There is no direct evidence that any god(s) exist. Likewise, there are no purely theoretical arguments that prove any gods either 1 . In addition to the lack of reasons for a God's existence, the Argument from Incoherence holds that the very concept of god is self-contradictory and impossible, therefore, theism is false and atheism is true. Omnipotence and omniscience contradict free will and themselves are logically impossible; its omniscience is impossible for it to validate and there are questions about its own being that it itself cannot answer (therefore, nothing can be omniscient). If it is a perfect being, then, there is no need to do any creating. If it is eternal and immutable, then its very thoughts are eternal and immutable - in other words, it has no mental states. If its basic emotional, behavioural and instinctive drives are all fixed (i.e., not created by itself, therefore, not under its own control, and unchanging), then it is hard to imagine how the being, existing in a world without stimulation nor change, can be conscious at all. Without free will, morality, omniscience the remaining "god" is only an automaton: a being that follows necessity and logic. But the concept of a creator god is even more problematic - for this 'creator of everything' must have inherent traits that it itself did not create. It must be intelligent and rational (therefore, it can't have created intelligence nor logic). It must have desire, drives, motivations, an amazing omniscient thinking mechanism, and it can't have created itself. So it seems impossible and untrue to say that "everything must have a cause, therefore there is a god". Each property of god is itself a contradiction of the idea that god is the sole creator. All those uncreated self-traits lead to an impossibly unlikely situation where a complicated and multi-faceted being is invoked in order to explain a Universe that is said to be too complex to have self-created. The very concept of a creator god contradicts itself, and is impossible and incoherent. The First Cause of everything is not a god at all, it is merely the natural laws of an atheistic universe.

There are four strong arguments that God cannot have free will. Here they are:

See:

2.1. How Can God Verify Its Own Creator-God Status?

If you knew everything, then you should know that you know everything. If you do not know if you know everything, then you don't know everything. So, would a god know everything? How would it know? There are some questions that even a god could not answer. One question proceeds from a possible being that God could create. God could create a solipsistic being and make that being so that it thinks it created the universe. It could give such a being all knowledge except knowledge that it itself was created. Such a being would have no idea that it was, in fact, a created being and that there was another, higher, creator. If God wanted to create such a deluded being, it could do so. The problem is, our theorized God itself does not know if it exists in such a state of ignorance. In short, God cannot know if it does actually know everything. There is no way for it to even verify that it is indeed the true creator god.

2.2. How Can God Verify That Its Knowledge is Complete?

All intelligent sentient beings must realize that without verification from other beings than itself or from science, it cannot know if it is correct in its world view. It doesn't matter how intelligent or knowledgeable a being is - if that being wants to verify its knowledge to make sure that it is correct then it needs to look to something more intelligent than itself, or to science. But what if you are the creator of science? You couldn't then use your own construct to test if your own construct was true, it would be a circular and invalid test. If god attempted to find out if it did indeed know everything, it would realize that it has no way to know. How does it know it knows everything? It merely thinks it does. God has no test, method or possibility of finding out if it does indeed know everything. God could itself be a created being, with another creator hiding secretly behind it. It wouldn't know. In short, it does not and cannot know if this is true. Also, what if God uses its power to intentionally forget something? For Christians, this is exactly what the Bible says God can do, in Isaiah 43:25. If an omniscient and omnipotent being has chosen not to know something, then it may, or may not, know that it doesn't know. The worst possibility is when it erases its own knowledge of self-forgetting. It can therefore never know that it doesn't know something. It can't check. God does not know everything and is not omniscient. In fact, no being can know everything because no being, however creative or perfect, can verify that its own knowledge is complete.

2.3. Thinking Beings Do Not Know Their Own Substance

"I think therefore I am" is as true for God as it is for any being. But: God cannot account for its own nature. Whatever facet of personality, willpower or desire it examines about itself, it will find that it cannot find out why it is like it is. Why does God know everything? Why is god good-natured, or, creative, or loving? (If it indeed it is those things, of course). It seems that all-knowing is not an attainable state. Immanuel Kant says that it is impossible, through self-reflection, to know your own substance. He adds:

“For as he does not as it were create himself, and does not come by the conception of himself a priori but empirically, it naturally follows that he can obtain his knowledge even of himself only by the inner sense and, consequently, only through the appearances of his nature and the way in which his consciousness is affected.” "Fundamental Principles of the Metaphysic of Morals" by Immanuel Kant (1785) 2

An omniscient being is in the same boat: it cannot self-verify. Gassendi came to the same conclusion, as reported by Voltaire:

