Doctor Joe Horton’s all-or-nothing problem, his solution, and my solutions to it


Author: Doctor Terence Rajivan Edward (or 0161__Rajivan, if that helps)
Version: 4 (30th August 2025, French added)


Doctor Horton's problem. Horton formulates the problem by first introducing an example, which borrows heavily from Derek Parfit but puts the material to different use. Two children are about to be crushed by a building on the verge of collapse. (An alternative, which may be more realistic, is you and children drowning, but a literary allusion is lost then.) You have three options: (i) do nothing; (ii) save one child; (iii) save both. However, if you take option (ii) or (iii), your arms will be crushed. There is no higher cost for you in taking (iii). Horton introduces these two propositions:
1. It is morally permissible for you to not save the children.
2. It is morally wrong for you to save only one child.
Proposition (1) is supported by the high cost for you in saving. Proposition (2) is supported by the fact that there is no higher cost in saving two. The conclusion inferred within the problem is: you ought to save neither child rather than save only one. But this conclusion is counterintuitive. The problem is solved by identifying what is wrong with the argument for this conclusion, or else arguing that nothing is actually wrong.


Solutions. Below I do not present all solutions in the literature, merely Horton's solution and the solutions I have conceived. All but the last three have appeared on PhilPapers before. Maybe I shall add some others later.


1. Doctor Horton's solution. Horton replaces (1) with: if you are not willing to save either child, it is permissible for you to save neither, owing to the large sacrifice involved; but if you are willing to save at least one, there is a moral obligation on you to save both (2017: 97). But does this solution help? (a) Consider the situation if you are not willing, but someone offers to save only one for a small sum of money. If you take up the offer, Horton's solution entails that you are paying for moral wrongdoing, because this person is willing and so is morally obliged to save both. We should not pay for wrongdoing, it seems. But that is counterintuitive. Surely it is better to pay for the willing person to save, even if only one. Horton’s solution leaves us with counterintuitiveness, much the same counterintuitiveness, it seems, as with the problem. However, there is a Razian defence of his solution, which is that partial fulfilment of an obligation is better than no fulfilment and so we should pay this person, who is obliged to save two. (b) People can be willing from pressure from others. Should they then be morally obliged to act in a way that leaves them armless? (c) A willing person who saves may be left with lifelong regret and so it seems something stronger than merely willing to save is needed to generate a moral obligation to save in this context. 
 
2. The exceptions solution (my favoured solution). The conclusion inferred from (1) and (2) requires a further premise: if it is morally permissible for you to save neither child and morally wrong for you to save only one, then you ought to save neither child rather than save only one. This premise is an application of a general principle: if option A is morally permissible and option B is morally wrong, then you ought to do A rather than B. But I propose that there can be exceptions to this principle when the following obtains: the moral superiority of A over B cannot be explained purely by comparing A and B (e.g. save no children versus save one child); to establish this superiority one has to refer to a third option (e.g. C: save two children at no greater cost). When this obtains, there is nothing in A in itself which makes it morally better than B in itself. One can therefore choose B.


3. The metaphysical solution. The metaphysical solution denies that there really are the options Horton describes. I illustrated it by reference to a different example: two children are drowning and you are on the beach. Horton's options are save zero and save one and save two. But here is a sequence which the option of saving zero (typically) consists of: stay on the beach as they shout for help - morally permissible, owing to the risk to your life of sailing out; stay on the beach as they submerge - morally permissible, owing to the risk. And here is a sequence which the option of saving one consists of: sail out to where the children are – morally acceptable; then pull one child on board – morally acceptable; then sail back, leaving the other child – morally wrong, because one can save the other child at no significant extra cost. There is nothing counterintuitive about this description of Horton's middle option, even with its accompanying moral assessments. The metaphysical solution says that this sequence is what there really is as a possibility, rather than the option of saving one: at best referring to “saving one” is shorthand for this. When we describe the option as it really is, counterintuitiveness disappears.
 
4. The compensatory solution. The compensatory solution denies (1) and replaces it with: it is morally permissible for you to not save the children if and only if you carry out actions to “compensate” for letting them die, such as giving a lot of money to charity. With this revision, there is no route to the unqualified conclusion that saving none is better than saving one.


5. The psychological solution. Saving only one is not a psychologically realistic option for most people. Horton’s problem as formulated does not apply to almost all people, greatly diminishing its interest.


6. The flowchart solution. The flowchart solution rejects the representation of a choice of three in Horton’s formulation of the problem: (i) don’t save; (ii) save one child; (iii) save both children. Instead, by flowchart representation or other means, it says that there is a choice between not saving and saving. And then, within saving, there is a choice between saving only one and saving two. The flowchart solution denies that one can conclude that saving none is better than saving one, because the choice is never between these two: it is between not saving and saving, or, after the latter choice has been made, between saving one and saving two.


7. A fictional solution. This solution seems to belong to fiction rather than philosophy given the assumptions of contemporary analytic philosophy. Any attempt to save just one child is sure to go wrong.


8. The annoyingness solution. In realistic examples which seem to give rise to Horton's problem, there is always a significant extra cost in saving another child (or person): each other person is annoying. According to this solution, the all-or-nothing problem does not apply to realistic situations (likely situations), because it misdescribes the option of saving two as carrying no significant extra cost. But are there really no likely situations in which it applies and what about unlikely situations? "J'agace." "Encore."


9 and 10. Anti-inductive solutions. Horton acknowledges that one cannot validly infer (3) from (1) and (2) alone. There needs to be a bridging principle, though he does not call it that (See Pummer 2019). He asserts that the bridging principle he identifies is supported by countless cases: the principle that if option A is morally permissible and option B is morally wrong, then you ought to do A rather than B. So he seems to justify it like so: case 1 supports the bridging principle, case 2 does, case 3 does, case 4 does, case 5, case 6 does… the bridging principle is true. But this is inductive reasoning and one might not accept inductive justifications. (Even if one does sometimes, one might justifiably take the fact that (1) and (2) and the bridging principle applied to Horton's example lead to (3) as evidence against generalizing from a number of cases to the unqualified truth of the bridging principle.) 
 
References
Horton, J. 2017. The All-or-nothing Problem. Journal of Philosophy 114: 94-102.
Edward, T.R. 2020. Farewell to arms? The all-or-nothing problem again. Available on PhilPapers: https://philpapers.org/rec/EDWHTA
Edward, T.R. 2022. A metaphysical solution to the all-or-nothing problem. Available on PhilPapers: https://philpapers.org/archive/EDWAMS-2.pdf
Edward, T.R. 2022. A compensatory solution to the all-or-nothing problem. Available on PhilPapers: https://philpapers.org/rec/EDWACS
Edward, T.R. 2022. The flowchart solution to the all-or-nothing problem. Available on PhilPapers: https://philpapers.org/archive/EDWTFS-2.pdf
Edward, T.R. 2022. Philosophy and fiction: common problems, uncommon solutions? (By D*n*ld D*vids*n?). Available on PhilPapers: https://philpapers.org/rec/EDWPAF
Pummer, T. 2019. All or Nothing, but If Not All, Next Best or Nothing. Journal of Philosophy 116 (5): 278-291.