[naasking]

From his comments:

> In my view, there is a way of viewing structuralism as undermining the success of the indispensibility argument, because no particular mathematical structure is ever indispensible, since it can be interpreted via alternative structure

I can see that, but on the other hand that alternative structure is equivalent up to isomorphism so you haven't really eliminated the structure. At best, you've probably shown that alternate theories that explain the same observations necessarily exist because our knowledge of reality's structure is incomplete and so we can't eliminate incorrect theories by the extra structure beyond the isomorphism. It does not at all undermine the idea that reality itself has some kind of structure.

[082349872349872]

Could you please briefly explain the indispensibility argument? (this being the first time I've run across the term; although if it's some philosophical thing I'm afraid I'm only interested in it as far as I'd be in the theological creation of the universe*)

My view of the relation between maths and physics is set out in https://news.ycombinator.com/item?id=39220159 , and because we go from physics to maths (f) and then back from maths to physics (f^-1), we can conjugate with any g,g^-1 pair, meaning that on the maths side we might as well mod out by isomorphics (only care about the partial order of equivalence classes of the preorder of structures)

(Similarly, we should find that we only care about the equivalence class [singular] of isomorphic realities [plural]?)

---

* this is not to say that I'm not interested; see https://news.ycombinator.com/item?id=39886966

Assuming a God who creates Creations, do we wind up with a best possible (principal) Creation? all possible (perhaps trivially so) Creations? if there is a set of Creations created, are they directed? Theologically, what happens if we have an infinite number of finite Creations, each an appropriate approximation, and we pass to their supremum?

[nyssos]

> Could you please briefly explain the indispensibility argument?

An extremely rough caricature:

- Scientific realists claim that we should believe the entities that are indispensable to our best scientific theories (electrons, for instance) exist.

- Mathematical entities are indispensable to our best scientific theories

- So scientific realists should be realists about mathematical entities.

[082349872349872]

Thanks. I guess I'm an instrumentalist then (due to having a strong pragmatist streak?) because I'm unconvinced that "existence" in this caricature even denotes.