Only to the same degree that first-order logic requires an ambient group of models (not necessarily sets) to make sense.
Well, it makes sense to me without any models. I can compute, prove theorems, verify proofs of theorems and so on happily without ever producing a “model” for the natural numbers in toto, whatever that could mean.
Well, it makes sense to me without any models. I can compute, prove theorems, verify proofs of theorems and so on happily without ever producing a “model” for the natural numbers in toto, whatever that could mean.