Although it is true that no human being, atheist or believer, can disprove the existence of god with empirical evidence, this is not a requirement for the Atheist position. I'm not in any way, going to make the claim that I will be the first homosapien to disprove the existence of god, but my doubt in god's existence relies in large part due to some logical contradictions that I think exist.
First of all, what do I mean by god? There are a myriad of different concepts of what god is, between religions and even within religious sects themselves. For instance, ask two believing Christians what they think is the nature of god, and you will get two totally different (and even contradictory) answers. With all these apparent differences in beliefs, I will try to focus on the general concept of the monotheistic god believed by Jews, Christians and Muslims.
To the three monotheistic traditions, god is an all powerful, omniscient, omnipotent, morally perfect, timeless being, who is essentially kind and compassionate, and who is the "first cause" in the creation of, at the very least, our universe. Now these properties of god all have slight variations in the beliefs among Jews, Christians and Muslims (as well all the other religions) and we all know this has led to centuries of bickering and bloodshed (praise be to god!). I am not here to argue these differences, but rather I am here to make a case for how a simplified, conflated view of these beliefs in god comes across some logical contradictions, just as the religions themselves do.
Part 1: The Logical Implausibility of a Timeless God
We are told that god is timeless, but what does this mean? Believers say that god exists outside of time, but how is this really possible? If god created the universe, then there was a moment when god existed alone, before he created the universe, and then there was a moment when god exists with the universe, after he created it. But you cannot have concepts of "before" and "after" without time. In order for god to do anything, there must be a time before, and a time after he does it. Therefore, it is logically impossible for god to exist outside of time.
Now if god exists inside of time, then that brings up other problems. For example, believers say that everything that begins to exist must have a first cause, except god (how convenient). But if god does not have a first cause, and exists in time, then he must have an infinite regression of time in his past. To have an infinite regression of time in one’s past, also means that there are an infinite number of events in their past as well. To quote an argument made by the Christian theist William Lane Craig in his debate on the existence of god with Christopher Hitchens, Craig states that "mathematicians recognize that the existence of an actually infinite number of things, leads to self contradictions. For example, what is infinity, minus infinity? Well mathematically, you get self contradictory answers." Craig is on the right page on infinity’s impractical implications and is using this logical contradiction in defense of god, however he is failing to realize that the very same argument he is trying to make for god, is better applied against god. In other words, if god exists in time and therefore has an infinite past, then it would take an infinite amount of time for god to get to the present, and thus he would never have enough time get here.
If god is immaterial, does it make a difference?
Now what if you hear the argument that god is immaterial, and therefore cannot exist in time? Something that is immaterial that is also not an abstract concept (like a number) but instead is a thinking, intelligent mind that has effects on the universe, such as intermittently violating its laws of physics, must exist in the same time that the universe exists in as well. In order to be conscious and timeless, one would have to be frozen still, like being paused. Not a single thought or action would be possible. The moment it thinks or creates a temporal event, its relationship with the temporal event forces it to exist in time since you will then be able to chart the being's chronology of actions on a linear path, and this requires time.
Does timelessness exist at all?
In black holes for example, time is said to stand completely still because of the immense gravity. But this state of timelessness is only relative to events in the black hole, the rest of the universe around it carries on in time unaffected. The black hold itself still has a temporal relationship with the universe and any object unlucky enough to get sucked into the black hole is said to become frozen into immobility as it comes near the event horizon. It is hard to wrap our brains around such a concept given that we (thankfully) don't live near any black holes. Hopefully as scientists research this field in greater depth, we will someday unlock the mysteries of time itself.
Aside from the extreme conditions caused by black holes, I know of no other place where timelessness can exist. If god existed in a timeless vacuum before he decided to create the universe, what was he doing? If god is eternal, does he have a conscious eternal past? If god decided to design and create the universe wouldn't he need time to do it before he materialized his design. I have never heard any theologian adequately explain how consciousness can exist together with timelessness since thoughts require time, and I think that logical contradictions involving consciousness, time and concepts of infinity will be mutually irreconcilable.
What then do theists have as an answer to this dilemma?
So in the end, what are the best logical arguments I have heard again this problem? We are often told that god is mysterious and that our intelligence, as best as it is, will never be able to understand the nature of god. Essentially, this is a cop out. It is like saying that my explanation for the cause of the universe is far too complex for anyone to understand and so it's exempt from scrutiny. Furthermore, this opens its own contradictions. Many of the brightest theists, when asked whether god can create a rock too heavy for him to lift will answer, "no". This is because the question refers to a logical contradiction, just as god cannot create a married bachelor, or a square circle. In other words, god can only to what is logically possible. But, if my argument is correct that god cannot be timeless and is also not created by his own "first cause" (i.e. god's god), then he must have an infinite past, which as Dr. Craig argues is logically impossible. Thus, the logical plausibility of god's existence comes into question, and since god cannot achieve that which is logically impossible, the traditional concept of the god of the bible is like a square circle - that is to say a concept that only exists in our minds.
When we cut to the bottom line, no matter how brilliant our brains, or how sensitive our insights and intuitions - it still comes down to a matter of faith in the sense of accepting things that cannot be proved.
- Raqaiyyah Waris Maqsood in "What Every Chistian Should Know About Islam"
Further reading on arguments against god:
The Kalam Cosmological Argument
The Fine Tuning Argument
Objective Morality Without God
Refuting William Lane Craig: "Is Good from God?" A Debate Review
Refuting William Lane Craig: The Moral Argument
God, Time & Creation: More Problems For William Lane Craig
The Ontological Argument: Putting the Absurd Where it Belongs