By Paul Almond, 20 October 2005

Introduction

Some theists claim that God is superior to logic, which is to say that God is unrestrained by logic and that God is 'above logic' in some sense. The problem with such claims is that they cause all proofs of God's existence to fail. This means that anyone making the claim that God is above logic is in the rather awkward situation of depriving him/herself of any good arguments in favour of God's existence. The purpose of this article is to demonstrate this. Incidentally, I do not believe in God.

The Basic Idea

If god is beyond logic then we cannot use logic to say anything about him. Various people have mentioned this. As just one example, when writing this article I found a comment on a website discussion forum asserting that if God is beyond logic: "If this is true, then even the best reasons for god's existence are only a matter of opinion." [1]

This sums up the situation quite well. We cannot do logic about gods who are beyond logic - even if that logic is to show their existence.

In this article I want to make a strong, detailed argument to justify this sort of objection to proofs of a god who is beyond logic.

The Idea of God Being Superior to Logic

The idea that God is above logic manifests itself in various ways, some of which are as follows:

• God made logic - This claim involves the idea that logic 'did not exist' until God created it. The claim is incoherent. One of its fallacies is that it views logic as a thing which is out there in the universe, rather than properly viewing it is as something that humans do - a human methodology or system of working. Theists could argue with me on this and suggest that somehow there is some hidden 'framework' of logic, created by God, which all things must follow and that human logic is merely using this and would not work in its absence.
• Logic is contingent on God's existence - This claim is similar to the preceding one but stops short of actually saying that God made logic at some specific time. Instead, the claim regards logic as a thing or framework like the preceding claim and simply maintains that it cannot exist without God existing. Logic comes from God. Logic depends on God. Whether God made logic or whether both God and logic have existed for eternity are not issues that are raised in this claim. God, however, is still quite clearly held to be superior to logic.
• God is not restricted by the rules of logic - This claim is somewhat vaguer. It could actually follow from one of the preceding claims or it could be combined with one of them. This claim suggests that any logical argument refuting the claim of God's existence is invalid because God is somehow beyond the idea of logic. The idea is simply that any logical human thought in the face of God is futile and any attempts by people such as atheists to use any logic are futile: God is much bigger than their logical arguments and he can swallow their logical arguments whole. Combining this with one of the previous two claims, the idea would be that the logic that an atheistic argument may use was probably made by God in the first place or is contingent on God's existence. When somebody like an atheist attempts to use logic to refute a theistic claim he/she is simply using something which only exists by God's permission in the first place.
• God can change the rules of logic - This would naturally tend to follow from the previous claims. If God made logic or it is contingent on his existence then the rules of logic should probably only apply by the permission of God. Should God change his mind about how logic is supposed to work then logic would immediately be altered. A theist making such an argument may not necessarily be saying that it is likely that God will change his mind about how logic works: he/she is merely asserting the capability. It is unlikely that many theists really think this is going to happen in the near future.

Why this Idea is Extreme

What is being claimed here is rather more than the idea that God made lots of things. Let us consider an example: We will start with two statements that we will suppose to be true:

1. All philosophers eat fish ( a rather silly statement, but let us just pretend that it is true).

2. Socrates is a philosopher.

It will be clear that we can apply logic and say:

3. Socrates eats fish.

If god is superior to logic then God is 'above' the very thing that we just did and 'above' the very principles of logic that we used to do it. This means that that last statement only followed on from the other two statements because God made the logic that caused it to follow on, or he decided to make that statement in particular follow on, or the statement followed on but only because he exists, or the statement follows on only with God's consent.

However it works exactly, one thing is clear: the claim assumes that, were God not to exist, then that last statement would not follow from the other two. It should be noted that the claim of God being superior to logic is not saying that we would somehow be obstructed from applying the logic in the absence of a God. The claim is saying that the very logic itself depends on God.

This makes little sense, for more than one reason. The refutation in this article will concentrate on only one reason for not accepting this idea.

Why are these claims a problem?

