An Interesting Failed Explanation for Existence

The problem with the solutions 3-10 for existence in The Biggest Big Question of All is they assume the laws of physics. But why were those laws selected for actuality? They do not solve the mystery.

Here is a 1-page summary of a more sustained attempt at an answer. 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. [Stenger]. 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 by some formal mathematical system. Call this system T. The question is: why does T exist?

Many formal systems can talk about themselves in some sense. Suppose T is a formal system that permits self-reference. Suppose it is equipped with the existential quantifier and the modal operator “necessity”: □. Then we want the minimal system that can assert that T necessarily exists. This will be T itself. So we have the first condition on T:

(1)

T expresses that T necessarily exists. Then, 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, the argument goes, existence is inherently relational. It is then sufficient that T talk about itself, since it is definitionally related to itself.

Ideally is there a unique maximal T. [] . If so, we 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.

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 relational existence, fails.[1] Even in a Platonic sense T does not exist any more than a theory which expresses it does not exist.

It is interesting to ask if there is a “proof” there is no structure-related explanation for existence.

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[1] 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. []