1
An omission is a value, not a gap
The rescue that was available and not performed is a variable whose actual value is 0. A model can flip it to 1 and recompute, so there is nothing about an omission that the but-for test cannot handle.
Lesson · Ethics and the Arithmetic of Welfare · Deontology
Doing, Allowing and Omissions as Causes
An omission is a rescue that was not performed, and in a causal model it is a variable like any other. Flip it, and the death flips: the omission is a but-for cause. Two would-be rescuers change the structure and not the answer, and whatever separates doing from allowing, it is not that one is a cause and the other is not.
an omission: a rescue variable set to 0
flip it: if the death flips, it is but-for
out of reach: flipping willingness is idle
doing and allowing both depend on you
An omission as a cause
Core ideas
What this lesson establishes
The previous lesson tested a harm for dependence. The same test now applies to something that did not happen.
2
Availability lives in the equations
Not everything left undone is a cause. The lifeguard’s unwillingness matters only because the lifeguard was in reach, and the equations say so by making the rescue depend on both.
3
A causal verdict is not a moral one
That an omission is a cause shows that the distinction between doing and allowing cannot rest on cause. It does not show the two are equally bad.
The material
A lifeguard who did not go in
One drowning, three ways the rescue can fail to happen, and what the test says about each.
Many people hold that killing is worse than letting die, and the commonest support is a claim about cause: the person who pushes causes the drowning, the person who watches only fails to prevent it. The claim is easy to test, because the but-for test does not care whether the cause is an event or an absence.
Let L be “the lifeguard is in reach”, W be “the lifeguard is willing”, R be “the swimmer is rescued” and D be “the swimmer drowns”. The rescue happens only if the lifeguard is both in reach and willing, and the swimmer drowns when there is no rescue.
R = L and W
D = not R
In the case as it happened the lifeguard is in reach and unwilling: L = 1, W = 0. So R = 0 and D = 1. Take the rescue not performed, R, as the candidate cause and the drowning as the effect. Setting R to 1 makes D 0, and the lab reports a but-for cause. The omission is a cause in exactly the sense that a struck match is a cause of a fire in “Counterfactual Causation and the But-For Test”.
Definition · Omission
An omission is the absence of an act that was available. In a structural model it is a variable whose actual value is 0, and it is tested for causation like any other variable: flip it and recompute.
The obvious objection is that this proves too much. Everyone has failed to rescue every swimmer in the world. The model answers it, because availability is an equation and not a footnote. If the lifeguard is out of reach, L = 0, the rescue does not happen whether or not the lifeguard is willing, and flipping W changes nothing. Of everything that was not done, the lab selects what was available.
Now two lifeguards. If either would suffice, R = W1 or W2, and both are unwilling, flipping either one alone produces a rescue. Each omission is a but-for cause, so the thought that neither is responsible because the other could have gone is not one the structure supports. If instead both are needed, R = W1 and W2, as when two people must carry a boat, flipping one alone changes nothing and the lab reports a joint cause: neither is a but-for cause and each is a cause together with the other.
Example · The shallow pond
A child is drowning in a pond shallow enough to wade into, at the cost of ruined shoes. Let W be “you wade in”, A be “the child is within reach”, R = W and A, D = not R and M = R, where M is the ruined shoes. Flipping W flips both the drowning and the shoes. The lab shows the dependence of the death on your choice; whether the shoes outweigh it is not a quantity it computes.
A pusher’s act is a but-for cause of the drowning too. So if pushing is worse than watching, the reason is not that the first is a cause and the second is not. Candidates are that the pusher initiates the harm and the watcher does not, that duties not to harm are stronger than duties to aid, or that the cost to the rescuer differs. Each is a premise about what matters, and none of them is computed here.
Interactive
Causes in a structural model
But-for, held fixed, and joint
Method
Testing an omission
Four steps. The second decides everything, because it is where availability is written down.
1
Name the rescue as a variable
Give the act that was not performed its own letter, with actual value 0, and give the harm that followed its own letter.
2
Write what the rescue depends on
Say what had to be true for the rescue to happen: being in reach, being willing, having help. These are the conditions that separate an available act from a mere possibility.
3
Flip the omission
Set the rescue, or the willingness behind it, to its opposite and recompute. A change in the harm makes the omission a but-for cause.
4
Check the other agents
If someone else could have rescued, write that in. Either one would do, and each is a but-for cause, or both are needed, and the cause is joint.
What the flip shows about an omission
Score 0 / 0Choose the answer you can justify.
The lifeguard, then a second lifeguard
The drowning depends on the rescue, and the rescue on who is willing.
R = L and W, D = not R, L = 1, W = 0
actual: R = 0, D = 1
flip R to 1: D = 0 so R is a but-for cause
two lifeguards, either would do: each is a but-for cause
both needed: neither alone, a joint cause
None of this says the lifeguard did wrong. It says the drowning depended on the lifeguard’s unwillingness in the same sense that a fire depends on a match, so any account of why failing to rescue is different from drowning someone has to look elsewhere than cause.
Common mistakes
1
Thinking an omission cannot be a causeA rescue not performed is a variable with value 0, and flipping it to 1 turns the drowning off. The lifeguard preset reports a but-for cause, by the same test that reports a struck match as the cause of a fire. What an omission lacks is a process, some transfer of energy from cause to effect, and the test does not ask for one. A philosopher who insists that it should is holding that dependence is not enough for causation, which is a position with a price: it must then say what the match has that the lifeguard lacks, since the drowning depends on each in the same way.
2
Spreading the responsibility until it vanishesWith two lifeguards, either of whom would have sufficed, the lab reports each omission as a but-for cause. The presence of another person who could have helped does not remove anyone’s dependence on their own choice.
3
Treating the causal verdict as the moral oneThe lab shows that the drowning depended on the omission. It does not show the omission was wrong, or as wrong as a push. The cost of the shoes in the pond preset is on the page and the lab cannot weigh it.
Check your understanding
✓
Finish when you can model an omission and say what the flip shows.
Given a rescue that was not performed, you should be able to write it as a variable, state what it depends on, flip it, report whether it is a but-for or joint cause, and say what the verdict leaves open.
Note: The Boolean model treats willingness as a switch. Real omissions come in degrees of effort and cost, and a rescue that was possible only at great risk to the rescuer is a different case that the model would need a new variable to hold.