Introduction

In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and relationships are. One must also make epistemological assumptions or metatheories of how one can test cosmological theories. Here I shall propose a Bayesian analysis in which the likelihood of a complete theory is given by the normalized measure it assigns to the observation used to test the theory. In this context, a discussion is given of the trade-off between prior probabilities and likelihoods of the measure problem of cosmology, of the death of Born's rule, of the Boltzmann brain problem, of whether there is a better principle for prior probabilities than mathematical simplicity, and of an Optimal Argument for the Existence of God.

Cosmology is the study of the entire universe. Ideally in science, one would like the simplest possible theory from which one could logically deduce a complete description of the universe. Such theories must make implicit assumptions about the ontology of the universe, what are its existing entities and their nature. They may also make implicit assumptions about the ontology of the entire world (all that exists), particularly if other entities beyond the universe have relationships with the universe.

For example, I am a Christian who believes that the universe was created by an omnipotent, omniscient, omnibenevolent, personal God who exists outside it but who relates to it as His creation. Therefore, the ontology I assume for the world includes not only our universe but also God and other entities He may have created (such as new heavens and new earth for us after death). However, my assumption that God has created our universe as an entity essentially separate from Himself means that one can also look for a theory of the universe itself, without including its relationship to God, although there may be some aspects of such a theory that can only be explained by the assumption that the universe was created by God. (For example, even though a complete theory of our universe would necessarily imply the facts that there is life and consciousness within it, since such entities do exist within our universe, there may not be a good explanation of these aspects of the theory apart from the concept of creation by a personal God.)