Claims such as these cause attempted proofs of God to fail. Even worse, they cause even attempts to provide good evidence to make a statistical argument for God's existence similarly to fail. Once claims such as these have been accepted God is merely a hypothetical being with no logical support whatsoever. This would hardly seem to be desirable to theists. The claims simultaneously give God huge powers that transcend logic while removing him to the realm of fiction, or at best the realm of unsupported hypothesis.

How is the problem caused?

All of these claims suggest that God exists in or inhabits some domain in which the rules of logic do not apply. Even if a particular claim for God being above logic does not actually state this, it is implicit in such claims. This is necessary for God not to be bound by logic and to be superior to logic.

I am happy to leave the meaning of the word 'domain' open and merely meaning whatever sort of place or equivalent of place God inhabits. It may even not be a physical place. We can consider a 'domain' to somehow be the scope of God's existence - that part of existence, or (as is frequently claimed) 'above' existence, where God actually is. If you like to imagine God being 'somewhere' then it is clear that at least that part of 'somewhere' that God inhabits is not ruled by logic. If you think the idea of God being 'somewhere' is laughably crude and materialistic then I suggest you think of the 'domain' of God as the area of logic where he is found - that area of logical argument that is directly relevant to God.

Why is a domain beyond logic a problem?

The problem with this is that it destroys any proof of God's existence. By definition any proof of God's existence must operate using logic which makes reference to God. This means that the logic of the proof of God's existence must be operating, at least partially, in the same domain as God. We have seen, however, that if God is superior to logic then the domain in which God exists is not constrained by logic. Therefore any proof of God's existence is actually invalid. It simply does not work because logic no longer works in the vicinity of God.

The case of a theist attempting to offer a proof of a god who is beyond logic is, basically:

1. God exists
2. God exists in some domain which is beyond logic.
3. I have a proof of God. X can only be explained by God. I have logic to show that, based on the existence of X, God exists.

… and the problem is that at least some of the logic in (3) - that part of the logic that refers directly to God - must be operating in the logic free domain introduced in (2).

An Analogy

There is a new kind of computer virus called SnurfelzXXX. Someone says that SnurfelzXXX is so unlike any other computer virus that it could not have been made on any computer that follows any of the rules of computation. They say that it must have been written on some unknown type of machine that works in a way that is somehow beyond anything we can know about computation so that none of the rules we use apply. They also say that it must have been written in a programming language called C++ as this is the only logical choice for someone who wants to write this sort of virus.

This claim does not make any sense. I know that some computer programmers will be sceptical about the idea that a particular language would be needed to write a given virus, but that is not the point. The claim's insistence that a computer can exist that is 'beyond anything we can know about computation' is probably incoherent, but let us look beyond that and pretend that it is not a problem. A more difficult problem is the claim's assertion that the C++ language would be needed to write the virus. Really? According to whose rules? The rules of normal computation? We have just been told that that the computer on which this was all done is beyond those rules!

This is why this claim fails. It claims the existence of a domain which is beyond what we can know about computation - this computer on which the virus was written - and then attempts to apply what we know about computation in that very domain.

This example is analogous to the sort of claim discussed in this article, with the computer that is beyond the normal rules of computation being analogous to the domain which is above logic, the computer virus being analogous to some characteristic of reality which is typically used to infer a god and the C++ language allegedly used to write the SnurfelzXXX computer virus being analogous to God.

Examples of Failure of Specific Proofs of God

The main argument of this article has now been made. Unlike some of my other articles, in this case it really is that simple: there is nothing more to it. I realize, however, that some readers will want more of an idea of why the proofs of God fail when he is superior to logic. I will give examples of some typical 'proofs' of God and how they collapse when you attempt to apply them to prove a god who is assumed to be superior to logic. I will not state the proofs in detail - the article is not really about that - but will simply give an idea of the sort of proof that is involved in each case and why it becomes problematic.

