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).

Content does not seem to matter to existence

(1)  The existence of this sentence is logically inevitable.

Is so relative to itself in the context of its (necessarily) possible definition...

But isn’t the definition contingent?

What we require is that in every possible world it is possible that (1) exists. But it is probably better not to use possible-worlds semantics at all. Then, (it would have to be argued) this possibility might have an ontological status indistinguishable from actual “self-apparent” existence. […]

So why wouldn’t every self-referential sentence exist? Compare (1) to

(2)  This sentence does not exist.

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

Nuts.

Can you see any way around it?

Can the content of the theory be made relevant to its existence?

Can the content of the theory be made relevant to its existence?

If  so, we could have a hierarchy of theories based on how likely they are to exist. Such a hierarchy might be based on something like the following. Starting with the least likely to exist, consider T such that

(1) T ¢  Ø$T

I don’t know, hopefully there is no such T. If there were (and it was consistent) it would render the notion of existence within a theory irrelevant to the notion of actual existence. If there is no such T the notion of existence from within a theory is possible.

(2) T ¢  ($x)(x=x)

This T is the default degree of existence, because so many theories have this property. I don’t know if this is still valid when T is self-referential:

(3) T ¢  $T

This T would be still more likely to exist.

(4) T ¢  ƒ $T

This T would arguably be the most likely of all these theories to “exist”.

--Are there conditions stronger than (4)?

We want to rule out theories for which (2), but rule in theories for with (4). This is because we want to rule out the idea that all consistent mathematical structures exist. This would not be an explanation as to why any of them exist. Given that they all have the same existential status, why is it not the case that none of them exist?

One clue as to a way to proceed is that we want the why of its existence to be inextricably involved with its form (content). What does T have in (4) that it does not have in (2)? One thing is self-reference, but many sentences are self-referential. The salient property is condition (4), namely T stands in relation to the logical inevitability of its existence. Why should that matter? Because T’s existence is a necessary possibility.

(I have to remind myself: the reason we want condition (4) in the first place is that if we knew our universe was theory T, then it’s existence would be logically inevitable. The necessary existence of the universe would be a physical fact.)

What is a necessary possibility? Well, what is a possibility? Well, what does it mean to say such-and-such could be the case? In what ways does a possibility exist?

It seems plausible to say that a possibility exists the same way a number exists. Both of these are descriptions of reality.

Anyway, the first thing we do away with is possible-worlds semantics. Suppose we say í$T. It is not true that $T in some worlds and Ø$T in some disjoint set of worlds. What is true “in all possible worlds” is í$T. (Recall it is possible because we make no assumptions, so we do not assume nothingness is more natural than the existence of something.) Apparently

(5)  í$T  ®  ƒí$T

I don’t know if this respects the true-in-a-world and true-of-a-world distinction.

Then, the argument proceeds, the existence of the possibility of T is sufficient, in view of its peculiar definition, for it to bootstrap itself in to a valid notion of existence.

Reese

The Structure of Possibility

William L. Reese
SUNY of Albany

"For all we know logical possibility is the sufficient condition of ontological possibility."

"…The natural response is to say that in between it had remained an ontological possibility which lacked the conditions necessary for its actualization. Heisenberg made exactly that response to the question where an electron is between orbits. It retreats, he suggested, into possibility, and reactualizes in a different orbit."

Morato

Vittorio Morato

Other conceptions of sentences might be available according to which such

entities are necessarily abstract entities, that exist independently on the exis-

tence of their utterances and this because they exist already once a primitive

vocabulary and syntactic rules for a language are given. This position, however,

does not, by itself, exclude counter-examples like those presented above in the

case the primitive vocabulary or the formation rules are, in turn, contingently

existing entities or ontologically dependent on contingently existing entities8.

If we reason in strict analogy with what happens in the formal semantics for

modal logics, however, the basic elements of a language may be taken as al-

ready given \before" the various possible worlds enter the play; the existence

of a language (and hence of sentences) could then be seen as some sort of a

\transcendental condition" of the logic and therefore as independent on any

contingency represented by what is going on within worlds.

Towards a Materialist Explanation for Existence

It may be the title of this blog should be Towards a Materialist Explanation for Existence, but they don't let you change it.

Focusing the Arguments

In light of Jesse's critique I sharpened a few requirements for T.

The first question is how do we justify the existence of T? The second question is why is it unique in existing?

The strategy for justifying the existence of T is: a reinterpretation of possibility, and a notion of relational existence.

We do not use the possible-worlds semantics for possibility. A possibility’s is ontology is not given by “possible” worlds semantics. In what ways does a possibility exist? It might be the case that the existential status of a possibility has some third truth-value u instead of t or f. This might be made plausible with an example form quantum mechanics. It is not the case that either x-spin is up or else x-spin is down for some electron in a superposition. We know this because Y-spin up is possible. So the existence of the possibility of y-spin up is not reducible to the worlds in which the x-spin is up and the worlds in which the x-spin is down. This way the possibility of the existence of T is not reducible to those worlds in which it exists together with those worlds in which it does not exist (recall we wanted to avoid the latter).

The second move is to say some things exist in a relative way. The number two exists relative to the number three. T exists relative to its own logical inevitability.

The second question is why would just T exist and not every possible thing? We want to argue that T is the theory most likely to exist out of all mathematical theories.

Brian Tenneson suggests that what exists is the maximal structure P (more later...).