When confronted with their own failure to provide proof or evidence of their god, many theists fall back on a common response: 'well, you can't disprove God.' Technically speaking, we also cannot disprove the existence of leprechauns or Santa Claus, and yet this is no justification for belief in either one of them. The theist's objection misplaces the burden of proof too, which can only be on the side making a positive, extraordinary claim. We do not decide something exists and then look for evidence to disprove it, we seek out evidence that it does exist before we jump to any conclusions. Asking one to prove a positive claim (i.e. God exists) is also far more practical than asking the same of a negative claim, because in the case of the latter there are infinitely more avenues to be explored before a safe conclusion may be reached, whereas the positive claimant can simply make his/her case based on evidence that is readily available.

However, it is not entirely true that God cannot be disproven. It is often assumed that because God is proposed as a supernatural being outside of our physical realm, our methods of logic and science do not apply. Yet the problem with this view is that believers consistently define God in ways that either cast him back into the natural world or serve no useful purpose in defining him. There are some gods that we can know not to exist, because of how they are defined. That's not to say all gods can be dismissed with absolute certainty, because many of them lack a coherent definition, but there are instances where a combination of attributes or doctrines leads to such a contradiction that it is logically impossible for the imagined god to exist.

I. Inviolable Truths

For as long as we have been on the earth and as long as our descendants will populate it in the future, there has never been, and there never will be, a square circle or a married bachelor. Because of how we define each of these words, the combination of some of them results in a logical contradiction. Squares and circles are two different types of the same category - that is they are both shapes. Married men and bachelors are also two different types of the same category. Square circles and married bachelors violate a logical principle known as the law of non-contradiction. This law states that A cannot be both A and non-A simultaneously. Since a square is not a circle, by definition, and a married man is not a bachelor, combining these terms produces only nonsense. Nonsense which can't even exist in the mind (can you mentally picture a square circle or married bachelor?)!

There are other laws of logic as well, like the law of identity and the law of the excluded middle, but for the purposes of this article, we will focus mainly on the law of non-contradiction. Does a violation of these laws really mean something cannot possibly exist? The laws of logic are also known as axioms, because they are self-evident truths that cannot be disproven. If one attempts to disprove the law of non-contradiction, he or she only winds up assuming its validity by arguing that it is false that something can not be true and false at the same time - in other words, they assume that the law of non-contradiction itself cannot be both true and false. Axioms like these are the very foundations of logic, the basis from which we make inferences. If we were able to violate the laws of logic, there would be no such thing as argumentation or evidence at all. Thus, something that violates these laws cannot exist because a self-evident truth cannot be violated or it ceases to be true, and as we've seen, even trying to disprove or violate these axioms only ends up affirming them.

Impressed by the powerful certitude of these laws, some apologists have contended that they must have a foundation to ground them and make them true. Predictably, this foundation is suggested to be God. However, as just stated, these laws are axioms, or self-evident truths that are self-evident because they prove themselves. It is not that we simply assume their validity, so the theist's 'grounding' of logic in a god is unnecessary. Nothing is conspiring to make the law of non-contradiction true, it is true by its own virtue. This theistic claim is dealt with more in the article on The Transcendental Argument for God, and of course, no matter how you think your god sustains logical axioms, if that god is logically contradictory in itself, it cannot exist to be the foundation of anything (and your argument also crumbles). So which gods are logically contradictory?

II. Defining God Out of Existence

i. Free Will and Omniscience

A staple of Christians, Muslims, and other faiths is the omniscient god who has a plan for each of us and yet lovingly allows us to have free will in the decisions that we make. But if God is all-knowing and has planned things out for us, then doesn't that mean we don't have free will? Some Christian apologists have countered by arguing that God doesn't interfere with our free will, while still knowing what choices we will make, yet we need not even deal with interferences or plans. Plain and simple, if God knows everything that happens before it happens, and this god is always correct, then we humans can only act how God already knows we will act. This is the opposite of free will, it is being constrained to a single type of behavior: only that which coincides with God's foreknowledge. If we are not free to act in ways that violate God's foreknowledge, then we do not have free will.

This conception of God proposes two logical contradictions. First is that God gives us complete free will, and yet his omniscient nature means we do not have free will (A and non-A are true simultaneously). The second one is that God is completely all-knowing, but because free will is so important, he doesn't know things that will inhibit our free will (again, A and non-A are true simultaneously; God is omniscient, but not omniscient). Apologists have tried to reconcile this problem by redefining free will and omniscience. However, if God is only capable of knowing what is logically possible, his knowledge is barely above that of a human, and there is nothing self-evidently false about knowing someone's future decisions or behaviors. Likewise, arguing that free will within certain confines is still free will may hold up for only being able to do what is logically possible, but not for being confined to do only what God knows we'll do. Free will within logical possibility still accommodates many different options, whereas 'free will' under an all-knowing God means you only have one option: to act as God knows you will.

Of course, the simplest solution would be to concede that either God is not all-knowing, or we do not have free will. Few theists seem willing to take that route though.

ii. The Omnipotence Paradox

Can God make a rock so heavy that he cannot lift it? This is one of the oldest and most famous challenges to a god boasting omnipotence as a defining characteristic. If God is all-powerful, should he not be able to make something too heavy to lift himself? If God can't do it, then he is not omnipotent, but even if he can, being unable to lift the rock also means he is not omnipotent. Either way, there is something God cannot do. Some have countered that omnipotence means God can only do what is logically possible, but this downgrades God closer to humans again, and there is nothing contradictory in the idea of creating something too heavy for you to lift. A man can build a boat that he can't lift, so why can't God make a rock he can't lift?