Attempted Proof 1: It is logically necessary that the universe had a creator

Why the Proof Fails

Some theists argue that the mere existence of the universe requires a creator. Such a theist may use the first cause argument. Others argue that some feature of the universe - usually complexity - shows that it must have a creator.

Suppose, first, that God is superior to logic on account of having created logic. Presumably he created logic just before he created the rest of the universe. It follows that before God created logic there was no logic. This is claiming that there was a time, or some other sort of domain, in which logic did not apply. This means that the cause of the universe came from within a domain that was not subject to logic. If this is the case then no matter how logical it is that the universe needs a creator, that logic can be ignored.

If I do have to accept the existence of this logic free domain, why could I not say that the universe can simply appear from within it without a creator being in there to do it? In the absence of any logic with which to attack my argument who can say that I am wrong? A theist may say that God acted within this logic free domain to make the universe, but I can say that anything else happened in this domain to make the universe. I can even make up some really absurd logic such as 'The universe originated from the domain above logic by the process of osmosis which can be proven by the fact that frogs like to ride bicycles in logic free domains,' and, in the absence of the logical checks and balances, which will not work where we have gone with the argument, there is no way of saying that it is wrong. In fact, I do not even need to say what it was that caused things: nobody can make any logical argument that it was God, which is all that matters.

A common theistic claim is that 'something can't come from nothing'. If there is any logical support for this - and I would say that the statement is of no relevance anyway - it would fail totally in a logic free domain. Ultimately, even the assertion that there must have been anything at all in this logic free domain that caused the universe is untenable. No matter how logical it may be to think that a thing has to exist in this logic free domain to cause the universe, it is irrelevant when logic will not work in that domain.

A theist desist from thinking that God made logic while thinking that God is superior to logic in some other way. For example, he/she may argue that logic is contingent on God; that is to say it only exists because God exists. This is just as bad. The claim is still being made that a domain which is not subject to logic exists and that the universe came from this domain. Attempting to prove that this logic free domain contains a God fails, just as it failed in the previous case.

Attempted Proof 2: Biological complexity needed a creator

Why the Proof Fails

Some theists point to the huge complexity of life on this planet as proof of a creator. They discount the theory of evolution by natural selection, often dismissing it as 'random chance making animals' (which is an incorrect representation of the theory as it ignores non-random natural selection) or using their idea of 'irreducible complexity', and also ignore the possibility of any other explanations for the existence of biological complexity.

If such theists also claim that God is superior to logic then their 'proof' from biological complexity runs into the same problems as the last one. If God made logic then God exists in a domain which is not subject to logic. If the cause of biological complexity came from this domain then logic is in no position to go in there and tell us that a God must have been required. If God did not make logic but is still superior to it then God is still in a domain that is superior to logic and the problem still arises.

Attempted Proof 3: The existence of right and wrong requires a creator

Why the Proof Fails

Some people assert that objective ethics exist - that some actions are clearly right and others clearly wrong in an absolute sense - and that this could not be true in the absence of God. They claim that ethics is contingent on the existence of God in the same way that logic is supposed to be.

If God is supposed to be above logic then such attempted proofs have the same problem as the previous two. If ethics is contingent on God then ethics is contingent on some domain in which logic does not apply. If ethics is contingent on some domain in which logic does not apply then it is rather presumptuous to use logical arguments in an attempt to prove all sorts of things about what goes on in this domain. As in the previous two examples, logic in the vicinity of God simply would not work.

Attempted Proof 4: The definition of a God ontologically implies his existence

Why the Proof Fails

Some attempted proofs of God are based purely on ontology and make no reference to the physical world. The idea is that logic alone demands God's existence.

One example of such an attempted proof is Anselm's ontological argument [2, 3]. Anselm's argument seeks to show that God's existence is required by his definition. Anselm defined God as the greatest being that can be conceived. He then stated that non-existence would detract from God's greatness. Surely, a being who did not exist would be less great than a being who did exist and, therefore, God must exist.

