Is God a logical contradiction?

[Anomalocaris]

"Are virtual particles matter? " I'm not sure what a virtual particle is.

According to quantum mechanics, quantum fields fluctuate all the time and these fluctuations give rise to transient particles that pop in and out of existence which, during their brief existences, resemble real particles.  They can be experimentally demonstrated to arise just as described by quantum mechanics.   

I would say matter isn't non-matter, it's anything made of atoms, no?

If you say matters are what are made of atoms, then according to modern understanding of the evolution of our universe, for a significant period during early history of our universe, there was no matter because there was not yet any atoms.   Atoms have not yet formed out of the more elementary particles from which they would later be made.   Yet despite the universe starting with no matter, here we are.   So If you take this view, then matter arises out of non-matter, so even intelligence that depends on matter to exist can arise out of non-matter.

I don't understand " we are not particularly good yet at predicting what emergent properties are possible in large system over long time horizons".

An emergent property is a property which a large system of interacting parts exhibits, but which its constitute parts do not.    Intelligence seems to be the archetypical emergent property.   The spiral arms of the Milky way may also be thought of as a sort of emergent property of a large gas and dust cloud.    Emergent properties are difficult to either theoretically deduce or to forecast with computer simulations, because it often depend on very precise understanding of the exact interaction.   So we are not very good at taking a large system of many interacting parts, and deduce how the system overall may behave.    In fact, if you remember the recent issues with Boeing 737 Max 8.   In some ways the disasters of that plane can be pinned to poor forecast of the behavior of the flight system when large number of subsystem interacts.

Some intelligent properties could emerge if you exclude neurons, I agree. But for the complete package material things are needed, like dopamine + neurons to create the non-matter / immaterial properties like thought and memory, is what I'm saying.

Do you really need dopamine, or do you just really need to have the ability for something that can assume different states to be able to communicate its state to something else?   Can the state be in the form of, say, the energy state of a photon?   Can the photon communicate its state by interacting with another photon?   In this case would the role of a neuron plus dopamine be partially fulfilled without any atoms involved?

Immaterial:
philosophy
spiritual, rather than physical.

This kind of immaterial is nonsense as far as existence of entity is concerned.

Spiritual:
relating to or affecting the human spirit or soul as opposed to material or physical things.

Hard to make sense of this kind of immaterial without a clearer and more verifiable definition of the "spirit" or "soul"

Spirit:
The non-physical part of a person which is the seat of emotions and character; the soul.

The is part is problematic.  such a seat has not been demonstrated to exist.

Non-physical:
not relating to or concerning the body.

That's rather broad.   If we assume computer intelligence is possible, then that would fit this definition of non-physical, immaterial intelligence.

Soul:the spiritual or immaterial part of a human being or animal, regarded as immortal.

One can add hypothetical parts to humans beings or animals till the cow comes home.   But that does make any of those parts actually exist.

I think we can clearly see that the definition immaterial just sends us in a circle from "immaterial" back to "soul". 'Immaterial means soul and soul means immaterial.'

The circle is formed by you when you draw lines between separate points that are not intrinsically related.

Also how can something not have a body, including neurons plus other chemicals and be intelligent? A contradiction.

Not being able to think of how things can be a certain way is insufficient to make it a contradiction for things to be that way.   You have to spell out why in principle  things can not be that way for asserting this to be that way to be a contradiction.    In our kind of intelligence it is not the neurons and chemicals that is fundamental.   It is the roles they play that is fundamental.   It seems quite conceivable how stuff not made of atoms can still be made to play analogous roles, as I suggested with the photon example.   So it seems conceivable non-material entities, by your definition of material having to be made of atoms, to be intelligent in a way that is fundamentally reminiscent of us.