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Saturday, December 11, 2010

An Interesting Failed Attempt at an Explanation for Existence

The question is why does the universe exist?

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 and the necessity modal operator □. Then we want (for reasons given below) the minimal system that entails that T necessarily exists. This will be T itself. So we have the first condition on T:

(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]

Tuesday, December 7, 2010

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.


[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. []

Monday, October 18, 2010

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).

Friday, October 15, 2010

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?

Thursday, October 14, 2010

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.

Tuesday, October 12, 2010

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."

Monday, October 11, 2010

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.

Thursday, October 7, 2010

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...).

Wednesday, October 6, 2010

Inevitable Existence by Jesse Folsom

The search for a unified theory of everything is hardly a new idea. None have succeeded in formulating such a theory as yet, at least one for which there is any sort of consensus agreement, and even if they did, at least one problem would remain unanswered. Such a theory might explain why everything is as it is, but it would still leave unanswered why there is anything at all. From a materialist perspective, it would seem that nothing existing would be far simpler and more sensible than all the complexities and interactions involved with something existing. Yet, the universe obviously exists.

What if the greater likelihood of nothing were illusory? What if the existence of something was not only more likely, but inevitable? Paul Merriam is attempting to formulate a theory which implies its own necessary existence without reference to any conditional statement. It's inevitability must, therefore, be totally self sufficient, proved without doubt within the statement itself, in the context of very bare predicate logic.

The difficulties of formulating such a theory are daunting enough in themselves, but the creation of such a theory is insufficient. Merriam must then attempt to correlate the structure of the theory to the physical universe. If this can be accomplished, a strong argument can be made that the theory is representative of the universe as a whole, but Merriam plans to go beyond even this. His claim is that the universe is actually pure mathematical structure, and that the theory is not just a representation of the universe, but is the universe itself. This is all towards the goal of a materialist explanation of existence.

Thus, an outline of his argument is:

  1. There exists a theory T, such that T's existence is shown to be logically inevitable within the structure of T.
  2. Some version of T, which we will label Tn, has a structure which reflects the structure of the universe itself.The universe is actually a set of mathematical relationships; it is pure structure, with all appearances of substance arising from this structure.The structure of Tn, being identical to that of the universe, not only represents the universe, but, because of the universe's nature, is the universe itself.Since the existence of T is logically inevitable, the universe itself, being T, is logically inevitable.





This idea is tempting, but is riddled with implied difficulties and even impossibilities. The existence of any such theory as T, which by implication necessitates its own existence in an unconditional fashion, is doubtful. It is easy enough to make a theory which states its own necessary existence, but there is no way to verify it. The basic structure of such a theory would be:

              T: Theory T necessarily exists.

Given that it contains no reference to any outside structure, there is simply no way to verify it. Its veracity is therefore indeterminate; it is not even worthy of being called “wrong”. This is why the theory cannot simply state its own logical inevitability; it must imply it through more verifiable assertions.

Merriam argues that since, according to part 3 of his argument above, all existence is relational anyway, T could exist relationally without any more “absolute” existence. Indeed, he goes so far as to say that it could exist in relation to itself. So long as it is possible that it exists, its relationship to itself could allow it to “bootstrap” itself into existence. Leaving aside whether it is even possible that such a thing exists, this would imply that anything which could possibly exist, does exist, since they would exist in relationship to itself.

An imperfect example is an imagined pink elephant towering over an imagined blue mouse. These two entities have a relationship to each other, he claims. Things must exist to relate to other things. But, of course, what exists in this case is actually a mental process, not an actual pink elephant and blue mouse. The pink elephant and blue mouse do not actually exist. This, in itself, should do away with the idea of purely relational existence, but in truth, the status of T, in this sense, is even worse. It is not relating to another object, even an imaginary object, just itself. Merriam says it exists “in relation to itself”, a circular and rather meaningless concept, and would mean that anything conceivable exists, which is clearly not true.

This brings us to a related difficulty. A theory is by its nature a mental object, residing within one or more consciousnesses. People formulate theories to represent some aspect of reality. But in order for this theory to accomplish its stated goal, showing the inevitability of the universe itself, the theory must not merely represent the universe. It must be the universe. Even if true, this implies that the universe is a mental object, and must have a consciousness to reside in. Given that the universe, apparently, predated any embodied consciousnesses, this places the materialist ends of this formulation in peril.






Another problem is that, even if the structure of the universe is purely relational, this leaves one big question: What does the universe relate to? If everything only exists in terms of relationships to other objects, what does the totality relate to to motivate its own existence? Saying it exists in relation to itself is meaningless, and further sounds rather akin to absolute existence. And what is the universe except the sum of its constituents?

