I'm learning some stuff about formal languages and structures for them. However there's this thing I don't understand.
How can we ever define/specify a structure for a language, if we do not yet have the language to talk about the structure?
If we were all platonists then this would be pretty easy to resolve, because we could just assert the existence of certain structures and rely upon our 'intuition' to convince ourselves that those structures are in fact models for the formal language.
However, since we are not all platonists, we need to:
- Specify the model
- Prove that it exists (I guess?)
- Prove, using some method, that the structure is indeed a model for the language
But I just don't see how this can ever be done in a rigorous way without already having a formal language to work in.
