean some method by which the truth value of any moral statement can be derived.

The most cumbersome formulation of the correct moral theory would just be a list of all possible moral statements, labeled true and false. Most moral philosophers think that there is a more parsimonious formulation of the correct moral theory, in the form of some rule or set of rules, from which the truth value of every moral statement can be derived. 

Another implication of moral realism is that moral claims are true or false for everyone. This does not mean that "Anna should not sell Christoph`s car" automatically implies "Christoph should not sell Christoph`s car". But if "Anna should not sell Christoph`s car" is true for Anna that also means that "Anna should not sell Christoph`s car" is also true for Christoph and everyone else. Just like "Elsa is taller than Anna" does not imply "Elsa is taller than Christoph". But if "Elsa is taller than Anna" is true for Anna that implies that "Elsa is taller than Anna" is also true for Christoph and everyone else.

This might seem trivial, but it actually puts some constraints on what the correct moral theory might be. For example, the correct moral theory cannot be "Everyone should sell everything that begins with a 'C', but nothing that begins with an 'A'.". According to this moral theory, the moral claim "Anna should not sell Christoph`s car" would be right for English speaking Anna, but wrong for the German-speaking Christoph, because "car" for him begins with an 'A' ("car" in German: "Auto").

It follows that the moral theory "Everyone should sell everything that begins with a 'C', but nothing that begins with an 'A'." cannot be the correct moral theory, because it is incompatible with moral realism.

Special relativity

Einstein’s theory of special relativity describes the relationship between space and time, and its predictions have been confirmed by many experiments (Roberts & Schleif,2007). One central statement of special relativity is that simultaneity (among other things) is relative. That means that for observers that move at different (constant) velocity, different events take place at the same time.

Figure 1: Two observers (A and C) moving relative to each other, perceive different events to happen simultaneously.

Let us take a look at the example of Anna (A) and Christoph (C) that can be seen in figure 1. Each of them is traveling at half the speed of light into the center of a square, coming from 2 adjacent sides of the square. From our perspective (in the rest inertial system of the square), both depart from their origin at the same time and arrive at their destination (the other edge of the square) at the same time. However, statements about which events take place at the same time, are not absolute and vary from inertial system to inertial system. From the perspective of Christoph, he himself does not travel with half the speed of light to the left but is at rest, and the square moves with half the speed of light to the right. Also, Anna's trajectory is different for Christoph than for us. For him, she departs from her origin, before Christoph departs from his wall, and she arrives at her destination after Christoph reaches his destination. (Or in Christoph’s terms: before his destination reaches him.)

For Anna, the situation is the other way around. In her inertial system, she departs after Christopher but arrives before him.

It is important to understand here that neither of them is more right than the other. Neither of them has false beliefs. This might seem counter-intuitive, as Anna claims, to arrive at her destination before Christopher, and Christopher claims to arrive at his destination before Anna. 

It seems as if at least one of these claims must be false. But in which order two (space-like separated) events occur, is just a matter of description. Just like the English-speaking Anna could point at a car and claim "The name of this object begins with a `C`." and the German-speaking Christoph could point at the same car and claim "The name of this object begins with an `A`.". At a first glance, these claims seem to be mutually exclusive, but once you understand that they use different languages to describe the same object, you realize that both can be right within the context of their own language. There is no one true language, to settle the question, what a car should be named.

There is also no preferred inertial system, out of which about the order of events might be settled. The statement that all inertial systems are equally valid and that the physical laws are the same in all of them is called the "relativity principle" and is a central claim of special relativity.

The thought experiment

In the following thought experiment, we assume both moral realism, and time discounting, and show how this leads to a contradiction. So, I am assuming that there is a correct moral theory and that this theory values events less, if they are further in the future.

Figure 2: For two observers with relative velocity (A&C), moral statements vary according to moral theories that contain time discounting.

Let us consider the situation depicted in figure 2: There is a big square. 

At the middle of each side of the square is one person: Sven (S), Elsa (E), Christoph (C), and Anna (A). 

At the time  Christoph begins traveling with a velocity of  in the direction of Sven, and Anna begins to travel with a velocity of in the direction of Elsa. In the middle of the square there is one carrot.

When the carrot arrives at Elsa or Sven, some event will be triggered, which is morally desirable according to the correct moral theory. If the correct moral theory was total hedonic utilitarianism with time discounting, this would mean for example that Elsa and Sven would be happy to receive the carrot. The moral desirability is the same whether the carrot arrives at Elsa of Sven.

Christoph and Anna arrive at the same time in the middle of the square, and only one of them can take the carrot with them. From our perspective, it makes no moral difference, who takes the carrot. If Anna takes the Carrot, Elsa would be happy to receive it, and if Christoph takes it, Sven would be just happy to receive it. And both would receive the carrot at the same time.

