But what the philosopher is stating, I think, is that no-one can state: (Rain(w,t) ∧ ¬Rain(w',t)) because no-one has the standing or perspective to be able to verify Rain(w,t) and ¬Rain(w',t) simultaneously.

Essentially:

w -> ¬w'

Is this attempting to strip objectivity from philosophy?

> w -> ¬w'

That doesn't work, because I can say something like "John dreamt he found a unicorn" which involves two different worlds (say, w & w'). Or, to make it more parallel, "John dreamt he wasn't dreaming". Which are both perfectly reasonable sentences and have perfectly reasonable predicate logic translations.

In "John dreamt he wasn't dreaming" the two observations either have different observers or happen at different times. At no point is John both aware that he is dreaming and also thinking that he is not dreaming.

In the original, we are not proposing separate worlds though, not in that sense.

1. I assert that it is not raining. 2. It is not raining.

This chap saying that 1 and 2 exist in the same world, and are therefore contradictory. Equivalence of statement and assertion.

It makes no sense to me to conflate logical statements and (human) speaker-anchored assertions. When semanticists work on natural language meaning, this requires use of the formal languages. It makes no sense to me to hard-wire human-speakers into a system of abstract logic (which we need when we reason about human speakers).