If we look at the standard universe ("model") of the natural numbers, we can see that it is not the only one. There are other non-standard universes ("models") with non-standard numbers:
These non-standard universes ("models") have a subtle influence on the standard one. They effectively leave their Platonic shadows on it. That is how we can detect their existence:https://en.wikipedia.org/wiki/Non-stand ... arithmetic
In mathematical logic, a non-standard model of arithmetic is a model of first-order Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934).
The incompleteness theorems prove that there are true facts ("G") in the universe ("model") of the natural numbers that cannot be predicted. According to the completeness theorem, this is only possible because these otherwise true facts are false in alternative non-standard universes. Hence, there must exist such alternative non-standard universes:Existence. There are several methods that can be used to prove the existence of non-standard models of arithmetic.
From the compactness theorem
From the incompleteness theorems
From an ultraproduct
If some facts are not predictable in our physical universe, e.g. because of free will, then the structural similarity with the natural numbers implies that there exist non-standard physical universes. In religion terms, the existence of free will is equiconsistent with the existence of heaven and hell.The incompleteness theorems show that a particular sentence G, the Gödel sentence of Peano arithmetic, is neither provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic. However, G is true in the standard model of arithmetic, and therefore any model in which G is false must be a non-standard model.
Given sufficient structural similarity between the universe of the natural numbers and our physical universe, and if free will exists, then heaven and hell also exist. Therefore, heaven and hell are not just "illusory". The structural impact of the multiverse on the standard universe of natural numbers may very well also exist in the context of the physical universe.