Let us now look at the situation from Anna's perspective. From Anna's Perspective, she arrives earlier at Elsa, than Christoph arrives at Sven. So, if Anna takes the carrot, the carrot would be received earlier than if Christoph would take the carrot. If the correct moral theory would not contain time discounting, it would still not matter who took the carrot because both Elsa and Sven would be equally happy to receive it. But because we assume here that the correct moral theory does contain time discounting, it is morally preferable that Anna should take the carrot, rather than Christoph. We can say that "Anna should take the carrot." is true for Anna.

For Christoph on the other hand, he arrives at Sven before Anna arrives at Elsa. For the same reasons "Anna should take the carrot." is true for Anna, it is false for Christoph.

Now we have the situation that a moral statement, namely "Anna should take the carrot." is true for one person, but false for another person. But this is in contradiction with moral realism.

Since we have arrived at a contradiction, we need to discard one of our premises. Either we have to discard moral realism and say that moral statements have no truth value like factual statements, or we have to discard time discounting, and say that the correct moral theory does not value events less, just because they take place further in the future.

Possible counter-arguments

In the following, I will list possible counter-arguments, one might have, and discuss their validity.

Too absurd thought experiment

Most people concede that thought experiments can be useful to probe moral intuitions and to explore the decisions to which different moral premises might lead. But even Derek Parfit, infamous for thought experiments bordering on the absurd, recognized that there is such a thing as a too absurd thought experiment. These he called "deeply impossible" and said that in such situations "We may be unable to imagine what such a case would involve"(Parfit,1984,388).

One might reject my argument because we need to consider too absurd a thought experiment for this argument to work.

Yet, Parfit's reason, and as far as I know the only reason, not to trust too absurd thought experiments, is that we should not trust our moral intuitions in contexts, so much different from what we ever realistically encounter. This is a good reason to distrust any argument that goes like this: "If we assume A, then it follows that we should do X in absurd scenario B. X goes against our moral intuitions. Therefore, we should reject A."

This is not the structure of my argument. My argument goes like this:  "If we assume A then it follows that we should do X in absurd scenario B. X is in logical contradiction to A. Therefore, we should reject A." My argument does not rely on moral intuitions.

Therefore, the counter-argument that the thought experiment is too absurd, cannot be applied here.

One might still use Minkowski norm discounting

Even though the time distance  between two events, and the space distance  between two events is relative according to special relativity, there is a form of distance which is still the same for all observers: The Minkowski norm 

If the correct moral theory would contain Minkowski norm discounting, Anna and Christoph would be indifferent to who takes the carrot with them, when they meet in the middle. But this time, Sven and Elsa come to different conclusions, who the carrot ought to go to. At the time (in Elsa's and Sven's inertial system), when Anna and Christoph meet at the carrot, the Minkowski norm between Elsa and the arrival of Anna at Elsa is bigger than the Minkowski norm of Elsa and Christoph arriving at Sven. So, for Elsa "Anna should take the carrot." would be true. For Sven, it is the other way around. For him "Christoph should take the carrot." is true. 

From this, it follows that Minkowski Norm discounting is also not compatible with Moral realism.


I conclude that time discounting is not compatible with moral realism. This means that any theory that can be considered as a candidate for the correct moral theory by moral realists, must count all consequences the same, no matter how long into the future these consequences may occur. 

This supports Graves and MacAskill's claim of "Deontic strong longtermism"(Graves & MacAskill,2020,2) that the best option is mainly determined by its long term consequences in a wide class of decision situations, from a moral realist point of view. This would mean that the most important moral consideration for moral realists would be the effect of their actions on the far future.


Jeremy Bentham (1780):” An Introduction to the Principles of Morals and Legislation “, published:  Oxford University Press (1907)

T.Roberts, S.Schleif (2007):” What is the experimental basis of Special Relativity?

Derek  Parfit (1984):” Reasons  and  Persons “, published:   Oxford  UniversityPress (1984)

Hilary Greaves and William MacAskill (2020):” The Case for Strong Longtermism





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This is a fascinating argument — thank you for sharing it! I think it's particularly interesting to consider it in the context of metaethical theories that don't fall neatly within the realist paradigm but share some of its features, like R.M. Hare's universal prescriptivism (see Freedom and Reason [1963] and Moral Thinking [1981]). However, I also think this probably shouldn't lead most discounting realists to abandon their moral view. My biggest issue with the argument is that I suspect (though I am still thinking this through) that there exist parallel arguments of this form that would purport to disprove all of philosophical realism (i.e. including realism about empirical descriptions of the natural world). I think statements rejecting philosophical realism are pretty epistemically fraught (maybe impossible to believe with justification), which leaves me suspicious of your argument. (It's worth noting here that special relativity itself is an empirical description of the natural world.)

I have a feeling that the right way of thinking about this is that the rise relativistic physics changed the conventional meaning of a "fact" into something like: a true statement for which its truth cannot depend upon the person thinking it within a particular inertial frame of reference. Otherwise, I think we would be forced to admit that there are not facts about the order in which events occur in time, and that seems quite obviously inconsistent with the ordinary language meanings of several common concepts to me. I know that relativity teaches that statements about time and duration are not objective descriptions of reality but are instead indexical reports of "where the speaker is" relative to a particular object, similar to "Derek Parfit's cat is to my left," but (for basically Wittgensteinian reasons) I do not think that this is actually what these statements mean.