Anselm's ontologically argument is seriously flawed for other reasons beyond the scope of this article, but if God is supposed to be beyond logic then one reason for failure is clear: if God is supposed to be in a domain that is not subject to logic then the logic of Anselm's ontological argument fails: talking about how the logic of definitions implies existence in a domain without logic is a double-standard.

Objections

Objection 1: It does not make sense for you to say that a logical argument that shows the existence of God, if God is superior to logic, has to work in a domain in which logic does not work. The existence of a domain which is superior to logic could be inferred from outside that domain without having to construct logical proofs that actually discuss matters inside that logic free domain. As an analogy, if we encounter something that does not obey the known laws of physics then we can infer that something outside the scope of the known laws of physics exists. We would not actually need to use whatever unknown laws of physics governed this thing, or make any argument that used them. We could show that the thing existed simply by reference to known laws of physics and showing that they are inadequate for dealing with it. Similarly, we could show that something outside of logic outside exists by showing that the rules of logic are not adequate for dealing with everything that exists. Such an argument would not be entering a domain with no logic but would be inferring its existence from outside, invalidating your whole refutation. Your argument cannot show that a domain superior to logic cannot be proven to exist.

Answer

I can accept the idea that things can exist outside the scope of the known laws of physics, but I do not think that it extends to being able to prove things outside the scope of logic. Logic is not a feature of reality, like laws of physics, but a methodology, and the idea of proving the existence of something 'outside' it is incoherent. We will not go into that deeply in this article, however.

The real problem with this objection is that it is a straw man argument. I never said that I was attempting to prove that the existence of a domain without logic and superior to logic could not be proved. That is not the point of this article. The point is to show that the existence of a god who is free of logic cannot be proved. Let us suppose that the domain without logic could exist. Let us also suppose, although I find it a quite incoherent concept, that a logical proof could show the existence of such a domain. This would mean that some logical argument could prove that something had to exist which was beyond logic, maybe by showing the inadequacies of logic for dealing with all things as suggested in the objection. I can imagine that some readers will think that Gödel's incompleteness theorem is relevant to this: I do not think it is, but I will not be bothering with that here. The problem is that this is not equivalent to showing the existence of the god. It is simply showing the existence of a domain without logic and nothing more. The theistic case goes further and says that not only does a domain free of logic exist, but that God exists in this domain. It would therefore be inadequate for a logical argument simply to show the existence of a domain superior to logic: the argument would have to go further and prove that in this domain God existed. To do this the argument would have to be extended into the domain. It would have to be talking about things which existed or did not exist inside that logic free domain and part of the proof would have to be operating in that logic free domain. Therefore, the objection is invalid.

I realize that this will not satisfy all readers. For this reason an alternative statement of the refutation will shortly be given.

Objection 2: You talk about some 'domain' which God inhabits. You have a rather simplistic view of God. God is not limited to a place. Why do you think God lives in a place somewhere as if he exists in space?

Answer

I made no such claim and I used the word 'domain' to avoid using a restrictive word such as 'place'. The word 'domain' is simply meant to refer to whatever scope God's existence has. If God is a part of all reality then the domain God inhabits is a part of all reality. If God inhabits some higher dimension then the domain that God inhabits is this higher dimension. If God is beyond the need for any place to inhabit, using some strange theistic logic, then 'domain' would simply mean 'beyond the need of any place for God to inhabit'. I am happy for the word 'domain' to widen its scope to include whatever theists feel should be substituted for 'place' in discussions of the nature of God's existence.

As with the previous objection I realize that not all readers will be satisfied. A key problem will be this idea of a domain. As with the previous objection I would point out that the alternative statement of the refutation which will shortly be given may address such concerns.

Objection 3: God is beyond logical requirements and physical limitations. He does not have any need for a 'domain'.

Answer

As I just stated, a domain need not be a 'place'. It could be 'that area of logic which relates to God' - that area of logical argument which God 'inhabits' - and if you claim that God has no need of this, so that it does not exist, you should not try to make theistic arguments which enter it!

