λiber wrote: Tue Jul 07, 2026 8:33 pm
Thricegreat wrote: Tue Jul 07, 2026 5:34 pm
I think the physical world is just a part of the reality restricted by the laws of nature. So it is a subset of the reality. Mathematics is also a subset of the reality too. It is not the whole reality because obviously The One transcends it. What I wrote is that the specific "3"s are just seeing "3" in the mathematical world from different perspectives and with different lighting.
There I think I disagree; "three-ness" to me requires the satisfaction of the constraints that make the number 3 (i.e. we could think of them in terms of sets, such that if there's n apples, {a_1, a_2, a_3...a_n} relies on the set of natural numbers {1, 2, 3,...n}, which in turn are formalized in different ways like Peano arithmetic; rather than the number 3 being existent in a "world" other than ours, the set of natural numbers only needs to satisfy axioms in order to exist, if that makes sense...
There are some axioms of Peano axioms, but I think the essence is quite simple. Natural numbers mean a structure in which the minimum element exists and for every element its successor exists. Though there are some more rules to forbid things like loops. And if a structure satisfies them, it is unique
up to isomorphism.
I think n apples satisfy the relations of {1, ..., n} and therefore it
is {1, ..., n}. The set does not need to be exactly the same because what Peano axioms say is that the set of natural numbers is unique
up to isomorphism. For example the set defined by 0 = {}, n+1 = {n} is also the set of natural numbers.
About "Other world", I think there is only one world. The usage of mathematical "world", physical "world", &c. is just for convenience. I don't agree with mathematical Platonism in that matter. Also I think the mathematical world and the physical world have a lot of intersections. But I think those are all still subsets of the world.
Thricegreat wrote: Tue Jul 07, 2026 5:34 pm
I guess you are a pragmaticist. That is totally fine and I think it is an attractive position.
The words came out wrong and the example I used doesn't work as well, my apologies. I'm not a pragmatist/empiricist, I suppose I could be called a rationalist. I think of structures as prior to their instantiations but I don't think of these structures as existent beyond their instantiations, their instantiations are the result of the constraints that create them. For example, you could say a chair needs to:
1. Have the functionality of sitting
2. Flat/slightly angled seat
3. A back-rest (such that it is not a stool)
4. For one person to sit on
And as things come to exist, there is an inevitability of the instantiation of something that satisfies these constraints. With that, a stool or a sofa can be an "almost-chair", because "chairness" is a list of constraints and the argument over whether "chairness" is instantiated in stools and sofas becomes moot.
Sorry for the misunderstanding. But also to add something, I used the word pragmati
cist as a person who follows Charles Sanders Peirce's philosophy. Rather than empiricist.
So you are doing a genus-differentia definition of Aristotle here right? Also the position about universals.
If I have to say something, I could say. Like the circle argument. But I guess it will just repeat previous historical arguments on this matter.
By the way do you study linguistics? If you signed up, it would be good to introduce yourself on the introduction thread. At least that is what Amlux said.