Litewave wrote:Absolute nothingness is probably not possible because if there was absolutely nothing then there would be the fact (truth, axiom) that there is absolutely nothing, but this fact would be something, resulting in a contradiction. So it seems that there is necessarily something, but what is it? It might be, for example, the simplest possible object, which we can imagine as an object that has nothing inside it (no parts). Or it might be some more complex object, which has other objects inside it, but this more complex object presupposes the existence of simpler objects (which are inside it) and ultimately also of the simplest object (the one that has nothing inside it). So the simplest object will exist in any case and therefore necessarily. This simplest object is in set theory called the empty set – an object that has nothing inside it. It is simultaneously the fact (that expresses) that there is nothing inside something but this does not lead to a contradiction because this fact is exactly this something (something with nothing inside it).
Now that we have found that the empty set necessarily exists we can ask if there is also something else. This something else would have to be outside the empty set (because inside the empty set is nothing). If we assumed that there is nothing else outside the empty set we would get a contradiction again, because there would be the fact that there is nothing else outside the empty set but this fact would be something else and it would also be outside the empty set (because inside the empty set is nothing). Therefore there is necessarily something else outside the empty set and this would have to be some more complex object. This more complex object might be the second simplest object, that is the set that only has the empty set inside, or an even more complex object but the second simplest object would exist in any case and therefore necessarily. So we already have two necessarily existing objects – the empty set and the set that only contains the empty set – and next we could ask if there is also something else than these two objects. In this way we would come to the conclusion that there must be an infinite number of sets whose basic building block is the empty set.
Set theory, built up from the empty set, is widely regarded as a foundation of mathematics, which means that these sets define all known mathematical truths. So it seems that not only does something necessarily exist but so do numbers, spaces and other mathematical objects. And I would also say that the set theoretical world/mathematics is the whole reality, because it includes all possible objects - from the simplest to the most complex.
This is the seminal post. There have been many others, all probing the question: "Why is there something rather than nothing". As for me, I've come to believe that if there really were nothing, then the "fact" of that nothingness would exist. I believe that facts don't exist in a vacuum, they must be archived. And, regardless of how such facts are archived, some sort of physically is necessarily implied.
So, I agree with the "seminal post" that "nothingness" is inherently contradictory. I also like the suggestion that set theory might possibly build-up reality, and actually be it's framework. But, set theory is a risky "framework" to trust as reality's guarantor. The most dire pitfall is the Mathematician Kurt Godel's proof that there must always be something about the mathematics-of-reality which can never be proved by the mathematics-of-reality.
So, if reality is mathematical, then there must be a meta-reality, such that certain unprovable aspects of reality can therefore be proved by a meta-logic. And, the same holds true of meta-reality, as well. It, too must have a meta-meta-reality, so as to guarantee it's own logic. It's pretty clear that we're dealing with an infinite hierarchy-of-realities, with us at the bottom.
Just imagine what this means. In order for our reality to exist, an infinity of realities are stacked overhead. You know, I really struggle to imagine this. I once saw a cartoon about Jack and the Beanstalk. The "beanstalk" wobbled thin, ever upward into the clouds. This is what I think of when I contemplate such an infinity-of-realities.
A "beanstalk" which never reaches the giant's lair, it just goes on and on, ever upward. And all of this so we might exist. I know that, just because I find an infinite-hierarchy-of-realities unconscionable, that's no reason for it not to exist. But, just consider that, because we exist other beings might therefore exist in a reality which owes it's existence to us. That's heavy, real heavy.
I don't trust infinities, being unimaginable, they ultimately contribute nothing to our understanding. To say that there is something, rather than nothing just because an infinity of 'somethings" make it so tells me nothing about the "somethings' all around me. And what about those "other beings"? We'd never be able to meet them. We're all contained within a mathematical framework, which separates us from all the other "frameworks".
The dizzying implication that our reality is mathematical, in nature is just too hard for me to accept. But, the suggestion that our reality is mathematical is too seductive for me to deny. Frankly, I'm stymied. I believe, balls-to-bones that reality must be mathematical, in nature. But, I just can't swallow the implications. This debate goes on inside my head, and I'm weary of it. What to do, what to do...
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