“'It is true,' says Gassendi, 'that you know what you think; but you are ignorant of what species of substance you are, you who think. Thus although the operation of thought is known to you, the principle of your essence is hidden from you; and you do not know what is the nature of this substance, one of the operations of which is to think.'” "Voltaire's Philosophical Dictionary" by Voltaire (1764) 3

2.4. Potential Self-Willed Ignorance

Assume that God does know everything. For some reason god chooses not to know something. It erases something from its own knowledge, and, makes it so that it hasn't known about it for all of time so it can't simply look into a different time when it did know. It then removes its own memory of having intentionally forgotten something. I argue in "The Four Dimensions and the Immutability of God" by Vexen Crabtree (2007) that God can't do such things. But I might be wrong, so here's the clincher:

How would god know now if it had intentionally chosen not to know something? It wouldn't be able to contradict its own will in choosing not to know, but if it destroyed the memory of making such a choice, it also wouldn't know if it had actually forgotten anything. This is another (admittedly tenuous) class of self-knowledge that any being lacks and can never know. Without an answer to this potential source of agnosia, no being that aspires to omniscience can be truly omniscient.

For a fuller discussion of the place of omniscience in world religions, see "Is Omniscience Possible? Does God Know Everything?" by Vexen Crabtree (2002). Its page menu is:

Also, as omniscience has a number of problems, there can be no omnipotent beings (as omnipotency requires omniscience).

That "God is Good" is a common assumption made by theists yet God could exist and be neutral (amoral) or malevolent (evil and immoral). But it cannot be "morally good". It if it perfectly good then it always makes the most perfect choices and therefore has no free will. A being with no free will cannot be morally good as it makes no moral choices; it can only be morally neutral like a robot. Also, if God's actions and wishes are automatically good by definition, then its morality is arbitrary and we ourselves have no moral reason to follow it, and may do so only out of fear of the consequences or of selfish want of reward. If God's actions are not by definition good, then, there must be an independent source of the definition of goodness. If God has always been good then God can't have been the creator of goodness; yet if it wasn't, then what was? The idea of a good god causes contradictions. If you do not accept purely logical, philosophical or theological arguments that god cannot be benevolent, then, the real-world existence of evil and suffering (of babies, etc) is also evidence that the world was not created by a perfectly good god. Natural disasters such as earthquakes and volcanoes appear to be universal and not linked to Human free will, yet they cause much destruction. It seems that morality and God are contradictory. God cannot be the author of morality nor can it itself be moral.

To be an eternal being that is responsible for creating the flow of time itself, is to be immutable and unchanging. God has existed for all eternity before the creation of the world, and all of eternity after the demise of the world. The created world - from beginning to end - is like an object in the hands of God, that can be rotated and examined. God can view every timeline from start to finish, and knows the conclusion of every test. This First Cause of the Universe sits on the outside of time, looking it, effectively omniscient. But God is not subject to the laws of the Universe that it created. It holds all of time and space in its hands but it is not itself subject to time. For this reason, God doesn't change. And for another reason, too: God is a perfect being. Any change away from a perfect state in order to achieve some aim or goal must be a step towards a good purpose: but, god, in being perfect, has already attained all good ends. God doesn't consist of an eternal series of mental states: God is one mental state, unchanging, perfect and eternal 7 . 8

The conclusions that God is unchangeable has been reached by some of the leading historical Christian theologians. St Thomas Aquinas in the second book of his Summae Theologiae concludes that god cannot change itself, or repent, or undo the past 9 . This is because these things are temporal events that require God to be subject to time itself; but as time is a dimension created by god, God is above and outside it 9 . The Bible supports this in Malachi 3:6, Numbers 23:19 and James 1:17.

The result is that God is immeasurably cold and emotionless 10 ; much more like an automatic process, rather than like the God that many people wish exists. It seems the very concept of God verges on being self-contradictory: It is more of a principle, unconscious and non-thinking. These and other theological problems have led many to the conclusion that God simply doesn't exist.

A fascinating discussion on temporal dimensions and god can be found here: "The Four Dimensions and the Immutability of God" by Vexen Crabtree (2007).

The concept of a 'perfect god' contradicts our idea of God's personality and drives. If God is perfect, then, it needs nothing. It cannot want anything, because a want denotes a lack, and a perfect being is short of nothing. If god exists in a perfect state, then, change is impossible. Any change towards a new state implies that god's original state was not the perfect one, after all. So, a perfect god is immutable and does not change 7 , 10 . But an unchanging being has no emotions, no feelings, no 'plans' as such - all of its plans existed in their perfect state right from the beginning; co-created in the same manner as god itself. With no changing emotions or desires, a perfect god is a frozen automaton, with its perfect plan rolling out whether or not it acts or thinks or moves or feels. The concept of a perfect god also contradicts reality: creation is not perfect and the existence of suffering, violence and other negative aspects means that god is not benevolent and perfect, at least not according to moral or functional definitions of "good" or "perfect".