As with the answers to the two previous objections, some readers will find this unsatisfactory. This alternative statement of the problem will deal with the matter differently.

An Alternative Statement of the Problem

Here is an alternative statement of the problem which avoids use of the idea of a 'domain':

1. Let us presume that something outside the scope of logic exists and we will call it X.

2. Let us suppose that we think that X is required to account for reality or some features of reality. We may do this, reluctantly, because we think that nothing else except X will suffice.

3. We now argue that X has some characteristic. The only reason for doing this can be that we have some logical argument for the possession of this characteristic by X. We may think that X has to have some feature to account for a feature of reality or we may think that X has to have some feature to be consistent with itself.

4. The problem with the previous step is that, even if we can infer the existence of X and accept the idea that X is beyond logic, any logical argument that tells us anything more about the nature of X is discussing something that is beyond logic. It simply does not have to obey the rules. For example, if we say that X has to have some feature for it to be self-consistent, then why does it need any self-consistency? It is supposed to be beyond logic! If we say that X needs to have some feature to explain something that we see around us in the world then why does X need to have that feature? Can X not simply use its ability to overcome logic to explain that feature anyway?

5. Declaring X to be a 'being' or a 'person' or to have any of the characteristics that we might associate with a god, other than the characteristic of being beyond logic, is therefore an invalid.

6. Therefore, there is no reason to call X 'God'. If somebody did give the label 'God' to X it would really be a semantic issue and nothing more. I could as easily give the name 'God' to my desk and insist that I had defined it thus.

The above argument may appear very different to the way in which the problem was stated previously, but it is essentially the same with the idea of the domain removed. Even if the logic free domain were held to exist (and I do think this is an incoherent idea, but let us pretend anyway) it would still be impossible to have any logical reason at all for presuming that such a logic free domain had anything in common with the theistic idea of a god.

Further Objections

Objection 4: Not all theists claim that God is actually beyond logic. Some theists accept that God must obey the rules of logic and that logic is not contingent on God.

Answer

This article is not intended to attack the claims of all theists but merely to refute the case, made by some theists, that God's existence can be proved and that he is beyond or superior to logic.

Objection 5: Your argument admits that the existence of something outside the scope of logic could be proven, but you insist that there could be no proof which shows this thing to be God. You have missed the point entirely: if something exists beyond the scope of logic then it is God by definition. God is simply a thing beyond the scope of logic.

Answer

Firstly, I have not accepted that the idea of something beyond the scope of logic could be relevant to reality or is even meaningful: I provisionally accepted it merely for the purpose of debate and I do not think it is a sensible idea at all

The other point in the objection is merely clutching at straws. In theology God is typically assumed to have the characteristics of a person. He acts with motivation. He displays intelligence. He can be made angry. He can respond to people. He can accommodate people's wishes. If God is simply removed to being beyond logic, then we cannot even say that he is a being beyond logic, because this in itself is giving him a feature which cannot be supported via logical proof. There would be no reason to give the name 'God' to such a thing. As an example, 'intelligent design', which appears to be creationism under a new name, says that all of the complexity in the universe was the product of a designer. This is not the same as saying all the complexity in the universe came from a cause which is beyond logic. Causes beyond logic do not design things or use intelligence to cause things. They cause things in ways that are beyond logic. Use of logical argument in this matter would be pointless.

Objection 6: Logic in the vicinity of god does not work. But clearly God is needed to cause a 'domain which is above logic'. Should it be shown that a logic free domain exists then god could be inferred merely by its existence. No proof actually has to enter this domain.

Answer

Something which is limited by the rules of logic cannot break them by making a domain which is above logic. Any cause of the domain's existence which is above logic would have to be in such a domain itself. This means that any logical argument which attempts to assert that the mere existence of a domain which is above logic is proof of God is actually being extended into the logic free domain to discuss God directly. It therefore fails for the reasons already given in this article. Should we be confronted with a domain which is above logic, it would be meaningless to discuss where it came from and what, if anything, caused it.

