Again, your definition of what exists is too narrow. — Wayfarer

I disagree with describing it "narrow". It is parsimonious, but leaves nothing unaccounted for. It's reasonable to methodologically treat abstractions as independent existents, but that utility does not depend on an ontological commitment.

Emphasis on the qualifier "independent", because this parsimonious ontology doesn't deny the existence of triangles and right angles, it just denies that they exist independently of the things that have those properties. The angles between the walls of my bedroom are 90 degrees - and this angle does actually exist, just not independently of the walls. Many other things have this exact same property, and that's why "having a 90 degree angle" is a universal.

My issue is that there's no good reason to assume "90 degree angle" exists independent of the things that have it. Sure, we can think abstractly about this property without considering the things that have it, and that's a product of our powers of abstraction.

If you don't accept my premise about parsimony (that we should minimize the ontological furniture), then you are free to assume "90 degree angle" actually is an independently existing Platonic entity. But you would need to account for the relation between this entity and the items that exhibit it.You also need to distinguish between abstractions that actually exist (like "90 degree angle") and fictions that exist only within minds (single minds, or even many minds) - fictions like Spider-Man.

I disagree with describing it "narrow". It is parsimonious, but leaves nothing unaccounted for. It's reasonable to methodologically treat abstractions as independent existents, but that utility does not depend on an ontological commitment.

Emphasis on the qualifier "independent", because this parsimonious ontology doesn't deny the existence of triangles and right angles, it just denies that they exist independently of the things that have those properties. The angles between the walls of my bedroom are 90 degrees - and this angle does actually exist, just not independently of the walls. Many other things have this exact same property, and that's why "having a 90 degree angle" is a universal.

My issue is that there's no good reason to assume "90 degree angle" exists independent of the things that have it. Sure, we can think abstractly about this property without considering the things that have it, and that's a product of our powers of abstraction.

That’s right. The issue is this should be self-evident and the problem is people just don’t understand the words. If they did it would be clear “abstraction” is a form of interpretation or understanding, and as such it requires an interpreter and grounding against any information will be understood.

I can look at a mountain and see a triangle, interpret it in terms of spatial relations and then abstract an idea of an angle from it. Someone else can interpret it as “no parking allowed here”. In any case without an interpreter to form a meaning or an idea, any information is just an arrangement of physical stuff, and there is no triangle out there, there is no angle, no mountain. There is only “stuff”, some of which we choose to isolate or abstract as a separate thing and put a label on it.


On the other hand, there are principles like path of the least resistance, Pythagoras' theorem, or inverse square law that are kind of opposing field / particle physics, in a sense that it is not quite clear what comes first, which laws, principles or physical properties are primary and which just a consequence. This sort of ontological dilemma, in contrast, is worth of discussion.

That’s right. The issue is this should be self-evident and the problem is people just don’t understand the words. — Zelebg

I think it's a product of the pedagogy of mathematics, physics, logic and some related fields. We're taught that triangles and laws of physics (expressed as equations) exist. This leads us to speak of them that way, and this leads to treating them as ontic, and not just as a manner of speaking.

From the point of view of a mathematician or physicist doing his normal work, it doesn't matter. It's convenient to treat them as existing, as a methodological principle. But when mathematician's and physicists conflate the methodological semantics with ontological claims, they've gone too far.