It is unlikely content has anything to do with existence

Does Content Have Anything to do with Existence?

Out of whatever it is that could exist, what is the relationship between content (what it is that would exist) and the likelihood of it existing? Two motivations for considerating this question are its intrinsic interest and how it casts the possibility of an explanation for existence.

If something is inconsistent the probability of its existing is 0. (Bill Vallichela)

What is the likelihood of something that is consistent existing?

I mention four cases 1. the actual universe, 2. possibilities 3. the sentences of a mathematical structure 4. quantum possibilia

1. the actual universe

We want an explanation not only for the existence of something, but for the specific universe we inhabit. In this case one would have to argue that our universe is that unique entity that could not not exist.

It is logically inconsistent that the universe not exist. But that would seem to be contingent and not a priori true.

The dualist would say I am giving too much weight to logic.

2. possibilities

What is the likelihood of the existence of a pink elephant outside my door right now? Given sufficient other information about the actual universe, there is a 0 probability. But why couldn’t there be a universe in which there things are pretty much the same but there is a pink elephant standing outside “my door”. (I put “my door” in quotes because I don’t know if it refers to the same ontological entity or not: there are two doors, one in each universe).

It has been speculated that all consistent things exist (see e.g. Tegmark()). This would at least give the answer to our question that consistency is necessary and sufficient for existence. This may or may not be true, but it leaves open the question of why something should exist just because it is consistent.

3. sentences

What if mathematical structure ontologically exists? Such structure is codified by the sentences of a formal system.

Might a sentence exist relative to itself? For the self-referential case we have

(1)  This sentence exists.

(2)  This sentence does not exist.

To the extent (1) is true (2) is false, but they exist equally. So the truth of a sentence does not seem to affect its existence. Therefore, it would be hard to argue that the content of a sentence makes any difference to its existence. As a result they all have equal likelihood of existing.

This would seem to rule out one kind of explanation for existence. The explanation involves the following. The universe is ultimately just mathematical structure. In fact, the universe just is the maximal theory T which implies that it necessarily exists. (Then, if we knew our universe to be such theory T, the necessary existence of our universe would a physical fact, and we would have an explanation for existence.) Without going in to it further, the problem is already apparent. Existential statements in T are irrelevant to the existence of T, as witnessed by (1) and (2).

What if sentences are not self-referential? I don’t know.

4. Conclusion

It doesn’t look good for an explanation for existence. On the other hand, I don’t know of a proof there is no explanation for existence (for some reasonable general class of notions of proof).