Sets or classes and numbers and functions were the abstract objects discussed in this video but here in my blog post I’ll specifically address numbers. Looking at it from a certain perspective it makes sense but this point of view leaves out the role of underlying reality in what deems the actual. Now, I’m sure Quine must have addressed this in some other video or text at some point. But, for this post I’ll just address explicitly what’s discussed in the video.
There may be something akin to what we call numbers and they may exist as patterns or fundamental units in reality. And yes they are abstract because two-dimensional objects don’t exist. There’s no perfect two-dimensional plane in reality. It’s conceptual and formed of images that have to be shown but can’t be. We may try to represent it in reality but unless they really do exist in the underlying reality, they don’t exist. We can try but the representation itself will be constructed out of more stuff than the pure imaginary form which cannot be shown. So, even if we perceive patterns or units or bits through sight, it’s an illusion because we’re not seeing the underlying reality. But, that doesn’t mean that they don’t exist in the realm of objects-in-themselves devoid of the properties we give them because those objects don’t have properties.
So, to summarize: All perception is Thought. And Thought is two-dimensional so it doesn’t exist. All numbers lie in the realm of abstracta and so they don’t exist in the physical world or even the perceivable world, at least not in any form we have keenly observed and thus discovered so far. And even if they exist in perception then they are illusions because the underlying reality doesn’t have abstracta as properties. And this is because Thought precedes properties and is two-dimensional. All concepts whether it be numbers or forms can be reduced to Thought.
I have once said that there is something to be considered in the realm of the metaphysical when trying to uncover the nature of numbers. I said that you have to go between and around them to see what they’re made of. I will post when I’ve made progress in that direction. Cheers, awesome upload as usual!
EDIT: These mathematical entities are Thought which itself might be reducible to some chemical reactions occurring in the brain. These reactions might be a process in matter. So ultimately the abstract objects might be given substance in the sense that they do need to materialize as Thought. So, Quine might be right after all. This could mean that Thought is just a mechanism like all the other mechanistic reactions taking place in the universe. So, one may not have to make a distinction between Thought and mechanism. Of course, all thoughts are abstract and if they can be reduced to matter or a process in matter that gives rise to them, then we might be living in a purely materialistic universe. The only true duality could be the difference in substrate and what a process in it gives rise to when concerning the living organisms. That said I still don’t know if mind and Consciousness are the same. My analysis tells me they’re different but that could just be a misunderstanding in perceiving Language or feeling the underlying reality or both. I am of a singular focus that Language and the ultimate/underlying reality are connected in some fundamental way.