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Ontology

The study of being, reality, or existence.  (from Greek onto-, being)

And truth is knowledge of things as they are, and as they were, and as they are to come; -- D&C 93:24

I Exist.

Every axiom system must start somewhere, and without this axiom, nothing else matters much. 

"Cogito ergo sum" is the best and most succinct proof of this.  Unfortunately, it is only a partial proof.  The proof that something exists becomes self-evident: thinking is an act, so something must be doing it.  Even the effort to deny this requires a thought from a being which exists.

The proof that I am doing the thinking is not complete.  The Hindus offer an alternative, that we are merely figments of someone else's imagination, such as Vishnu's dream.  No one has yet found an argument to prove it one way or the other, so we take the I on faith, because the alternative would be a meaningless existence.

Something else exists.

I accept this based on the evidence that I receive communications from other "existences" which are different from myself, distinguishable because their ideas are different from mine.  Thus, similar to how thinking is evidence of my existence, certain forms of learning or teaching are evidence of the existence of another being.

Conversely, everything else could simply be a figment of my imagination.  The only evidence I have of other things comes through some admittedly fallible senses.  For example, if I were to concede that I imagine God, how could I not also concede that I am only imagining you?  Again, there is no way to prove or disprove either alternative, but I'm not fond of the idea of leading a lonely, self-deluded existence, so again I accept on faith, the alternative which allows my existence to have greater meaning.

The world exists as my senses perceive it.

Although my senses are somewhat fallible and filtered, if I do not trust that something is tickling them, I have no other basis for perceiving any world at all.

This is the first axiom of physical existence.  The previous ones merely imply mental existence, but both are necessary preconditions for the physical world.  If I don't exist, there is no reason why the world I perceive would exist.  And if nothing besides me exists, the physical world does not exist either.

Why should I trust my senses?  If they can be fooled once, they can be equally fooled any number of times.  No amount of repeated experimentation can entirely remove this doubt, that the true reality is there before it, and we are conveniently ignoring it.  Here is where faith in our senses has to be tempered by a sufficient amount of doubt as to our own infallibility.  For example, when Einstein considered that gravitational mass and inertial mass were not merely coincidently equal, but were in fact the same thing and therefore indistinguishable, then he gained real insight into the truth about gravity and space/time.  It was there for us to perceive all the time, but no one really looked close enough until then.  In fact most major discoveries in science are the result of someone looking beyond what everyone believed that their senses were telling them, and accepting that their senses were actually telling them something different from what they believed at the time.

The alternative, that I cannot trust my senses at all, leaves no room for believing in any sort of physical world, or any objective reality at all for that matter.  That would be another lonely, meaningless existence.  So I believe, again on faith and because it gives life meaning, that the senses are fundamentally reporting truth to me about a world which really exists in objective reality.

However, because there is much more to reality than I can ever sense (I must filter most of the possible impressions out in order to select the important ones), and as a result the senses are fallible (as evidence from magicians, etc proves), while this axiom is fundamentally true, it is not always and absolutely true.  We must temper our faith in reality as we sense it, with a recognition of our own limitations and fallibility.  Thus objective reality, while certainly there, may be difficult to perceive correctly and in full detail.  Doubt is "the lack of faith in one's own certainty, which leads to greater knowledge."

The world follows consistent and predictable laws.

This is the second axiom of the physical world.  It is necessary for the workings of the physical world to be discoverable by science and the scientific method.  We have faith that it does, and haven't found any real counter-examples yet, such as reality changing simply because someone believes it should.

A miracle such as the sun moving backwards while a battle is being fought (Joshua 10:13) would be a significant counter-example for disproving this axiom.  One can either stop believing in science, ignore such fantastic claims, or allow that the doer of such feats knows a lot more about how the physical laws work than we do.

Scientific Empiricism (i.e. natural laws are discoverable via the senses) follows immediately from the first and second axioms of the physical world.

Something beyond the physical world exists,
or, Free-will exists.

