Joyce does a rather strange interpretation in The Myth of Morality p. 121. He writes:

However, I doubt we even need concede that much. These “conditional reasons” are very shady customers. Take what seems to be a straightforward one mentioned above: one’s reason to save a drowning child if one exists. There are two readings:

(i) If there exists a drowning child, then S has a reason to save him/her.

(ii) S has a reason to save a drowning child if one exists.”

The absence of a comma after “child” in (ii) makes the difference. (ii) is saying that S has a reason all along: when there are no drowning children, when S is asleep, while S is witching TV, etc.”

Normally conditional sentences can be written in two ways in english (and other languages that I am familiar with), forwards and backwards. Forwards being what is similar to their logical structure and backwards what is not similar. Take the conditional sentence “If I don’t have a job, then I will not get money”. It is forwards for it is similar to its logical structure P→Q (with the obvious interpretation keys). The sentence “I will not get money if I don’t have a job” seems to express exactly the same conditional (i.e. proposition), but Joyce apparently thinks that it does not (if he accepted an analogy with his own example).

When I read the passage above I spent some time thinking about how to properly formalize his two interpretations. I came up with this:

I. (∃x)(Dx)→(∃y)(Ryx)

That there exists an x such that x is a drowning child materially implies that there exists an y such that y is a reason for S to save x.

II. (∃y)∧(∀x)(Dx)→(Ryx)

There exists an y and for all all x, that x is a drowning child materially implies that y is a reason for S to save x.

It seems to capture what he meant.

How Joyce made up these interpretations I don’t know. I note that (I) does not imply that (if there is no drowning child, then S does not have a reason to save one) [¬(∃x)(Dx)→¬(∃y)(Ryx)].

Joyce goes on to make distinction in a strange way:

This observation is entirely generalizable, to the conclusion that there are not really any “conditional reasons.” Anything true of the form “S has a reason to Ø if C obtains” should be read as “If C obtains, then S has a reason to Ø,” not “S has a reason to Ø-if-C-obtains.”

Joyce would have benefited from using logic here for clarification instead of this. It’s not the case that Joyce wanted to completely avoid using logical symbols in his book anyway, for just two pages earlier we find some simplistic predicate logic formalizations of sentences. (Assuming that he would not have them there if he did not want logical symbols in the book.)

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