¶ … Roger Smith, a quite competent swimmer, is out for a leisurely stroll. During the course of his walk he passes by a deserted pier from which a teenage boy who apparently cannot swim has fallen into the water. The boy is screaming for help. Smith recognizes that there is absolutely no danger to himself if he jumps in to save the boy; he could easily succeed if he tried. Nevertheless, he chooses to ignore the boy's cries. The water is cold and he doesn't want to get his good clothes wet. "Why should I inconvenience myself for this kid," Smith says to himself, and passes on. Did Smith do anything wrong? Explain. What aspects of this situation would have to be different for you to conclude otherwise?

Yes, I can support an assertion Smith did something wrong, from the way the question is asked, and the evidence provided. Metaethics reveals Roger made a flawed equation between his own preference and the boy's. Entailments arise from the way the question is phrased, which I describe and compare amongst themselves and against propositions derived from the rest of the question. I then examine resulting conclusions, without assumptions not supplied in the prompt. Finally, I remove some of the particular given constraints, to see how different conclusions could result.

I constrain myself to the "given language" not out of any motive or fear of reprisal, but because we don't need anything else. A metaethical analysis can derive all the principles we need from the word 'wrong.' Nor do we need posit 'wrong' implies some opposite "right," because this does not necessarily follow from "wrong," "right" is not asked for, and is effectively irrelevant.

In order to ask if something is wrong requires the word has a meaning we agree on. It may have multiple meanings, but there is one which is the meaning we are discussing. We have to restrict the meaning of "wrong" to one we agree on, because otherwise we achieve multiple outcomes. If we can arbitrarily assign any word any meaning we want, then language loses its functionality in a mathematical sense, where a variable stands for or represents only one value.

In fact math provides a useful, if not perfect analogy. If we allow the number 2 to equal 2, 8 and 40 at the same time, we can use it for calculation even if that becomes extremely complex. The problem lies in that we achieve multiple, simultaneously accurate results. If we want a single answer, as our question asks -- yes or no -- we have to discuss each of the possible meanings of 'wrong' separately. Otherwise language becomes useless or at least extremely subjective, if we can simply just say anything we want, and say for example "the birthday party" to mean "that boy." I call this principle 'consistency.' Contradicting results persist if one person calls the boy "boy" and another person calls it 'aardvark,' where they both mean the same thing, or call two different referents 'that boy' at the same time.

Under the same reasoning, we must apply the agreed-upon meaning to different actors in the same way, or else we have a weakening of our ability to refer the same concept, for which the word 'wrong' is a placeholder. If we say for example inflating a tire and deflating a tire are both wrong, then 'wrong' has a non-exclusive meaning that must refer to something other than moving air in or out of a tire. Likewise if we say that person A inflating a tire is wrong but person B. inflating the same tire under effectively identical circumstances is not wrong, then we have a weakening of definition that we then have to find another way to express. We can try to haggle about the similarity of circumstances but that line of reasoning can be waved away with a qualifier like "effectively identical." This is the product of our defining the word "wrong" as standing for a meaning we agree on, which I call "universality."...

We have required "wrong" to mean the same thing in all effectively identical circumstances, for all actors, as the result of defining the term. Otherwise I could say 'aardvark' and you could say 'banana' for the same referents and observers and language would be meaningless gibberish.
This generalization to consistency and universality reveals the flaw in Smith's logic regardless of whether we phrase our discussion in consequentialist Kantian-deontic terms of "if, then should" or utilitarian welfare maximization, ethical egotism, duty to care, or virtue or axiomatic rule reflection or any number of terminologies. Roger violated consistency and universality arising from our metaethical need for the word "wrong" to mean something.

We do not have to consider reasons why Roger "chooses" not to save the drowning boy, but only establish he violates consistency and universality. Roger had a choice of two options, save the boy or not, he equated the two, and acted on one of them. His mistake lied in equating the boy with himself where the two are fundamentally different, because one had a choice where the other did not. The stipulation that the boy was "screaming for help" indicates that he did not have a choice to help himself. If not, we rediscover the problem of using words ('screaming for help') for multiple meanings, in which case the discussion can proceed in terms of 'aardvark' meaning 'kill' and 'totem pole' at the same time and/or for different actor/observers.

The result is that the boy did not have a choice, Roger did, he equated his inconvenience with the boy's life (we are told) as if they both had choice ("free will," in existentialism) when one did not, this is a violation of consistency and universality arising from our agreement that words refer to the same thing for everyone in identical circumstances, and so Roger committed an error in a mechanical sense, even before we specify what the term "wrong" means, without needing concepts like "right" or utilitarianism or the Golden Rule, et cetera. But Roger violated those too.

The principles I derived above, consistency and universality, are however embedded in what is commonly expressed as a/the "Golden Rule": If I agree to having action X done to someone else, I should agree to it being performed on myself (and therefore everyone) "in effectively similar" circumstances. I phrased that in a consequentialist, Kantian-deontic mode, but we could change that to an axiological mode like "Justice requires that we treat people the same when they do identical acts, or we act arbitrarily, and lose our claim to moral right. In order to claim moral right, where Justice is necessary for that, we have to treat people the same when they do the same thing."

This all requires Roger acted, which we are conveniently told he did, but which we can imply from his verification that he could have saved the boy were it not inconvenient.

He also violates utilitarianism if a life is more valuable than convenience, because then net social welfare would be increased by sacrificing convenience for the life, which Roger did not. If everyone's maximum utility is equal, then net happiness would be zero whether Roger saved the boy or not (at maxima), and so utilitarianism would be normatively useless in the same way the word "Roger" would be useless applied to say 'slavery' and 'freedom' at the same time. Likewise ethical egotism: If we use 'wrong' arbitrarily for every individual to mean, " do whatever you want at all times," it becomes an infinite referent which delivers no normative utility or even conceptual value that we can exchange through its use. Nor does moral relativity destroy the requirement words…