What is the meaning of the sentence "That dog won't hunt." Or maybe of the sentence "Tomorrow is Sunday." Or maybe of the sentence "Two plus two equals four." It's this last question that perplexes Lundberg and perhaps, Wolfgang.
My problem is more basic - what are we doing when we assign meaning to any sentence? The best answer I can come up with is that "meaning" is all about conveying a message from someone to someone else. That means that meaning is contextual - it depends on speaker (or writer) AND on listener/reader. The "Tomorrow is Sunday" sentence has a meaning only in the context of a specific space-time locale. "That dog won't hunt" can be specific but is likely to be metaphoric. "Two plus two equals four" can be an example clarifying the meaning of the word plus, an experimental discovery, or a theorem in Peano arithmetic.
Hope this helps clarify the "ontological status of numbers" - but I'm not optimistic.
I find it slightly amusing that the philosophical study of ontology, or the nature of existence, has been kidnapped by artificial intelligence to mean the specification of a conceptualization, that is, the relationships that exist among concepts (usually words) in some domain of discourse. It is one of the primary tools of machine understanding. I thought my exposure to this kind of operational ontology made a lot more sense to me than the stuff I read in the philosophical literature.