If you’re using math to model something, or even could so use it, that is sufficient for it to have a correspondent for purposes of the correspondence theory of truth.
But that is not suffcient to show that all maths models.
… okay, you were confusing before, but now you’re exceptionally confusing. You’re saying that the standard model of particle physics is an example of math that doesn’t model anything?
Well, it doesn’t model our universe. And the Standard Model is awfully complicated for someone to build a condensed matter system implementing a randomized variant of it. But it’s still a quantum mechanical system, so I wouldn’t bet strongly against it.
And of course if someone decided for some reason to run a quantum simulation using this H-sm-random, then anything you mathematically proved about H-sm-random would be proved about the results of that simulation. The correspondence would be there between the symbols you put in and the symbols you got back, by way of the process used to generate those outputs. It just would be modeling something less cosmically grand than the universe itself, just stuff going on inside a computer. It wouldn’t be worth while to do… but it still corresponds to a relationship that would hold if you were dumb enough to go out of your way to bring it about.
The thing about the correspondence theory of truth is that once something has been reached as corresponding to something and thus being eligible to be true, it serves as a stepping-stone to other things. You don’t need to work your way all the way down to ‘ground floor’ in one leap. You’re allowed to take general cases, not all of which need to be instantiated. Correspondence to patterns instead of instances is a thing.
And of course if someone decided for some reason to run a quantum simulation using this H-sm-random, the anything you mathematically proved about H-sm-random would be proved about the results of that simulation.
Which, as in your other examples, is case of a model modeling a model. You can build something physical
that simulates a universe where electrons have twice the mass, and you can predict the virtual behaviour
of the simulation with an SM where the electron mass paramter is doubled, but the simulation will be made
of electrons with standard mass.
The correspondence would be there between the symbols you put in and the symbols you got back, by way of the process used to generate those outputs. It just would be modeling something less cosmically grand than the universe itself, just stuff going on inside a computer.
It wouldn’t be modeliing reality.
The thing about the correspondence theory of truth
..is that it is a poor fit for mathematical truth. You are making mathetmatical theorems correspondnce-true
by giving them something artificial to correspond to. Before the creation of a simulaiton at time T, there
is nothing for them to correspond to.This is a mismatch with the intuition that mathematical truths are timelessly true.
is that once something has been reached as corresponding to something and thus being eligible to be true, it serves as a stepping-stone to other things. You don’t need to work your way all the way down to ‘ground floor’ in one leap. You’re allowed to take general cases, not all of which need to be instantiated. Correspondence to patterns instead of instances is a thing.
You can gerrymander CToT into something that works, however inelegantly, for maths, or you can abandon it in favour something that doesn’t need gerrymandering.
But that is not suffcient to show that all maths models.
Well, you can use math for something other than modeling, sure. Can you give a more concrete example of some math you claim doesn’t model anything?
The Standard Model with its 18 parameters set to random values.
… okay, you were confusing before, but now you’re exceptionally confusing. You’re saying that the standard model of particle physics is an example of math that doesn’t model anything?
No, I am saying a mutated, deviant form doens’t model anything -- “with its 18 parameters set to random values”.
Well, it doesn’t model our universe. And the Standard Model is awfully complicated for someone to build a condensed matter system implementing a randomized variant of it. But it’s still a quantum mechanical system, so I wouldn’t bet strongly against it.
And of course if someone decided for some reason to run a quantum simulation using this H-sm-random, then anything you mathematically proved about H-sm-random would be proved about the results of that simulation. The correspondence would be there between the symbols you put in and the symbols you got back, by way of the process used to generate those outputs. It just would be modeling something less cosmically grand than the universe itself, just stuff going on inside a computer. It wouldn’t be worth while to do… but it still corresponds to a relationship that would hold if you were dumb enough to go out of your way to bring it about.
The thing about the correspondence theory of truth is that once something has been reached as corresponding to something and thus being eligible to be true, it serves as a stepping-stone to other things. You don’t need to work your way all the way down to ‘ground floor’ in one leap. You’re allowed to take general cases, not all of which need to be instantiated. Correspondence to patterns instead of instances is a thing.
Which, as in your other examples, is case of a model modeling a model. You can build something physical that simulates a universe where electrons have twice the mass, and you can predict the virtual behaviour of the simulation with an SM where the electron mass paramter is doubled, but the simulation will be made of electrons with standard mass.
It wouldn’t be modeliing reality.
..is that it is a poor fit for mathematical truth. You are making mathetmatical theorems correspondnce-true by giving them something artificial to correspond to. Before the creation of a simulaiton at time T, there is nothing for them to correspond to.This is a mismatch with the intuition that mathematical truths are timelessly true.
You can gerrymander CToT into something that works, however inelegantly, for maths, or you can abandon it in favour something that doesn’t need gerrymandering.
It’s not gerrymandering. What you are doing is gerrymandering. Picking and choosing which parts of the territory we are and aren’t allowed to model.
The territory includes the map.
But not as a map. Maphood is in the eye of the beholder.
The eye of the beholder is part of the territory too. It is a matter of fact that it takes that part of the territory to be a map.
Maphood is still not a matter of fact about maps.