Another problem is that a theory is static. A theory, once changed, is a different theory. Therefore, any theory of the universe cannot really be about how the universe is in all its detail, but only its regularities, those aspects which are unchanging. The differences within the universe from moment to moment, much less across eons of time, prove that the structure within those regularities is highly variable. Thus, this still leaves the question open as to why things are as they are. Why do humans exist, for instance. Modern experiments seem to show that even the quantity of matter in the universe can change, so this is not a regularity. So even if this theory were found, the question would remain why anything but a series of regularities would exist. Perhaps because regularities are only meaningful because they regulate the behavior of something? Even with this possible explanation, the deep logical quandaries of such a theory begin to be revealed.

Another issue, which Merriam freely acknowledges, is that a universe of pure structure disregards such phenomena as qualia. Such features, which are ineffable by nature, cannot be expressed in any symbolic language. As such, they could not be expressed in the symbolic language of the theory, nor even truly addressed within it. Yet even time is qualia-like in this respect, and a theory of the universe that doesn't explain time is a poor theory indeed.

What really dooms this theory, however, is how inconceivable it is to even get it off the ground. While Merriam denies this, while it is relatively trivial to write a theory that implies its own existence, implying necessary existence is an altogether different matter. Establishing necessary existence in the first place is likely impossible. If one could establish the logically inevitable existence of anything, one could then prove the necessary existence of at least some universe, such that the thing would exist.











Well, you could, except for an even deeper problem with this formulation, which involves the nature of logic itself. Merriam and many other modern scientists and mathematicians seem to think that logic and mathematics exist somehow independent of the universe, almost as if they were some sorts of Platonic ideals. But the truth of the matter is that logic arises as an epiphenomenon of the definitions we give symbolic language. That this cannot be not this arises from the definition of the word “this”. In other words, trying to claim some sort of truth-value to logic outside of semantics results in a circular argument. The logical properties of “this” are inherent to the definition of “this”. It is just a word, a collection of sounds with an arbitrarily assigned meaning. The symbols of formal logic are not words, but their meaning is arbitrarily assigned, nonetheless. If logic arises from language, then how can it be used to construct any universe, much less a logically inevitable one, in the absence of such symbolic thinking?

Thursday, September 23, 2010

State of the Art of the Attempt

Towards a Rational Explanation for Existence

Is it possible to give a rational explanation for existence? Below is a web of suppositions which, if borne out, would allow us to claim to have a rational explanation for existence. It is interesting to see how far we can get with the project.

Some considerations

Why does anything at all exist? This question already makes an assumption. It just assumes that nothingness is more warranted than the existence of something. But what justifies this assumption? Without making any assumptions at all what we can reasonably expect is that something could exist. Indeed it could turn out to be the case that the existence of some particular thing is logically inevitable, while nothingness is not.

Hypothesis: what ultimately exists is pure structure (the relations between mathematical objects...)

I will not go in to this hypothesis except to say it is consistent with materialism and inconsistent with dualism.

By the hypothesis, we are after some mathematical structure that finds its own existence to be logically inevitable. It is sufficient to consider the case where the mathematical object is the web of sentences of some formal system T. Beyond that we want a theory that, in some sense, asserts it’s own inevitability. In other words, the mathematical theory T is such that

(1)  T® á$T

But even supposing we could make sense of this and find such a T, this condition is not enough to guarantee actual existence. All we can assert is that there could be some mathematical structure, such as T, that derives its own logical inevitability. But all we really know is that the existence of T is possible. In the many-worlds semantics of possibility this leads to two cases, worlds W for which T exists, and the disjoint worlds V where T does not exist.

We want to motivate the existence of T. In the worlds W where T exists, there is only the issue of finding a (the) T that satisfies (1). In the possible worlds V however, it is not obvious how to motivate existence. In these worlds T does not exist, so it is not around to assert anything about itself. In this case there is no way to get existence off the ground, so to speak.

Happily, there may be at least four ways out of this conclusion.

The first way out is to argue that the possible-worlds semantics of possibility is misleading here. In possible worlds semantics there are some worlds W in which T exists and some V where it does not. But this contains the trick of forcing an either-or decision upon us about T’s existence where it may be inappropriate. We do not want  or else . What we want is to consider the possible worlds in which it is possible that T exists. It is true that in every possible world there is the possibility of T. If we give the notion of possibility this status, it might be enough, in view of condition (1), to allow the theory to bootstrap itself into existence.

Returning to the possible worlds V and W, a second way out is to argue that, for the possible worlds V, a sentence t may not exist[1], but t’s relations to other things might nevertheless exist. Thus there are second-order properties of t that claim existence in spite of t’s own non-existence.

