Shermer gives 8 candidate explanations in “The Biggest Big Question of All” [Online]. The problem with these candidate explanations is they each assume the laws of physics. But the question is: why were those laws selected for actuality? Shermer’s candidate explanations do not provide an answer. Here is a 2-page summary of another attempt at an explanation for existence. However, it, too, fails.
There are regularities in the behavior of matter. But what is matter? It is consistent with the regularities that matter is ultimately mathematical structure. We take this as a working hypothesis.
Hypothesis: the universe is ultimately mathematical structure.
Note this hypothesis is consistent with materialism but inconsistent with dualism.
The logical place to start is with the question: why is there something rather than nothing? The counter-move is to note this question just assumes that nothing is more natural (or makes fewer assumptions) than the existence of something. []. But is that assumption justified? Might it not turn out to be the case that the existence of something is more “natural” than nothing?
Because of the hypothesis, it is sufficient to consider the case where the universe is definable as some formal mathematical system. Call this system T. The question is: why does T exist?
Many formal systems can express things about themselves. Suppose T is a formal system that permits self-reference. Suppose it is equipped with the existential quantifier
(1) T T
T entails that T necessarily exists.[1] The point is this. If the actual physical universe were T, it would be logically necessary that T exists. T does not merely represent the universe, it is the universe. If T satisfies (1) it would be a physical fact that the universe is logically necessary. If we knew our universe to be T, we would have an explanation for existence.
But why would T exist in the first place? Perhaps existence is inherently relational. The number 2 exists relative to the number 4, and this chair exists relative to this table.[2] Assuming this notion could be worked out, it would be sufficient that T talk about itself, since it is definitionally related to itself.
Ideally is there a unique maximal T. [Tenneson] . If so, one could pursue the thesis that T’s being related to its own necessary existence would make it the “most likely” structure to exist, out of all possible mathematical structures. In principle one could compare the structure T with the observed physical laws of the universe and get confirmation or refutation the universe is T.
The problem is this. Consider the two sentences:
(2) This sentence exists.
and
(3) This sentence does not exist.
Evidently, the two sentences (2) and (3) exist equally. But (2) is true to the extent (3) is false. So the content of a sentence does not have anything to do with its existence.
The upshot is that the program of justifying the existence of T, as being the unique theory that “bootstraps” itself into existence, fails.[3] Even in a Platonic sense T does not exist any more than a theory which expresses it does not exist.
Starting from the example above, it is interesting to ask what is the most general setting for which one could give a “proof” there is no structure-related explanation for existence.
[1] In fact T should imply that the existence of T is logically inevitable, which is an even stronger statement then that T necessarily exists.
[2] Does the collection of things that exist form an equivalence class?
[3] There might be a loophole in the theorem that if T permits self-reference and has strong negation then it cannot contain a truth predicate, but I don’t know. [Tarski]
