This can be pushed only so far. We might be convinced by some general argument that addition is a total function always defined. Then it is conceivable that we might know “\(1 + 4\)” designates some number, but not know what it is. But this cannot be captured using the semantics outlined thus far, assuming arithmetic terms behave correctly. If at some state we know \(\exists x([\lambda y\ x = y](1 + 4))\), that is, we know “\(1 + 4\)” designates, then at all compatible states, “\(1 + 4\)” designates, and since arithmetic terms behave correctly, at all compatible states “\(1 + 4\)” must designate 5, and hence we must know \([\lambda y\ 5 = y](1 + 4)\) at the original state. We cannot know “\(1 + 4\)” designates without knowing what.