A third way out of the conclusion above, slightly different from the second, is to first show that T exists in the sense of T. Then, the argument would go, it is sufficient that T exists in the sense of T, because this existing-in-the-sense-of is all we need for a kind of absolute existence. But it is not obvious what it means to exist in the sense of something that only possibly exists…

A fourth way out is to argue that all notions of existence are relative, and so there is no problem for the relative kind of existence in the third way out (above) because the existence predicate in T is implicitly relative, and absolute existence has really just been relative existence the whole time, etc.

My own preference is for argument (1) combined with argument (3).

Here is an attempt to lay bare the argument:

1)  2 + 2 = 4 is in some sense true whether or not the universe or anything at all exists. The interrelatedness of the definitions of 2, +, 4, and = in some sense precedes the question of existence.

2)  Now define a consistent theory T that contains the statement:

“The existence of this statement is logically inevitable.”

(How this might be implemented is discussed below.)

3)  T is actual relative to itself, it is “reliable” relative to itself, and is necessarily possible   

4)  In some important sense, existence does not recognize the difference between T’s self-apparent existence and our actual existence. They are equally valid. Perhaps our actual existence is a kind of self-apparentness.

5) The universe is T (and does not merely represent T), and it admits a rational explanation for its existence, namely 1-4.


Argument (1) Combined with Argument (3)

We want to argue T’s self-apparent existence is sufficient because we can define T. We use the supposition:

(2) the essence of structures is prior to existence

I tried to make this plausible in “1)” in the first section.

Infinite numbers are definable (as in set theory), even though the physical universe may be only finite. Nevertheless we often “prove the existence” of this or that infinite number (such as a set). In this case we might be able to say that infinite numbers exist relative to the theory that defined it (e.g. set theory).

Then,

(3)  if (1) is satisfied T (necessarily) exists relative to itself.

Now, it would be argued, this relative kind of existence is what we really mean by “existence”. This would also apply to actual existence. The collection of things that exist forms an equivalence class. 

If relative existence is the only kind of existence there is, (3) is sufficient for actual existence.

What if things have “intrinsic” or “absolute” existence? In this case (3) would seem to be insufficient to generate actual existence… But by the hypothesis, the universe is ultimately mathematical structure. Can’t parts of a mathematical structure exist relative to each other? Suppose we say

(4) the number 2 exists relative to the number 3

One objection might be that it may be true, but presupposes absolute existence. But how do you know? If absolute existence is, in fact, relative existence, we would not know the difference.

Another objection could be that this is a false option, and (4) is neither true nor false. But it is either a sentence of the system that

(5)   

or else it is not.


In the system T we want something like

(6) 

This says if there is an x then there also exists (relative to the formal system) the assertion that there is an x. This is plausible since x is itself an assertion of the formal system.


To pick up where we left off with (9), we can say that relative to the definition, the theory necessarily exists. So relative to the definition, the definition itself exists, that is because the theory asserts it’s own logical inevitability. The interrelatedness of the definitions generates its own necessary existence, since the definitions are, in fact, so interrelated. Here is something (the interrelatedness of the definitions) from nothing (what the definitions are definitions of). The (necessary) possibility of such a definition is all we need.

Then we would use the supposition

(9)  absolute existence is relational existence

to conclude that T has an absolute existence.

(One might ask: where did the possibility for something being more logically inevitable than nothing come from? An answer to this question must lie outside of our capacity to reason (such as qualia do…), since it is asking for a reasonable explanation of reason, i.e. it presumes reason.

Now suppose we have a candidate theory T. T finds itself to be logically inevitable (and T does not find nothingness to be logically inevitable). According to the hypothesis above, T does not merely represent the universe, it is the universe. If we chose to say that T has physical existence, then it would be a physical circumstance that the universe is logically inevitable.

Finally, if we knew T is our actual universe, we would be justified in claiming to have a rational explanation for existence.

Finding T

We take (1) as an axiom. It is a reasonable, though probably not the best way to express logical inevitability. To express (1), the deductive system T must contain 1st-order predicate calculus, equality and the modal operators. We make no assumption about models for T. Let T1 be the collection of sentences closed under implication and use of the rules of inference. Now construct a model, in the sense of model theory, M2, such that the universe of M2 is exactly the collection of sentences T1. Let T2 be the theory of M2. Construct a model M3 out of T2 in the same way, and continue this process indefinitely.

Conjecture: this process reaches a fixed-point theory TFP

Claim: TFP satisfies (1)

The idea is that TFP is our universe, and in being so asserts its own logical inevitability.




Somewhere in there it should be added that the reason we want an ultimate explanation is that existence cannot be contingent on anything—is that if the explanation uses any assumptions we can always ask why state of affairs described by that assumption obtains.


Paul


Thanks John Mazetier and especially Jesse Folsom.


[1] Recall that the sentences are what exists.