The quickest and easiest way to prove that god does not exist is simply ask for a proper definition of god. You cannot say something exists if by definition it doesn't entail any properties that are seen in reality. You could can go as far as saying it impossible to exist if that definition would contradict itself. Now there are several different versions of what a god is:
Pantheism- god is the universe.
Panentheism - god is the universe and more than that as well.
god-lings - immortal beings with powers.
Classical theism - an omnipotent, omnipresent, omniscient, omnibenevolent, atemporal, immaterial being.
Three of the four are improper or contradictory definitions of god.
What pantheism seem to suggest is that the universe is conscious and has a will and intentions of it own. The problem that this proposes is that conscious is typically aware of things other than itself. While being self aware is a component of consciousness, you cannot have that awareness without there being something other than yourself to relate to. Consciousness allows you to understand your relation to the rest of your surroundings. For the universe, there is nothing to be related to. That all there is. Another interesting property of consciousness that it is a very highly interconnected phenomenon. Every part of the brain can communicate with every other part. For the universe it is expanding faster than the speed of light. This means if a beam of light left the earth now, there are some parts of the universe it would never reach. So this "consciousness" has nothing other than itself to be aware of and not all of it could possibly be in contact with itself. So how is this consciousness at all?
Panentheism has all the flaws of pantheism and more. So instead of the universe being all there is, there is more that is transcendent of reality. So how is the universe a part of god? Is is god's fingernail? Is it his skin? Is it a part of his mind? What? How is there a way that we can know (actually know an not have a strong conviction of) of the transcendent? What does it even mean to transcend reality? Reality is all there is. It is one thing to transcend matter (what even meant by that?), but all of reality? Transcendent seems just to be an unknowable thing making it useless to talk about it at all.
God-lings are the only thing that can seem can be a part of reality and known potentially. A "natural" god if you say. So if something may join with nano-technology down to the cellular level... and that granted it biological immorality and maybe laser beam eyes... that would be a god like. Now this doesn't entail that it is indestructible or all powerful but that has been god(s) in the past none-the-less. The Olympian gods and all other pagan gods could fall in this category as well. But with no evidence of these beings, there is no reason to believe they exist. You can say the may exist but that is the best you can do. Agnosticism isn't an argument for theism, just agnosticism. However, these are still natural. Some may say that for a god to be a god. It must be supernatural. That however may be noncognative as well.
Now for the god that nearly every Jew, Christian and Muslim say they think exists. This one by far is the most loaded concept of god. All the omni attributes are simply relational attributes. That doesn't describe anything. The immaterial and atemporal are negative properties. That REALLY doesn't describe anything either. Now lets look at each of them closer.
Omnipotent... yes lets talk about the rock that god cannot lift. Now many will say that it is meaningless to talk about doing logically impossible things. This may be true for things like making a square-circle but this isn't the case with the problem of the rock. Let me modify it so to make my point. Can I make a bench press so heavy that I cannot lift? Yes, this is a possible state of affairs that is meaningful. But can god? For this the question cannot be answered because either way it fails to be met. This is due precisely to the concept itself, thus proving it to be flawed. The only reasonable solution is to drop the concept entirely for a more coherent one. My suggestion is to swap it with "maximally powerful". This does not suffer of the problem of rock because it recognizes a limitation. This, however, is still a relational attribute and the end does not tell us what god is.
Omnipresent. Now there are two ways of taking this one. One that is possible and another that is contradictory. One that is possible is that just that god is aware of every spacial point and can exercise his power in any spacial point. The only thing that is left after that point is to describe how that state of affairs is possible or how it would work. The second way is to say that god is actually present in the same sense that everything else is present at its point in space. The problem with that is that has to be material in some way which that directly conflict with the immaterial quality. But either way still does not tell us what god is.
Omniscient. For this one to be even possible is that all things could be know. According to Gödel's incompleteness theorem that is not possible. With in every system there are a set of axioms that are assumed true and from there you work out what is true and what is not. With in the liar's paradox this an demonstration of that the axioms cannot be used to prove themselves. If a liar tell you he is lying.. then that means he is telling the truth.... but telling the truth is what a liar does not do. This is unsolvable problem. This may be in reality that there maybe no set of axioms to which to be used to prove everything else and itself. How is it possible for an omniscient being to be aware of what it is like to be ignorant? To be aware of that means not to be ignorant. Even accepting this as possible this still does not tell us what god is.
Omnibenevolent. Here, obviously, I will have to talk about the problem of evil, but I will not go into much detail. I will do a more robust defense later. Simply put you cannot be aware of someone's suffering and be able to remedy it and at the same time do nothing about it. Being benevolent would become meaningless if no action is required to be a benevolent person. To get around this they say that "god has a morally sufficient reason to allow suffering." I could say why that is contradictory, but I will do that next blog.
Atemporal and immaterial. How is that a person is without time? There are no events, nothing to react to, no continuity what-so-ever. Everything at once, for lack of a better description, would occur at the same "time." So how it is said that god does anything or chooses to do anything?- because that would imply events within a time line. Then there is not being composed of matter... Everything that we know of is of matter. Now I am not saying that everything that exist IS matter but it is still a fact everything we KNOW OF is matter. So what is not matter? Some say that immaterial just means that it has no parts. That doesn't make sense either. If it exist, then it at least has one part. So god is a conscious being but only has one part. That is impossible because consciousness has many parts. Consciousness requires emotion, memories, thoughts, senses, and awareness. All these not only require time as a part of their description but in psychology these are indeed separable modules in human consciousness. This making it unlike anything that we would call conscious. Robbing any possible of meaning by using that word. The phenomenon of consciousness is not reducible to one singular explanation, nor is it possible to describe without time. So, atemporal and immaterial are incompatible with the idea of a personal god.
Now many would respond and say that god is simply-complex but little do they know, that is my point. It is a contradiction. God has no meaning just like a square-circle has no meaning. So, I ask, without using relational descriptions and negative properties, what is god? If you cannot answer, then why do you expect me to believe in such a thing?
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