We have already proven the mental existence of a being capable of thought.  And we accepted the existence of the physical world.  It is not clear what the relation between these two modes of existence is.  It is clear that there is a perceptible difference between the physical world and a mental or spiritual existence denoted by words such as consciousness, spirit, God, etc.  (Is dualism, or the belief that body and mind/spirit are separate, required for religion to be different from science?)

On one hand, one may argue that the mental existence is a mere phenomenon which arises naturally from a complex enough physical system.  This implies that the mental world must also follow consistent and predictable (i.e. deterministic) laws, and in particular that free-will is an illusion.

All the mental or spiritual things we conceive to exist are conscious, free-will beings of some sort, and free-will rules out the "consistent and predictable" axiom we have for the physical world.  Indeed, free-will may be taken as the distinguishing characteristic of the mental/spiritual world of existence.  Physical laws describe a "must" because physical objects have no free-will.  Moral laws describe an "ought" because conscious beings have a choice to follow them or not.

There is also a unifying argument made possible by quantum mechanics and its need for a probability wave which collapses in a non-deterministic fashion.  Perhaps this is the means by which free-will beings are able to influence the physical world.

Good definition of free-will: "the ability to simulate possible futures within the brain and choose from the available options." -- Jonathan Malo

The spiritual world must be perceptible

If it is not, then it doesn't matter whether it exists or not, because it cannot affect us.  If it can affect us, it must be perceptible.  But because of the free-will axiom, the methods of science may not be sufficient to prove its existence.  A being with free-will may not always choose to show up at the laboratory or respond the same way to experiments.

Mental existence is thought and feeling within the self, analogous to the "I exist" axiom.  Spiritual existence is distinguished by the communication of thoughts and feelings with other spirits/mental beings, without the need for language and physical senses, analogous to the second axiom, "something else exists".  The essential difference between "mental" existence and "spiritual" existence is communication between mental entities without the physical senses, or direct spirit to spirit communication.

How do we perceive the spiritual?  Those who claim to have experienced spiritual things recommend certain rituals, some of them are referred to as "prayer" from which we obtain mental and emotional impressions, and others are referred to as "obedience" to commandments, from which we obtain sometimes inexplicable "blessings" as if some spiritual beings were able to help and/or reward us.

If we pray and/or have spiritual experiences, do we trust our senses, in the same way we trust our senses to tell us about the physical world?  The way we confirm scientific observations is with repeated experiments.  There is no reason why we should not repeat our prayers and seek out repeated spiritual experiences, in order to confirm the reality of our spiritual experiences.

If I perceive God and spiritual impressions, I can either accept them as reality or assume I am self-deluded.  The reality where I have no free-will and God is a self-delusion seems rather pointless to me, so just as at the earlier steps I choose the option which gives life meaning: free-will and God exists.  It would be logically inconsistent to choose the other path at this point, and I have repeated perceptive experiences to back up my faith. 

Concluding remarks on God

This might be a new argument for the existence of God, but it can never be considered a proof of the existence of God. Although the argument is superficially similar to the teleological argument for the existence of God, it is self-aware that it is merely an argument (not a proof) for faith in God, since most of the steps are assumptions. These assumptions are necessary in order for life to have meaning and moral sense, because the same justification for disbelief in God can also be used to justify disbelief in the lower axioms of the existence of the physical world, the existence of others, or even the independent existence of the self. But in the end, they are still assumptions. 

But once we have accepted that our assumptions are consistently based on choosing the side with gives meaning to existence, it would be logically inconsistent to make an assumption at a later and higher stage of the analysis of existence which would result in a worldview with less meaning. In other words, given any philosophical but scientifically undecidable question, the logically consistent choice is the option with gives existence more meaning. And this leads to the question of what sort of reality would have the most meaning. Perhaps it is this: "The Spirit itself beareth witness with our spirit, that we are the children of God: And if children, then heirs; heirs of God, and joint-heirs with Christ." (Rom 8:16-17)