Any statement can exists. Even if it’s in contradiction to other statements. After all, would you deny that the statement “the set of all sets that don’t include itself” exists? Or “the soldier who shave’s all soldier’s that don’t shave themselves”? As statements they exist. But they can never come into BEING. They have a Potential of Being, infinitesimally approaching zero. So, the universe we live in arises (comes into being, gains persistence) from an infinite set of statements that don’t stand in any contradiction to themselves and others. Theoretically such a set should exist. Right?
Capacitator has correctly identified this as the attempt to come up with a Unifying Theory. Such a theory must explain not only our physical world but also our mental world. Most modern ontologies assume that information is embedded in a deterministic layer constrained to local causalities. This fundamental physical layer has residue of ideas expressed by Hume and other proponents of corpuscularism. Although today’s ontologies aren’t atomist, they still rely extensively on descriptive mechanisms of such models. And it’s understandable to some extent. It’s easier to picture particles than it is to picture probabilistic fields. What all these models rely on are static absolutes called dimensions, within which geometric objects governed by certain laws give rise to our macroscopic world. A String, a one dimensional entity with nothing but length, is an example of such a geometric object.
To begin with, it beckons the question how this geometry arose. Furthermore, a deterministic world constrained to local causalities has trouble explaining the phenomenon of consciousness and free will. The human experience is reduced to acts predetermined by genetic disposition and behavioral reinforcements a la Skinner. Ultimately, everything becomes reducible to external physical forces. Free will is often seen, even today, as a pipe dream of foolish idealists. Everyone shrugs their shoulders and say “Whatever”. Yet secretly, I suspect, we all reserve ourselves the illusion of choice, even the most materialistically inclined of us. In my mind, however, there’s no doubt that someone can suddenly act for no reason that can be attributed purely to external forces. But, in our modern physical world, entities act not on their own accord but because some force acts on them.
It is currently postulated that the evolution of the Universe was set in motion by a Big Bang, an explosion in Nothingness of immeasurable proportions. This is the First Cause, the reason we’re here. From Big Bang and onwards, it’s all clockwork. Or? Well, QM (quantum mechanics) suggest that it might not be so simple. Note, though, that on a pure quantum level, the Universe remains deterministic. It is only when we “elevate” this level to our macroscopic world that things get weird. I’m more troubled by this strong determinism in contemporary thinking than the idea some eternal geometry. After all, you could argue that a proposed informational space beckons the question where it came from. But, then we end up with infinite regression. We must accept that there are epistemological limits to what we can know.
However, it seems clear to me prima facie that Being and NotBeing is the most fundamental level of all, not geometric space. To facilitate our denotation, we use 0 to represent NotBeing and 1 Being. Now let us address what statements are. Statements are a set of words that are linked together in some given way. A statement’s meaning emerges not from the words in-and-of-themselves, but the relationships that they syntactically form. We can essentially treat statement as a system of words where the whole is greater than the sum of its parts (meaning is emergent). Even words themselves can be treated this way. “Dog” has no meaning as a word in-an-of-itself. It only has meaning has it relates to other entities in our life-world. It’s conceivable that “dog” may have different connotations in different dialects, even languages.
Now a dog may refer to an entity that has being (1), that exists as a physical manifestation. Through negation, we can also reference the abscence of such being (0). For example: “there is no dog such that…”. What about the meaning not of the word, but the entity that the word refers to, i.e. | DOG |? Well, even a dog is meaningless except in how it interacts with entities around it. The idea of meaning applies to so well abstract as physical things. It is in how they relate to one another that is important. Also, let it be noted that the level between physical and abstract may at times be extremely muddled. Voices heard by schizophrenics are certainly very real and frightening. It would be foolish to think we can distinguish the two worlds with any absolute certainty. This is why we today would rather speak of inter-subjectivity than unquestionable observables.
So, as we see, there are ENTITIES (meaningless in-and-of-themselves), RELATIONSHIPS (that form meaning) and POTENTIAL OF BEING. Let’s assume there are an eternal number of entities that have a potential to mean just about anything. This would mean that any entity can be linked to any other entity. Each such relationship has a Potential of Being. To distinguish this potential of being from physical being (the highest of all stages), we’ll call it a STRENGTH.
We can represent this (just to make it a bit easier) as a two dimensional table, each object listed once along the columns and once along the rows. Sort of like the tables used to indicated the distance between various cities in the world. Each entity is represented by a unique and infinite sequence of 0s and 1s. In each cell will write the STRENGTH that determines the level of connectivity between two entities. A strength of 0 would be written out using an infinite sequence of 0s and a strength of 1 an infinite sequence of 1s. We can now define the level of contradiction as being the case where two entities have two different STRENGTHS. Take, for example, the relationship between 0…001 and 0…100. In the column for 0…001 we go down to the row for 0…100 and find a strength of 0…000. In the column for 0…100, however, we find that the row 0…001 states a strength of 1…111. Clearly the level of contradiction has reached its extreme. No meaning can emerge from this relationship.
To define all possible combinations of ENTITIES and STRENGTHS, we will need an infinite number of tables. Each table represents the potential for an emergent physical Universe. A fully meaningless Universe would be the one where all cells are filled with 0…000. No entity relates to any other entity. It’s as if they didn’t exist to each other. Or, where every cell is filled with 1…111. Why? Because if all entities are connected, they become indistinguishable. What about a Universe with only 0.5 strengths (000…01…111)? In such a Universe, the ambiguity of relationships is at it’s maximum. In such a Universe, dog becomes related to any number of other things, all dispersed across all of space-time. Presumably, our physical Universe must be represented by a table where their are both strong and weak relationships, distributed somehow in an critical pattern. There may be an infinity of such patterns given that there are infinite number of tables. The question is how many of these tables will give rise to a stable yet dynamic enough Universe to result in higher consciousness.
Consciousness can be defined as some emergent structure that connects back to the most fundamental level of potentials. This would be why it is possible to imagine just about anything although we are constrained to act within the structures of some given limited (yet infinite) set of non-contradictory potentials.
So that’s it? We have this static Universe? Not quite, because however many entities we list, we can form a new one. How ever many! Even if that number is infinite. The trick? Cantor’s diagonal trickery. This is how it goes. Take an infinite sequence:
0…0001
0…0010
0…0011
0…0100
…
1…1111
Is there a number we haven’t listed? Let’s see.
Take the first binary digit of the first entity and change it to its opposite. In our case this would be 1 which becomes 0. To the same for the second binary digit of the second entity. And the third digit of the third entity. And so on and so on. In our case we get:
0…1100
This entity will differ from all the entities we have listed in at least one digit. So even if we list an infinite number of entities, we will always have missed one. Therefore, there will always be an entity that has an undetermined relationship to all other entities. And, as capacitator pointed out, such an entity might destabilize our entire Universe! Or part of it. This also means that new relationships will pop up for the whole continuum of eternity, no matter how pedantic God is. In fact, God could be said to be this continuum. Certainly, Cantor’s unlisted real numbers are as mysterious as the Creator Herself. No?
