No, they are not. They never were. Scientists believed them true for a long time and now they believe otherwise.
No, I didn't. I responded to your claim that models are not true of false and I got that right.
Newton's model is false and always was. And yes, it was also useful and in fact still is, but that doesn't change the fact that it's false.
This falsifies your claim that models are not true or false.
The fault, however, is probably on my end for not being clear. To say that the reals are or are not real depends on the context. That's because they are part of a model which is not the same thing as the objective reality which we model. Models have a recursive objective quality, that is, as a model is is objectively real, but the question of whether that reality is fully equivalent to the subject of the model requires the context.
The thing is, I didn't even address that aspect of your post. How can you say I didn't understand it?
The question of whether models are true or false is distinct from
and independent from (
the reverse is not true) the question of whether mathematical abstractions are real. You are effectively conflating, as indeed many people do, the epistemological question of the truth of an abstract model with the ontological question whether the model is real, i.e. whether whatever is represented by the model has somehow the same essence as the model. A model need not be real in this sense, or "essentially true", i.e. true in essence, or "
fully equivalent" as you put it, in order to be true simpliciter.
The OP concerns both questions, inevitably. Reality implies truth, if only because things are all true of themselves, but truth does't require and therefore doesn't imply reality. If the reverse was true, the notion of truth would be vacuous and people would be idiots talking about truth.
EB