The purpose of this blog is solicit help in solving the deepest question: that of a rational explanation for existence. The philosophy relating to existence needs to be clarified and a particular mathematical theory needs to be identified.
What we are after is a rational explanation for existence. But which explanation is it?
Is there a theory T that appears to itself to exist? By “appears to itself” I mean T as a model satisfies T as a theory. If so, we would have a rational explanation for existence at hand.
We can use T’s apparent existence because all that is required of T is that it appear to inevitably exist relative to the elements of the base space. The appearance is ontologically real in the same sense that it has mathematical existence—it cannot tell the difference between existing in the sense of T or not existing at all. In some sense T would be more inevitable than non-existence.
For a first guess at what T is take predicate calculus. Call this theory T1. It is a deductive system that has no axioms, functions or constants. What is the theory of T1, call it T2, that T1 is a model of? T2 is the theory of the Lindenbaum-Tarski algebra of T1. I don’t know if T3 is different from T2. Anyway, continue this process until it reaches some fixed point, call it Tfp. Then Tfp appears to itself to exist as itself, and intrinsically contains the explanation for its own existence.
Then the project would be to look for evidence of Tfp in our universe.
But, would Tfp be a theory of absolutely everything? Actually, I don’t think so. The problem, as I see it, is those entities well-known in the philosophy of mind, qualia. It is likely that an explanation for them is itself an experience (as opposed to a mere concept about something), and thus not a mathematical structure. But if you have a better idea lets hear it!
Appendix
Okay, so what’s T3? It is the Lindenbaum-Tarski albegra of T2. But does every proposition in T2 count as an element in the model’s base space or do we mod out by something for some reason? In the first case, it is clear the naked predicate calculus T1 forms a different base space than that of its LT algebra as a base space. Therefore T3 is different from T2.
So, in other words, you are trying to show that the universe exists because logically/mathematically, it must? But then, as you say, it's not really the physical universe outside ourselves we want explained, but our own existence. Those subjective factors are the most important, the physical details are side notes. Seems to me, anyway.
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