Friday, October 1, 2021

A simple moral preference circle with infinities

Here is a simple moral preferability circle. Suppose there are infinite many human strangers numbered ..., −3, −2, −1, 0, 1, 2, 3, ... all of whom, in addition to two cats, are about to drown. Consider these options:

A. Save the strangers numbered 0, 1, 2, ....

B. Save the strangers numbered −1, −2, −3, ... and one cat.

C. Save the strangers numbered 1, 2, 3, ... and both cats.

Option B beats Option A: If we had to choose between strangers 0, 1, 2, ... and strangers −1, −2, −3, ..., we should clearly be indifferent. Toss in the cat, and now it looks like we have a reason to save the second set of strangers.

Option C beats Option B: If we had to choose between strangers −1, −2, −3, ... and strangers 1, 2, 3, ..., we should be indifferent. But now observe that in Option C one more cat is saved, and it sure looks like we should go for C.

Option A beats Option C: Option A replaces the two cats with stranger 0, and surely it’s better to save one human over two cats.

If you don’t think we have moral reasons to save cats, replace saving the cats from drowning with saving two human strangers from ten minutes of pain.

I am now toying with an intuitively very appealing solution to problems like the above: we have no moral rules in such outlandish cases. I think this can be said on either natural law or divine command theory. On natural law, it is unsurprising if our nature does not provide guidance in situations where we are far from our natural environment. On divine command theory, why would God bother giving us commands that apply to situations so far from ones we are going to be in?


Li Zhen said...

Dear Professor Pruss, I'm really glad to comment here. I’m from China. The general understanding of Christianity in our country has been impacted by Nietzsche, Freud and Karl Marx, which overrides the notion of existence of God and attempts to explain the origin of religion.

The public knows little about apologetics in contemporary analytic philosophy, but perhaps those who know it learn from John Perry's work. Some CS Lewis’ books on apologetics have been translated into Chinese, which helped a lot to come to faith. I’m also fond of Prandinger, Snubwin, and McGrath's books, but very few people have heard of them.

I am very grateful to God for the opportunity to learn about you and the work you have done. I am sure they are pleasing to God. So, thank you.

In China, communism is taught to us since childhood. School officials would interrogate students who have religious backgrounds; christians have limited freedom to gather due to persecution in some parts of China.

I’m 19 now, and I will continue to follow your work. Thank God for them. Ah, I wish more would recognise them too. You have really done a lot great works.

I don't know English. I use Google (with VPN) to translate books of apologetics into Chinese; they mostly make sense. This comment is also translated from Chinese to English (by a friend).

I will continue to remember you in my prayers.

Ibrahim Dagher said...

Might this support causal finitms? I have the feeling one might be able to construct moral circles, or even contradictions, from the possibility of infinite causal chain. The set up used here doesn't need a infinite causal history, but I imagine one could construct a setup that requires the infinite causal chain. So:
1. If an infinite causal chain is metaphysically possible, such-and-such scenario is metaphysically possible.
2. But, such-and-such scenario entails a moral circle/contradiction.
3. So, such-and-such scenario is not metaphysically possible.
4. So, an infinite causal chain is not metaphysically possible.

Luke Hill said...

Well an actually infinite number of people is impossible, and since you are saving an infinite number of people regardless of what you choose, you should pick the option with two cats. We also don't have any measurement of the value of certain people, and arguably there are more valuable people than others. Say the set 1, 2, 3... contained Hitler. Thus we would want to pick -1, -2, -3... since it contains Mother Teresa (I picked a Catholic, just for you :) ). I'm not sure this thought experiment seems too basic.

Alexander R Pruss said...


I don't see why an actually infinite number of people is impossible.

You should assume that you know nothing about any of the people on the list, or else that they are all of equal value.


It could support causal finitism, but it goes beyond that, to finitism, which I don't want. :-) So instead I am trying a different direction for a solution.

Ibrahim Dagher said...

Hi Alex,

How would it support strict finitism? I would think that any situation creating moral circles/contradictions would have to have its members [at least capable of] being in some causal network or relation. Usually, my being in a moral situation will be such that I can causally affect every relevant part of the situation. If there are infinitely many relevant parts, we don't get to strict finitism, but some kind of causal finitism.

