Should Parfit do more semantics?

So I previously put forward an argument I called a parity argument. The basic structure was this: Prudence is like this, so morality must be like this too. Such arguments claim that there is parity between the properties of prudential and moral reasons.

Such arguments need work, in many ways. But I can't claim that they're entirely my creation. Very closely related is this. In Reasons and Persons, Parfit claimed that the self-interest theory was objectionable because it was a hybrid view. It requires us to be person-partial and time-neutral. But why think that we should treat times and people similarly anyway? These are very different kinds of entity. Here's what I take to be Parfit's answer to that question:

"this analogy [between persons and times] holds only at a formal level. Particular times do not resemble particular people. But the word 'I' refers to a particular person in the same way in which the word 'now' refers to a particular time […] given the analogy between 'I' and 'now' a theory ought to give both the same treatment." (p140, his emphasis)

This does not seem like a strong argument. The ways in which words refer does not obviously give us insight into how we ought to treat the things to which they refer.

I'm a huge fan of Reasons and Persons, as well as Parfit's work more generally. But as Parfit himself says, even great philosophers make mistakes. Is this one such mistake, or am I missing something?

(c.f. Williamson's interesting paper (via))