When I say that the Pythagorean theorem exists, grandfather's umbrella exists, the future exists, a stone exists, I exist, a spirit exists, or God exists, each time using the same word, I am saying something entirely different. Each of these things, and I could surely keep listing more, exists differently. When we say that something exists, we rely solely on intuition.
If you asked a physicist or a mathematician, they would explain the relationship between the physical world, the world of reason, and the world of abstraction, where all three create one another. However, if we were to divide things by their mode of existence, we would be dealing with even more worlds.
The sensation of color cannot be described. It can, however, be made dependent on the wavelength of light and the response of receptors in our bodies. Redness exists differently in the physical world and in the subjective world of the perceiver. We see a clear coupling between the two worlds, but does a set of transformations exist that would connect them both? And if so, in what way? A physical one?
We are still missing one element before reaching the first important conclusion. In theology, a spirit is defined as a being without time or place. That is, one that exists, but never and nowhere - in other words, it is futile to search for it in the physical world, and one cannot ascribe to it the same rules of existence that we ascribe to matter or even to a human being. The world of spirit may have its own mode of existence, just as the world of abstraction exists differently from the real world. The nonexistence of beings in the real world in no way violates their existence in abstraction; the absence of abstraction does not cause real beings to cease to exist. On the other hand, if there are any rules connecting the two - they belong neither to abstraction nor to reality - and yet reality is partially coupled with abstraction. The only postulate I put forward is the possibility of beings existing in yet another way. Beings that also couple with reality, but it is futile to search for what connects both worlds.
Here I put forward the postulate of the possibility of God's existence in His own way. Different from all other modes of existence. Inaccessible to either physics or abstraction. It is futile to search for Him through empirical experience or logical reasoning. What we experience empirically exists in reality, logic creates the world of abstraction, and we are now postulating yet another form of existence.
Long ago, Descartes said that a human being is composed of soul and body, committing in the process an error that cast a shadow over future centuries of philosophy. The issue was finding a bridge between the worlds of spirit and matter. Since a human being is composed of two elements, it was expected that they must interact with each other. The error lay in the expectation of some kind of physics between the worlds. Some force that, by moving the spirit, would also move the body and vice versa.
Had Descartes not thought of soul and body as components of a human being, but instead stated that a human being is simultaneously soul and body, this subtle difference would have allowed him to understand that such a dependency cannot be found, and that a human being may be an entity manifesting existence in two different worlds. Just as redness manifests existence differently in the consciousness of the perceiver and in the physical world. So too a human being can exist in the physical world, subject to its limitations, and in the world of spirit simultaneously, where different rules prevail. The only criterion connecting them is the person themselves and their own existence.
I do not wish to convince anyone that unverifiable forms of existence exist, especially since arguing for the existence of God is doomed to failure. However, there are qualia - things perceived through pure intuition - that cannot be described in any other way than to point at them and hope that others experience them the same way. They do not fit into any verifiable world, and there is no method similar to the scientific method that would prove their existence, or at least their scientificity.
What I am trying to do, however, is protest against understanding the world only in categories that are provable, by showing that if we swing Occam's razor too broadly, we will cut away beings that we know are there, yet for which we have no tool to verify their existence other than plain intuition. I also believe that just as through intuition we see redness, so too faith, which allows us to perceive the spiritual, is a form of such intuition.