The Myth of Morality and carelessness

I'm currently reading The Myth of Morality by Richard Joyce. In the summery section of chapter three he presents a central argument thus:

1. If x morally ought to Ø, then x ought to Ø regardless of what his desires and interests are.

2. If x morally ought to Ø, then x has a reason for Øing.

3. Therefore, if x morally ought to Ø, then x can have a reason for Øing regardless of what his desires and interests are.

4. But there is no sense to be made of such reasons.

5. Therefore, x is never under a moral obligation. (p. 77)

This argument is not valid under a straightforward interpretation. However Joyce earlier clarified the structure of the argument. He stated that the form is:

1. If P, then Q

2. If P, then R

⊢ 3. If P, then (Q and R)

4. Not (Q and R)

⊢ 5. Not P. (p. 42)

However this does not correspond well to the words above. First, notice the wording in (3). It is “can have”, which expresses a possibility, not an actuality like (2) does; “has a reason”. (3) should be either reworded (probably the best solution) or the formalization changed to ◊R (“it is possible that R”). Second, (4) does not correspond very well to the formalization at all. Third, (5) contains the word “never” which is a temporal concept not found in any of the other premises. Indeed they don't feature temporal words at all. Accordingly, the wording of (5) should be changed or the formalization changed (to something like GQ, using these formalization keys). If we ignore the word “never” in (5), then the argument is valid even though (3) is a about a possibility instead of an actuality. This is of course because (∀P), from P, ◊P follows. (P→◊P is a theorem of S5) So, given the above, I think that Joyce is a bit careless. More careless than professional philosophers should be. Especially a professor!