Past a certain degree of complexity, there are lots of decisions about representing objects that are “ours, not reality’s”. For example, even if you represent the 10 particles as 10 vectors in 3D space, you still choose an origin, a scale, and a basis for 3D space, and all of these are arbitrary.
The 30-dimensional particle makes correct predictions of the behavior of the 10 particles. That should be enough.
Treaing a mathermatical formula as something that cranks out predictions is treating it as instrumentally, is treaing it unrealistically. But you cannot’ have coherent notion of modeling or representation if there is no real territory being modeled or represented.
To argue that all maths is representational, you either have to claim we are living in Tegmarks level IV, or you have to stretch the meaning of “representation” to meaninglessness. Kindly and Luke Sommers seem to be heading down the second route.
A correct 30D formula wll make correct predictions, Mathematical space also contains an infinity of formulations that are incorrect. Surely it is obvious that you can’t claim eveything in maths correctly models or predicts something in realiy.
Predicts something that could happen in reality (e.g. we’re not rejecting math with 2+2=4 apples just because I only have 3 apples in my kitchen), or
Is an abstraction of other mathematical ideas.
Do you claim that (2) is no longer modeling something in reality? It is arguably still predicting things about reality once you unpack all the layers of abstraction—hopefully at least it has consequences relevant to math that does model something.
Or do you think that I’ve missed a category in my description of math?
It is arguably still predicting things about reality once you unpack all the layers of abstraction
I don’t see what abstraction has to do with it. The Standard Model has about 18 parameters. Vary those, and it will mispredict. I don’t think all the infinity of incorrect variations of the SM are more abstract.
Past a certain degree of complexity, there are lots of decisions about representing objects that are “ours, not reality’s”. For example, even if you represent the 10 particles as 10 vectors in 3D space, you still choose an origin, a scale, and a basis for 3D space, and all of these are arbitrary.
The 30-dimensional particle makes correct predictions of the behavior of the 10 particles. That should be enough.
Treaing a mathermatical formula as something that cranks out predictions is treating it as instrumentally, is treaing it unrealistically. But you cannot’ have coherent notion of modeling or representation if there is no real territory being modeled or represented.
To argue that all maths is representational, you either have to claim we are living in Tegmarks level IV, or you have to stretch the meaning of “representation” to meaninglessness. Kindly and Luke Sommers seem to be heading down the second route.
A correct 30D formula wll make correct predictions, Mathematical space also contains an infinity of formulations that are incorrect. Surely it is obvious that you can’t claim eveything in maths correctly models or predicts something in realiy.
I’d say that math either
Predicts something that could happen in reality (e.g. we’re not rejecting math with 2+2=4 apples just because I only have 3 apples in my kitchen), or
Is an abstraction of other mathematical ideas.
Do you claim that (2) is no longer modeling something in reality? It is arguably still predicting things about reality once you unpack all the layers of abstraction—hopefully at least it has consequences relevant to math that does model something.
Or do you think that I’ve missed a category in my description of math?
I don’t see what abstraction has to do with it. The Standard Model has about 18 parameters. Vary those, and it will mispredict. I don’t think all the infinity of incorrect variations of the SM are more abstract.