Why there is something rather than nothing

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 - this is the set-theoretic world described by set theory.



Set theory 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-theoretic world/mathematics is the whole reality, because it includes all possible objects - from the simplest to the most complex.