7. The Features and Properties of God Were All Non-Created, Which Contradict the Idea of a God as the Sole Creator

If god created anything according to a thought-out logical plan, or, if God had a desire to create anything that wasn't pure random chaos, then, god's thoughts must have been framed around logic. This logic allowed god to think and create, and, gave motivation to God. Logic must have been the first cause; but if logic is a requirement for God and existed before God could create, then God cannot be the First Cause, and therefore, creator-god theism is false, and atheism is true.

We have seen how many of the properties of God contradict each other, and themselves turn out to be impossible. There is no possibility of any being existing with the properties that we would recognize as godly.

But the concept of a creator god is even more problematic - for this 'creator of everything' must have inherent traits that it itself did not create. It must be intelligent and rational (therefore, it can't have created intelligence nor logic). It must have desire, drives, motivations, an amazing omniscient thinking mechanism, and it can't have created itself. So it seems impossible and untrue to say that "everything must have a cause, therefore there is a god". Each property of god is itself a contradiction of the idea that god is the sole creator. All those uncreated self-traits lead to an impossibly unlikely situation where a complicated and multi-faceted being is invoked in order to explain a Universe that is said to be too complex to have self-created. The very concept of a creator god contradicts itself, and is impossible and incoherent.

An uncaused God is more complicated than an uncaused Big Bang. When it comes to comparing arguments where there is no hope of actually getting any physical evidence, there is a long-standing heuristic to help distinguish between theories, called Occam's Razor: after all evidence is accounted for, the theory with fewest assumptions is more likely to be true. God requires many properties and complexities such as consciousness, thought, personality, creative drive, love, an internal logic ordering its thoughts so that it can think coherently and rationally, memory, etc: All of these properties must have been derived from somewhere. It turns out that God is a vastly more complicated thing than the Big Bang and the fundamental laws of the Universe.

“The Universe exists. Both theists and atheists believe in one uncaused cause: atheists think that the Universe itself, with a few universal laws, intrinsic traits and properties, is responsible for everything including itself. However theists think that it is ridiculous that the Universe can exist without a cause, and, have come to the much more reasonable assumption: the Universe was created by God, who itself exists without a cause, complete with its range of intrinsic traits and values. Putting it like that, we can see that although theists believe in god(s) and atheists don't, both have some similar assumptions about how the universe came to exist. Theists and atheists both believe in some universal laws of logic and/or nature which exist as the first cause. But the theist position adds on a list of personality traits to this first cause, and, calls the result "God". Whether these additional assumptions are warranted or not is hard to prove, hence why we say that the additional assumptions under theism are based on faith. These theistic assumptions include attributes about God: it is all-powerful, omniscient, benevolent, it has memory, it has rational and ordered thoughts running along logical lines, it is emotional, it wants to be worshipped and other particular assumptions of various religions. Even if it was found that the First Cause must be a conscious god, then, it is not reasonable to automatically assert that all those other assumptions are true too. There have been a great many variant concepts of god in history 12 partially because it's not clear what properties and features God should have. In comparison to all that, atheists make far fewer ad hoc assumptions about reality, meaning, that their position is more likely to be correct.” "The Assumptions about God and Creation, of Both Theists and Atheists" by Vexen Crabtree (2014)

“The scientist, however, may wish to challenge the assumption that an infinite mind (God) is simpler than the universe. In our experience, mind only exists in physical systems that are above a certain threshold of complexity. [...] While it is possible to imagine a disembodied mind, there must be some means of expression of the pattern, and the pattern itself is complex. So it could be argued that an infinite mind is infinitely complex and hence far less likely than a universe. [...] According to our best scientific understanding of the primeval universe it does indeed seem as though the universe began in the simplest state of all - thermodynamic equilibrium - and that the currently-observed complex structures and elaborate activity only appeared subsequently. It might then be argued that the primeval universe is, in fact, the simplest thing that we can imagine.” "God And The New Physics" by Paul Davies (1984) 13

The additional assumptions of theists are discussed on my page The Assumptions about God and Creation, of Both Theists and Atheists. Its list contains the following items - click on each for a discussion and some comments on the logical problems associated with them: