Why do we exist? version 1b

Can we find a rational explanation for existence?




This note outlines a strategy to find such an explanation. We start with possible existence (of anything at all), move to a relative existence (things may exist relative to each other), and argue for a resulting necessary existence (of the universe). A prototype of an argument to find what the universe must necessarily be is then given.



Start with possible existence.

The existence of nothingness is a simpler hypothesis than the existence of something, so why does anything exist at all? But, really, how did we determine that nothingness is the better hypothesis? In fact it could turn out that the existence of some particular mathematical structure is more inevitable than the existence of nothingness. On the other hand, it is better not to assume the positive existence of some particular structure, either.



All we can say is that for any given mathematical structure, it might exist.



Part 2 is the “relative existence” move. What does it mean to exist? It is sufficient to consider the cases of relative existence. If X exists and it is evident to X that Y exists then Y exists.



Hypothesis 1: existence is mathematical existence (i.e. ultimately what exists are mathematical entities)



Let be “it is possible that” and be “it is necessary that”. The idea is that the nature of existence is such that



(1) if x xy then y



where xy means y exists in the sense of x.



Why should we believe (1)? There is the intuition that relative existence is sufficient for a kind of absolute existence. That, morally, if xy then x too. This latter term means that a state of existing relative to x is a state that exists itself. One could also argue that “exists” in x was (implicitly) relative also, in some way.



For y to exist in the sense of X when X is a formal system means that



(2) X y



What we want is a mathematical theory T that sees itself as inevitably existing, so that



(3) T t



for all propositions t in T.



Under these circumstances, if we could be sure T is our universe, then we would be justified in claiming we have a rational explanation for existence.





Is it possible to find out which theory T is? Call our first guess T1. Let T1 be standard first-order predicate calculus, enlarged to contain the two modal operators above. These are needed to express p. However, T1 does not contain any axioms, functions or constants. This would seem to be the choice with fewest assumptions. From T1 we can construct some model M2. The elements of the base space of M2 are exactly the propositions of T1, the relations in M2 codify implication in T1, etc. Then what is T2, the theory of M2? It would seem to at least contain T1 as well as the theorems about the Lindenbaum-Tarsky algebra of T1.

Repeat this procedure for T3, T4 …



Conjecture: this process reaches a fixed-point theory TFP.



Claim: the meaning of TFP is that what is logically inevitable is the existence of TFP