My second pillar of Science is elegant hypotheses, that all else being equal we should prefer explanations which are (some combination of) "simple, uniform, common-sensical and aesthetically pleasing". In a Bayesian analysis, this factors into our choice of prior probabilities, i.e. the probabilities we would assign to various theories before we consider any observational evidence.
There is no "neutral" choice of prior which assigns equal probabilities towards every conceivable hypothesis. In other words, we are all biased in one way or another. However, not all bias is bad. Having a bias towards elegant explanations is a good thing, because simpler explanations are more likely to be true.
On the other hand, it very frequently turns out that the universe is more complicated than one expects. So you don't want to overdo it.
Now, how "elegant" is Christianity as a philosophical system? What are the different "moving parts" of theology, and how well do they explain the things they are supposed to explain? Before asking how probable Christian theology is, we should start by asking what kinds of entities Christian theology postulates.
The question of what exists ("ontology") is one of the most basic questions of the area of Philosophy which is called Metaphysics. Among scientists, this is a bit of a swear word: people use it in a derogatory way to refer to unmeasurable and potentially meaningless claims. While some metaphysical questions may be unsolvable or meaningless, it is foolish to say we know absolutely nothing about the answer to this metaphysical question (i.e. we know that penguins exist, so that's a start). And the scientistic claim, that Science is the only possible source of knowledge about important questions, is easily refuted.
I'm about to make a list of the different entities which Christians believe in. However, there's a few caveats I have to discuss before I do so. First of all, even atheistic, naturalistic philosophers disagree about things like whether numbers and abstractions etc. really "exist", whether objects are completely reducible to their parts, how to interpret the physical universe, and so on. Since these arguments have little direct connection to religion, I'm going to gloss over them here.
Another thing which even atheistic philosophers disagree about is the philosophy of mind; whether it is possible to explain consciousness, the meaning of thoughts, and other psychological aspects of our minds in a purely materialistic way. This question, however, is closely bound up with the religious question of the "soul" and so I don't think I should ignore this one.
The second issue is that Christians don't all agree on how to interpret Christian theology. Some Christian theologies (such as Roman Catholicism) have a very long list of official doctrinal claims, some have shorter lists, others have non-traditional theologies, or "liberal" views which water everything down in order to accomodate naturalistic sentiments, modern ethical views, or cultural relativism.
However, if we exclude the liberals and few wacky outliers, there is a large set of beliefs which are common to the theologies of almost all traditional supernaturalist Catholics, Orthodox, Coptics, Protestants etc.—what St. Lewis called "Mere Christianity". However, in a couple places (souls and sacraments) I will make note of potential disagreements amongst Christians about interpretation.
All right, then. Christians believe that the following thing exists:
(Α—Ω) God, the One and Only, the First and the Last, the fundamental object in the universe, who is uncreated, eternal, and exists absolutely ("I am who I am"), who is absolute goodness and therefore also holy, whose identity consists of three persons related to one another as Father, Son, and Spirit.
This is the only thing that exists absolutely. All other things exist only in relation to God, because God chose to create them and to love them. The distinction between Creator and created is so great that it is misleading to put them in the same list together, as though they were two things existing side by side in the same universe, instead of one being completely dependent on the other.
Created things include the following:
(1) The material universe that we know and love, including (α) the land and all its animals, plants, and people, (β) the sea and everything in it, (γ) the sky with its clouds and birds, and (δ) the solar system, the galaxies, the entire observable universe, and whatever lies beyond it.
(2) The "souls" of animals and human beings, whether or not these happen to be reducible to material objects such as the brain. (Yes, in traditional Christian thought animals have souls! In fact our word animal is derived from the Latin anima and means thing-with-a-soul.) Traditionally human souls are conceived of as being immaterial and—supposedly for this reason—immortal, but in my view this is not actually required by the Bible. So, I'm listing it separately, but with the caveat that it may be best regarded as part of (1). More on the subject of souls and immortality later.
(3) At least one other universe besides this one, which we can refer to as "Heaven". Words generally have more than one meaning, and in the Bible the term "heavens" often refers to something more like (1γ) or (1δ). But I take it that no scientifically educated modern person believes you can get to the religious-type Heaven by going far enough in a spaceship, so these are distinct concepts. (Why do I not mention Hell? Because my primary concern here is not with what happens to people when they die. Most of the occurences of the word "heaven" in the Bible are not concerned with the afterlife.)
(4) Angels and demons. (These are traditionally regarded as holy and unholy versions of the same type of angelic critter, just as Hitler and St. Bonhoffer are both human beings.) I presume that angels are normally denizens of Heaven, but they sometimes interact with people in our universe, which is how we know that they exist.
That's pretty much it. Of course, there might be additional created things, besides the ones we know about.
Sci-fi fans should notice that (3) is a kind of parallel universe and (4) is a kind of intelligent alien. So if you're wondering if the Christian faith will be shaken to its foundations if either of these two things are discovered—I've got news for you: we already believe in them. Admittedly, we don't know for sure whether there are other life-bearing planets in our universe, but in any case we don't think we are the center of the cosmos, or that God is only interested in us.
Next time I will discuss the interactions between the different things I mentioned, particularly how things have changed, and are going to change, as a result of God coming into the world as Jesus.