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Logical Constraints on God: What Can God Not Be?

Logical Constraints on God: What Can God Not Be?

It is often said that although we cannot prove there is a god, we also cannot prove there isn't. This is used to justify the idea that atheism is just as much of a faith position as religion, or that the most rational position is agnosticism. However, these lines of thought focus purely on science and empiricism.

It is impossible to "prove" anything through science; we can only provide evidence for or evidence against. However, if it can be shown that two things contradict each other, then they can't both be true. For example, there can be no such thing as a square circle. This is the basis of logic.

This begs the question, what kind of god is logically possible? If we examine the concept of god and notice that it contains inherent contradictions, then we can dismiss the concept as definitively, inarguably false. We will have proven that god cannot exist.

Empiricism vs. Logic

There are only two ways of working out whether or not something is true or false: through inductive reasoning or through deductive reasoning. Roughly speaking, induction is the basis of empiricism and science, while deduction is the basis of logic and mathematics.

An example of an inductive statement might be "all fire is hot". The more times we encounter hot fire, the more certain we can be that fire is always hot, but we can never completely rule out the possibility that cold fire might exist in the universe. Hence we cannot prove that fire is always hot, only provide a massive amount of evidence for.

All inductive reasoning takes this form. The more times something has been seen to happen, and never observed not to occur in the same circumstances, then the more certain we can be that it will always occur in those circumstances.

In contrast, deduction is based on the principle of noncontradiction - as already stated. For example:

1. All mammals breathe air.
2. All dolphins are mammals.
3. Therefore all dolphins breathe air.

There is no possible way for the first two statements to be true, and yet for the third statement to be false. If all mammals breathed air, and dolphins were mammals but did not breath air, then there would be a contradiction: we would know the first statement was false. We can thus conclusively prove and disprove things through logic.

Does God have to Obey Logic?

I have heard people say that god is beyond the laws of logic. But this is absurd, because, as I have already covered, the basis of logic is noncontradiction - or, that no thing can possess two mutually exclusive properties. It is impossible to discuss truth in the absence of logic.

To say that god does not have to obey the rules of logic is exactly the same as saying "the existence of god can be true even though it's false" - and this undermines the argument. To even claim that god does exist is to assert that something cannot both exist and not exist, and by extension, the assertion must necessarily be logical.

In other words, there must be logical constraints on god. What are those constraints? There are many different conceptions of god, but most lie on a scale - from an almighty, human shaped supernatural being, to a transcendent but sentient mystical force, to the embodiment of a higher reality from which all existence emerges.

What all of these have in common is the idea of a creator, supporting the belief that the universe is not just the result of physical forces but some purposeful act of creation, with an architect who is personified to greater or lesser degrees.

Common (but not universal) characteristics ascribed to this personification include infinite power, infinite knowledge, superlative moral righteousness and an involvement in human affairs. For the sake of argument, I shall define god as a transcendent being (if not human-like, then at least possessing consciousness and a capacity for purposeful action) who created the universe.

God's Attributes are Mutually Exclusive

Many of the attributes listed above are mutually exclusive. For example, because there is suffering in the universe, it is impossible that an omniscient, omnipotent being could have created the universe and also possess supreme moral rectitude. Such a being must have known that suffering would arise (omniscience), been capable of constructing a world in which no suffering occurred (omnipotence), and yet chosen to create a world containing suffering anyway.

It does not matter that such a god might have had reasons for allowing suffering to exist (e., allowing free will or teaching moral lessons), because, being omnipotent, such a being could have achieved those same aims without allowing suffering to exist.

Equally, the idea that humans are incapable of understanding the motives of god does not stand up, since an omnipotent god would be capable of explaining its motives in terms understandable to humans.

If such a god possessed omniscience but not omnipotence, it must have known that it was creating a world in which some beings would experience intense suffering with no respite, and yet created that world anyway.

If such a god possessed omnipotence but not omniscience, it could still have altered the world to eradicate suffering once it realised that suffering existed - or even altered time so that suffering had never existed - but must have chosen not to. Supreme goodness is thus incompatible with either omnipotence or omniscience.

God's Attributes are Inherently Invalid

In addition, the concepts of omniscience and omnipotence are logically flawed in themselves. It is impossible to have infinite knowledge, because by definition knowledge must be bounded. To know something, I must know all of something, and it is impossible to know all of something which is without end.

Even if we take a lesser definition of omniscience, and say that it is merely knowledge of everything that exists, has existed and will exist (knowledge of all possibilities), we are still left with logical inconsistencies. Such a being would know the conclusions to its own thoughts, and thus be incapable of thinking, theorising or creating, since to do these things is to advance outside the boundaries of what is already known.

In this case, such a god would not know how to do things which I can do - things which are dependent on ignorance - and so would not have complete knowledge. Or, put another way: a being knows everything - does that being know ignorance?

Similar questions can be used to demonstrate the internal inconsistency of omnipotence. Can an all powerful being create an object so heavy that it is incapable of lifting it? If the answer is either yes or no, then that being cannot be omnipotent.

The point isn't whether or not a being is hypothetically capable of infinite power; it is that the very idea of omnipotence itself is logically flawed.

Some theists have tried to argue that the problem here is in the question rather than the concept of omnipotence: that the question is equivalent to asking if god can create a square circle, something which is logically impossible because the definition of "square" excludes the definition of "circle".

However, this is clearly not the case. I personally am capable of creating a weight so heavy that I cannot lift it - by pouring increments of concrete into a mould, for example, and allowing it to set. There is nothing inherently impossible about the terms of the task.

God as Creator

All of the above has dealt with the common attributes of god. The concepts of omnipotence, omniscience, omnibenevolence, etc., are invalid. However, I have to conclude that it is at least logically possible that a conscious being could have deliberately created the universe. There is nothing inherently contradictory about this: humans might one day possess the technological power to create universes, for example.

This is the only logically possible god: a species of being living outside the universe and possessing the power to manipulate physical reality to such a degree as to be able to create new universes. However, what reason could there be to believe this being actually exists?

I suggest that if a person can imagine not believing in god, then they will not believe in god, because "there must be a creator" arises only from "I don't understand how there could not be a creator". If you can understand how the world can work without the need for a god, there is no longer any reason to believe in a god.

In fact, to think that the universe must have been created is to enter into another logical error. If I suggest that a complex system like the universe needs an intelligent being to create it, then I cannot escape the idea that that intelligent being needs an even more complex designer still. I am left with the question, who created the creator? Far from providing me with a solution, this explanation causes the problem to recur infinitely, and so is logically invalid.


Once, in our ignorance, we believed that physical forces were the result of an all powerful human-like being, because this was the most immediate explanation we could think of. Humans are social animals, and we are more deeply hard-wired to think about the motives of other humans than we are to comprehend the mechanics of physical forces.

The mind has evolved to think in terms of motive, because socially, understanding motives is a survival benefit. When we ask ourselves why physical things happen, it is natural for our minds to think in terms of motive and volition.

But our instinctive assumption that the world works according to the will of some vast sentient creature, much like ourselves but more complex, has never once been proven correct.

In the sixth century BC, Xenophanes of Colophon stated that men make gods in their own image, and that if horses could create images they would imagine the gods to look like horses, and lions like lions, and so on.

It is easy to recognise the short sightedness of believing that the world must have been created by an entity resembling a giant human being. It is slightly harder to realise that imagining the world needs to be created by a conscious being, just because we are conscious beings, is merely a more subtle variant of this same fallacy.

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