Ultimately, if you're someone who, like me, believes that a correct analysis of the question, "What is the right thing to do?" must start with a correct analysis of the logical properties of the concepts invoked in that sentence (see R.M. Hare, especially Sorting Out Ethics [1997]), and you believe that those logical properties are determined by the way in which those concepts are used (see Wittgenstein's Philosophical Investigations [1953]), then I think this argument is mainly good evidence that the proper understanding of what moral realism means today is the following: "Moral realism holds that moral statements are facts, and the truth of a fact must be universal within the inertial frame of reference in which that fact exists; that is, that truth cannot depend upon the person thinking the fact within that inertial frame of reference."

Thanks for that comment and your thoughts! I am unfortunately unfamiliar with the works of Hare, but it sounds interesting and I might have to read up on that. 

I totally agree with you, that there are statements to which we assign truth values, that depend on the frame of reference (like "Derek Parfit's cat is to my left", or the temporal ordering of spacelike separated events.) 

I would also not have a problem with a moral theory, that assigns 2 Utilons to an action in one frame of reference, and 3 Utilons in another. 

I do however believe that there are some statements that should not depend on the frame of reference. 

We have physical theories to predict the outcome of Measurements, so any sensible physical theory should predict the same outcome to any measurement, whichever frame of reference we use to describe it. 

We have moral theories to tell us what actions we should do, so any sensible moral theory should prescribe the same actions, whichever frame of reference we use to describe them. 

If you however do not have that requirement to a moral theory, I see that discounting realists would not have to change their views.

This is a beautiful thought experiment, and a really interesting argument. I wonder if saying that it shows an incompatibility between moral realism and time discounting is too strong though? Maybe it only shows an incompatibility between time discounting and consequentialism?

Under non-consequentialist moral theories, it is possible for different moral agents to be given conflicting aims. For example, some people believe that we have a special obligation towards our own families. Suppose that in your example, Anna and Christoph are moving towards their respective siblings, and we neglect relativistic effects. In that case, both Anna and Christoph might agree that it is right for Anna to take the carrot, and  that it is also right for Christoph to take the carrot, even though these aims conflict. This is not inconsistent with moral realism.

Similarly, in the relativistic case, we could imagine believing in the moral rule that "everyone should be concerned with utility in their own inertial frame", together with some time discounting principle. Both Anna and Christoph would believe in the true statements "Anna should take the carrot" and "Christoph should take the carrot". They would acknowledge that their aims conflict, but that is not inconsistent with moral realism.

I think the analogy here is quite strong, because you could imagine a time discounter defending their point of view by saying we have stronger obligations to those closer to us in time, in the same way that we might have stronger obligations towards those closer to us in space, or genetically.

On the other hand, when you consider General Relativity, there are no global inertial frames, so it's interesting to imagine how a steelmanned time discounter would adapt the "everyone should be concerned with utility in their own inertial frame" principle to be consistent with General Relativity. Maybe anything they try would have some weird consequences.

Thanks for posting this!

You might be interested in this from On the Overwhelming Importance of Shaping the Far Future:

The Separated Worlds: There are only two planets with life. These planets are outside of each other’s light cones. On each planet, people live good lives. Relative to each of these planets’ reference frames, the planets exist at the same time. But relative to the reference frame of some comet traveling at a great speed (relative to the reference frame of the planets), one planet is created and destroyed before the other is created. If we treat space and time asymmetrically, we would have to claim that, relative to the reference frame of the planets, this outcome was not as good as it is relative to the reference frame of the comet. But this is very hard to believe. The value of this possible world should not be relative to any reference frame.

Also it's worth pointing out that "regular claims about the world (like 'Elsa is taller than Anna')" are also not "real" in the sense you are using the term. I'm not super familiar with the subject, but I wouldn't be surprised if many moral realists are okay describing moral claims as "only" as real as claims about length.

Could the seeming contradiction be resolved by greater specificity of statements?

For example, rather than abandoning "Everyone should sell everything that begins with a 'C', but nothing that begins with an 'A'." as a norm, we might realize we underspecified it to begin with and really meant "Everyone should sell everything that is called by a word in English that begins with a 'C', but nothing that begins with an 'A' in English.". We could get even more specific if objections remained until we were not at risk of under specifying what we mean and suffering from relativity.

In the same vein, maybe the contradiction of the through experiment could be resolved by being more specific and including more context about the world. For example, cf. this attempt at thinking about preferences as conditioned on the entire state of the world. Maybe the same sort of technique could be applied here.

Yes, good point. I agree that sufficient specification can make time discounting compatible with moral realism.  

One would have to specify an inertial system, from which to measure time. (That would be equivalent to specifying the language to English for example.) 

Then we would not have a logical contradiction anymore, which weakens my claim, but we would still have something I would find unplausible: An inertial system that is preferred by the correct moral theory, even though it is not preferred by the laws of physics. 

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