Infinite Ethics
Does Your Choice
Matter At All?
If the universe is infinite, it already contains infinite happiness and infinite suffering. Can anything you do make a difference?
Consider this: modern cosmology suggests the universe might be spatially infinite. If so, and if matter is roughly uniformly distributed, then there are infinitely many galaxies, stars, planets, and beings.
Infinitely many beings experiencing joy. Infinitely many experiencing agony. Right now. Forever.
Now you want to do something good—save a life, reduce suffering, create happiness. But wait...
infinity + 1 = infinity
Add any finite amount of good to infinite good, and you still have infinite good.
Remove any finite amount of bad from infinite bad, and you still have infinite bad.
Your action seems to change nothing.
This is infinitarian paralysis—the apparent collapse of ethics in an infinite universe.
The Infinite Cosmos
Current cosmological observations suggest the universe is either infinite or so vast that the difference does not matter practically. In an infinite universe with roughly uniform matter distribution:
- Every possible configuration of matter appears infinitely many times
- There are infinite copies of Earth, with infinite copies of you
- Every possible decision you could make is being made by some copy right now
- The total amount of happiness and suffering is already infinite
The Infinite Universe
If space is infinite and matter is roughly uniform, there are infinite copies of everything.
Observable Copies
1
Total in Infinite Universe
infinity
In an infinite universe with finite configurations, every possible arrangement repeats infinitely.
Including infinite copies of you making this exact choice.
The cosmological argument:
If space is infinite and the cosmological principle holds (matter is uniformly distributed on large scales), then for any finite region containing intelligent life, there are infinitely many such regions. The same logic that produced you produced infinitely many beings throughout the cosmos.
The Arithmetic of Infinity
Here is where things get mathematically strange. Standard expected value calculations require adding up utilities. But infinite sums behave very differently from finite ones.
Finite arithmetic
100 + 1 = 101
Adding makes things bigger
Infinite arithmetic
infinity + 1 = infinity
Adding changes nothing
Your Action's Impact
How much does your good deed matter in an infinite universe?
Total Good in Universe
1.0Q
Total Bad in Universe
500.0T
Your Impact
1.00e-11%
100 / 1.0Q
The utilitarian formula "maximize total utility" requires comparing sums. But if both options lead to infinite utility, how can we choose?
The Paralysis
Action A: infinity good + infinity bad
Action B: infinity good + infinity bad
Both actions produce the same totals. Neither is better.
Not All Infinities Are Equal
There is a glimmer of hope. Mathematicians have developed multiple ways to compare infinite quantities. Perhaps ethics can borrow these tools.
Ways to Compare Infinities
Not all infinities are created equal - or are they?
Cardinality counts "how many" elements. Surprisingly, the natural numbers (1, 2, 3, ...) have the same cardinality as the even numbers, because we can pair them up perfectly. This is why infinity + infinity = infinity by this measure.
Could these alternative measures help us escape paralysis? If we use density instead of cardinality, an action that improves things locally could increase the "density of goodness" even without changing the total.
The Hope
Just because two sets have the same cardinality does not mean they are the same in every respect. The natural numbers and even numbers both have cardinality aleph-null, but their densities differ. Perhaps ethical value works similarly.
Which Ethical Theories Survive?
Infinitarian paralysis does not affect all ethical theories equally. Theories that rely on aggregating total welfare face the most severe challenges. Others escape relatively unscathed.
Which Ethical Theories Survive?
Click each theory to see how it handles infinite ethics
Classical Utilitarianism
BREAKSCore Principle
Maximize total utility (sum of all wellbeing)
Under Infinite Universe
Cannot sum infinite positive and infinite negative values. infinity - infinity is undefined. Every action leads to the same "total" - infinite good and infinite bad.
1
Broken
2
Problematic
3
Survive
Notice the pattern: aggregative consequentialist theories struggle because they require summing utilities across all affected beings. Non-consequentialist theories and virtue ethics focus on local features—intentions, character, duties—that do not require cosmic aggregation.
This might seem like a point against utilitarianism. But defenders argue that practical ethics can still function locally—we should maximize expected value among the beings we can actually affect, not worry about cosmic totals.
Why Aggregation Fails
The problems run deeper than just "infinity plus one equals infinity." Infinite sums are mathematically pathological in ways that make ethical aggregation genuinely impossible.
Why Summing Utilities Breaks
Three ways infinite sums fail for ethics
The Problem
Infinite alternating sums have no well-defined value. The series 1-1+1-1+... can equal 0, 1/2, or 1 depending on how you compute it.
These are not exotic mathematical curiosities—they are fundamental obstacles to any theory that tries to sum welfare across an infinite population:
Path Dependence
The sum depends on the order you add things, but there is no natural order to infinite beings.
No Canonical Total
Different legitimate methods of summation give different answers for the same population.
Finite Irrelevance
Any finite improvement vanishes when compared to infinite totals.
Ways Out of Paralysis
Philosophers have proposed various solutions to infinitarian paralysis. None is universally accepted, but each offers a path forward for ethical reasoning in potentially infinite universes.
Proposed Solutions
Click to explore each approach to infinite ethics
The Practical Takeaway
Even if we cannot solve the theoretical puzzle of infinite aggregation, we can still act ethically by focusing on the beings we can actually affect. Local ethics remains meaningful even if cosmic ethics is undefined.
What Does This Mean For You?
Infinitarian paralysis is not just an abstract philosophical puzzle. It has implications for how we think about ethics, meaning, and action.
Your Actions Still Matter Locally
Even if cosmic totals are undefined, the beings you actually affect are real. The suffering you prevent is real suffering prevented. The happiness you create is real happiness created.
Aggregation Has Limits
The drive to maximize total utility may be fundamentally misguided. Ethics might need to be more humble about its scope, focusing on local relationships and duties rather than cosmic optimization.
Uncertainty Is Profound
We do not know if the universe is infinite. If it is finite but vast, standard ethics applies. If infinite, new frameworks are needed. Our ethical uncertainty extends to the nature of reality itself.
Character Over Calculation
If calculating total consequences is impossible, perhaps virtue ethics and deontology have an advantage. Being a good person might matter more than achieving optimal outcomes.
The universe may be infinite. Your life is not.
Perhaps the deepest lesson of infinitarian paralysis is that meaning cannot come from cosmic significance. It must come from somewhere else—from the connections we make, the character we build, the local worlds we create and sustain.
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Reference: Bostrom (2011), "Infinite Ethics"