What does it mean for something to exist? The data view

I've heard a few definitions of existence over the years:

1) To exist is to be the value of a bound variable.

2) To exist is to instantiate at least one property.

3) To exist is be an indispensable property. 

4) To exist is to explain at least one point of data; to explain our experiences.

The last one is interesting. To exist is to explain data. We have two kinds of data: privately accessible and publicly accessible. Both cry out for explanation. If I have a religious experience where I strongly feel the presence of God, then we broadly have two explanations for this data: 1) God exists. 2) God doesn't and something else is causing this feeling that is being misperceived as the presence of God.

There are two kinds of data, again: a priori data and a posteriori data, or data that depends on perception, observation, and science, and data that depends on concepts, language, meaning, and understanding.

To not exist is to fail to explain any data. Does God exist? That depends. Is there any data that God explains, that could not be explained otherwise? Theists say yes: The beginning of the universe, contingent facts, the advent of life (especially: life capable of feeling love from and for God), the advent of consciousness, and morality are five key data points theists say require God for explanation. Non-theists argue that we do not need God to explain the beginning of the universe (maybe because there isn't one), contingent facts, the advent of life, the advent of consciousness, or morality.

Do numbers exist? That depends. Is there any data that numbers explain that could not be explained otherwise? Nominalists will say we don't need numbers to explain numerical data, only ideas or thoughts about numbers. After all, we don't need unicorns to explain our thoughts about unicorns, we just need the thoughts! Just as fictional entities are explained by ideas in the mind, so too are numbers explained by ideas in the mind.

Realists can say that this doesn't cut it, because we can trace any fictional entity to real properties (or to real objects that have properties). We can trace fictions to an author's mind. While we cannot trace the unicorn to a single author, we can trace the unicorn to ideas of horse, horn, magic. We can further trace magic to real properties. So thoughts about unicorns are thoughts about <list traceable properties here>. If numbers don't explain data, and only thoughts about numbers do, then what are the traceable properties of numbers?

What is data if not experiential? And so to explain data is to explain our experiences. This includes direct data, like when we see a tree in front of us, and indirect data, like when we hear scientists talk about quarks and leptons. I experience scientists talking about these things. What explains this experience? Here is an explanation: scientists are talking about quarks and leptons as if they exist because the scientists have experienced reading experiment reports, or conducted experiments themselves, that cause them to experience data that cries out for explanation, and they have posited quarks and leptons to explain that. So we have degrees of "directness" of data. Some data is direct, most of it is inferential.

Moral data, therefore, in the form of intuitions, is absolutely data. Anything we experience is data. If someone wrongs me and I feel strongly that they have done something truly incorrect, what explains that feeling? Or when we hear about a dog owner locking her dog up in a room and then going on vacation for weeks so that she can get rid of her dog, and the dog slowly dies of thirst trapped in that room, and we feel so strongly that this was an evil thing to do that ought not be done, what's causing this strong feeling we have? Are there moral facts that cause us to feel these convictions, or is it just evolutionary programming?