It has been suggested that this paradox is a violation of the laws of logic, like square circles and married bachelors. Christian apologist C.S. Lewis complained that the question is meaningless, because an unliftable rock is an example of non-omnipotence which is clearly incompatible with an omnipotent being [1]. This response misses the point of the paradox though. The question is whether or not an omnipotent being makes its own omnipotence impossible. If omnipotence is truly incompatible with non-omnipotence, as Lewis claims, then the paradox has succeeded in exposing the flaws inherent to the concept of omnipotence. An all-powerful being that does not have the power to create things beyond the scope of its own power is not all-powerful.

The idea of God being only capable of logically possible things is at odds with the bible too. For "with God all things are possible", reads Matthew 19:26, and "nothing is impossible with God", according to Luke 1:37. Conditions are not placed on these descriptions of God's power, and these statements came long after Aristotle and other famous philosophers had begun discussing logical possibility and logical impossibility. Modern apologetics has redefined omnipotence into at least five different forms to escape paradoxes and challenges like this one, and in each new form omnipotence becomes less and less powerful. An omnipotent being is a logical contradiction, because whether it can or cannot violate its own omnipotence, it does not possess all conceivable power.

iii. Fully God and Fully Man

Another logical contradiction is the Christian doctrine of Jesus being both fully God and fully man. Passages like John 1:1-2, 1:14, and 2 John 1:7 serve as the basis for this teaching. The problem with this view of God is that a god and a man are two distinctly different things, and the overwhelming majority of believers already accept this. God is the immortal creator of the universe, while man is a mortal flesh and blood creature. Numbers 23:19 states, "God is not a man, that he should lie, nor a son of man, that he should change his mind." In other words, God is not man, nor is he even really like man, and man is not God, nor is he even really like God. Because man and God are two separate entities, the idea of a being that is both 100% man and 100% God at the same time is a logical contradiction, no different than a square circle.

Of course, this doctrine is usually taken on faith without regard for logic, but it is puzzlingly believed even by some apologists who claim that God cannot act in ways that violate logical laws. There is apparently no contradiction seen by these people in a being that cannot act to violate the laws of logic, yet whose very nature (or two natures, rather) are in direct violation. Apologists William Lane Craig and Ravi Zacharias are noteworthy for expressing such conflicting beliefs. As usual, theology takes precedence over rationality when necessary, even for those who deem themselves 'rational believers'.

iv. The Intervening Scientific God

There is another sort of god that we can know not to exist, and this is the god of creationists, one that has intervened and left its mark on our universe in the past and sometimes continues to do so today. Generally, science avoids the issue of God's existence, because God is a supernatural proposition which is untestable and unverifiable to natural science. This is the way that it should be, but every so often, a theist drags God into the realm of science in an attempt to prove his existence. Claims of a global flood, six thousand year age of the earth, and other details are testable to science, and when someone suggests that their god intervened with human affairs and our physical reality, we can at the very least examine the effects that might be left in such a case. Creationists waste no time in coming up with evidence of these effects, but time after time their proposals have been debunked and disproven.

Is it really possible to fully discount the existence of a god based on lack of evidence? That's just the thing, it isn't merely a lack of evidence, it is also the presence of positive, contradictory evidence that makes this type of deity a logical impossibility. For example, we are not simply dismissing the creationist arguments for the age of the earth without reason, we are dismissing them based on loads of collected data and observations that tell us the true age of the earth to be 4.5 billion years. The earth cannot be both 4.5 billion years old and the 6,000 year product of the creationist god. God could not have created us all as unchanging forms and yet also caused us to evolve. These are contradictions describing mutually exclusive things, yet again. When faced with this kind of disconfirming evidence, one cannot simply remain undecided unless there are strong biases at work.

Now this does not mean the god of Judaism is logically impossible, because there are a variety of ways to interpret the book of Genesis, and not all Jews or Christians accept the dogmas of creationism. All this tells us is that a god who created the world in six days, six thousand years ago, and formed every species exactly as we find it today does not exist. These works attributed to such a god have been disproven. Just as science can tell us with certainty that Earth is not flat and the moon is not made of cheese, we are able to know with certainty that our universe and planet only testify against the possibility of the biblical creationist's god.

III. Blasphemous Certainty

One of the most common criticisms of atheists is that they claim to know for certain that there is no god, making them just as dogmatic as religious fundamentalists. The irony to this statement is that even Richard Dawkins has only ranked himself a 6 on a 1-7 scale of how convinced he is that there is no god [2], and you'd be hard pressed to find an atheist advertisement anywhere that does not stipulate that 'there probably is no god,' as opposed to definitely. It is possible that some god exists, and it is also possible that this god is totally unknown to our world at this point, so there is nothing wrong in withholding absolute declarative statements out of principle.

This is not necessarily true for all gods though, and because of how some of them are defined or how proofs are attempted for them, a degree of certainty can be given to rejecting the possibility of such beings, when contradiction is all that turns up. Some atheists even seem to recoil at the idea of expressing their disbelief with any solid conviction, but the fact is that one is no more of a fundamentalist for knowing that logically contradictory gods do not exist than for knowing that square circles and married bachelors do not exist.

1. Lewis, C.S. (1944) The Problem of Pain.
2. Dawkins, R. (2006) The God Delusion. p.51. Houghton Mifflin: New York.