Peter Singer gave a famous argument in Famine, Affluence and Morality that made an analogy between saving a drowning child in a pond at the expense of getting your clothes wet, and donating the equivalent amount of money to save children from dying in developing countries. The cost of getting new clothes to save a child is equated with the cost of donating money to save a child elsewhere.
What would be the Singer response to the following counter-argument:
Suppose that it takes $10 to buy new clothes and that we can afford the $10, and that for that amount, when donated, one could also save a child in a developing country from dying of hunger. Then by Singer's analogy, we ought to give the $10. Suppose now that there's a second child that can starve and can be saved for an additional $10, that we can also afford comfortably. Then clearly by the same logic, we should give another $10.
If we iterate this N many times for N-many children (with the safe assumption that there are always more children that can be saved from death of hunger in the current state of world affairs), then eventually we cross the point where we can no longer give comfortably or where we run out of money. Therefore, giving money to the Nth child is less morally pressing or important (and in some cases, impossible) than giving money to the Mth child, if M < N. Similarly, giving money to the Mth child is less important than giving money to the Lth child, where L < M.
We can iterate this argument back until we get to the first child. By the same logic, giving $10 to the second child is less morally pressing than giving money to the first child. We can ask, what makes the first child anymore important than the rest? The ordering is arbitrary.
For this reason, it can't be that giving money to the first child is as important as saving the child drowning in a pond.
What would be a Singer-like response to this argument? I'm not necessarily convinced by this argument, but would like to hear the response.