Luke Hill said...


As Craig has pointed out, infinity is just an idea in the mind, not something of actual substance. You would never be able to reach the point at which you hit an infinite number of people. (God I feel so naive talking to a doctorate holder in math, please destroy me ;) )

If we assume that we know nothing of the people on the list, then we should save the 2 cats along with 1, 2, 3, ... Cats are objectively awesome (no faulty logic there), and you save an infinite number of people regardless.

Thanks mate!

Alexander R Pruss said...


If infinity is just an idea in the mind, probably so are finite numbers. That there are infinitely many people does not force infinity to be a real substance, just as that there are eight billion people does not force eight billion to be a real substance.

I know that Craig has argued that there cannot be an actual infinity of things, but I think all these arguments fail.

If you go for the two cats option, you are trading the life of person #0, who despite their ugly name is a being in the image and likeness of God (like all persons are), for two cats. For you could save person #0 instead of the two cats by going for option 1. Wonderful as cats are, it is better to save person #0.

Alexander R Pruss said...


That's interesting. My causal finitism says that there cannot be infinitely many causal arrows all pointing TO one thing. But you could have a reversed causal finitism on which there cannot be infinitely many causal arrows all pointing FROM one thing.

Note that theism + reverse causal finitism implies finitism. For if theism is true, then everything that exists is either God or created by God. But reverse causal finitism implies God can only create finitely many things (there can only be finitely may causal arrows pointing from God).

Note, too, that while I presented the paradox with the people being all simultaneous, they need not be. They could be situated at different future times.

Luke Hill said...


Since you are saving the infinite number of people, and we don't know the value of their character outside of being made in the image of God, we shouldn't worry about leaving behind 0, due to the fact that statistically you will have a nearly exact person in relation to 0, if that makes sense.

I'm basically saying that there's a chance that we find that person 7584 is the same as person 0.

Ibrahim Dagher said...


That seems mostly right, although I'm not sure it gets us to strict finitism. For theism + reverse causal finitism entails all things created by God will be finite in number, but reverse causal finitism tells us nothing about the things in God himself. In other words, one might still endorse actual infinities that exist in God's mind [conceptualism with respect to abstracta].

So I think this argument would prove some sort of finitism with respect to causal relata, ie, concrete entities outside God. But I think one can happily accept reverse causal finitism and still hold to the existence of some 'abstract' infinities. Reverse causal finitism doesn't seem to prove TOO much. Thoughts?

SMatthewStolte said...

If you are right that there are no moral rules in these outlandish cases, that solves the problem of the circle but it forces us to accept that our moral intuitions are wrong in these cases. For our moral intuitions tell us that Option B beats Option A. But if there are no moral rules in these cases, it doesn’t. So we have a kind of Kantian paralogism, I guess. I suppose that’s better than having a real moral preference circle. But why do our intuitions misfire here instead of just telling us the truth that the question “Which option is better?” isn’t well formed?

Alexander R Pruss said...


I think it's not hard to give an error theory. We feel B beats A because when dealing with finite numbers, sets of equal cardinality of equal individuals are on par. We then incorrectly generalize to the infinite case.

An alternate version would be this: we have general principles that in finite cases do not yield a preference circle; in the infinite case they still apply, but yield a preference circle. But that's OK, because our principles aren't designed for infinite cases, and so it's no surprise that they do weird stuff in that case (in this case, that they generate a set of mutually unsatisfiable obligations). On this story, ought-implies-can is true in circumstances that fit with our normal environment, but in outlandish cases, ought-implies-can fails. We can think of ought-implies-can as akin to the smoke not coming out of a calculator. In normal usage, smoke isn't one of the spec'ed outputs of a calculator. But maybe if you load 3.6V AA-format Li-Ion batteries instead of the 1.5V AA alkalines it's spec'ed for, smoke comes out of the calculator, but that's no fault of the calculator.

Alexander R Pruss said...

Li Zhen:

I admire Christians in regimes like China. God bless and keep you, and give you strength, and may he help you lead your neighbors to him.

I lived my first nine years in Communist Poland.

Arath55 said...
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