Objection 7: Doesn't your argument apply to itself? By definition it must be attempting to work in this domain which God inhabits. Your own argument is attempting to work in the vicinity of God. If logic intended to prove that the creation of the universe by God or the need for ethics to be asserted by God fails in the vicinity of God, on account of him being beyond logic or superior to logic, then similarly your own argument intended to actually prove that such a failure of arguments occurs in the vicinity of God would become a casualty of itself and fail.

Answer

I am sure that some readers were thinking I missed this one!

Using this objection would actually show a double standard. If the argument in this article fails and becomes a casualty of itself then argument failure does occur in which case the argument is true - even though it being true would not make it true. This is like the Star Trek episode in a robot's head burn out by telling it "Everything I say is a lie." The whole system becomes nonsensical at this point.

This is actually not a good reason to presume God exists. Rather, it should focus our minds on the incoherence of suggesting that any domain can exist for God to inhabit which is beyond logic. If you have created a system that invites logic that results in contradictions you cannot simply wish that logic away. Either we can apply logic in domains that are above logic or we cannot, or, just maybe, it is incoherent even to discuss the matter. None of these help proofs of a god who is above logic.

Some theists would say, of course, that there is no problem and that all we have to do is say that the logical arguments which prove God are correct, while any other logical arguments do not work in a domain that is above logic. You cannot suggest that God is somehow beyond logic and then pick and choose which logical arguments will apply and which will not. If God is beyond logic then all logical arguments in the vicinity of God will fail. If you want my logical argument to fail then it is clear that your arguments should fail by vicinity to God as well.

If a theist wants this argument, and any other problematic arguments, to fail due to God being above logic, and for all the proofs of God to remain valid then it should be clear what is happening: the idea of logic failure in the vicinity of God is being applied selectively. At such a point I do not think that any more argument by me is worthwhile: it should be clear at this point that anyone taking this view is merely using a logical free domain to see what he/she wants in it, like a wish-fulfilment vehicle or a cosmic ink-blot test and if this is not clear to someone it is unlikely that any argument would suffice: the matter has already been decided without recourse to logic.

Objection 8: Sir Roger Penrose proposes that physics is non-computable [4], which means that it cannot be represented by an algorithm. If this is true then a domain above logic exists - the laws of physics themselves. Clearly, great mathematicians disagree with you.

Answer

Leaving the appeal to authority aside, Penrose's proposal is controversial and even if the laws of physics were above logic this would not be proof of a god. The main problem with this objection, however, is that, regardless of the merits of his claim, Penrose is not claiming that something exists 'outside of logic'. He makes it clear that he thinks his 'non-computable physics' cannot be modelled by an algorithm but can still be formally described. This would put it well within the scope of logic.

Objection 9: You don't understand. Your whole argument fails because God is beyond logic. None of the silly logic in this article can touch him.

Answer

Sigh.

Conclusion

This article has shown that it is inconsistent to claim simultaneously that God is superior to logic, beyond logic or not bound by logic, or that he created logic, while also claiming to have a proof for God's existence.

This also applies to statistical claims for God's existence. A theist may desist from claiming to have a proof of God's existence while claiming that some feature of the universe shows God's existence to be highly probable. Even an argument like this would fail because the underpinnings of a statistical argument are still logic: logic is still required to justify assertion of probabilities.

It seems we have only two options. Either we can abandon any idea that God is superior to logic or, if we wish to claim that God is superior to logic, we can abandon any idea that we can make a good case for his existence - which would make the claim that he is beyond logic rather pointless.

References

[1] 'spidergoat'. (2004). Why a creative 'God' cannot Exist. Retrieved on 16 October 2005 from http://www.sciforums.com/showthread.php?t=33996&page=2
(Online discussion forum rather than a formal article).

[2] Holt, T. (2003-2004?). Anselm's Ontological Argument. Philosophy of Religion. Retrieved on 6 October 2004 from http://www.philosophyofreligion.info/anselmontological.html.

[3] Banach D. (?). Anselm's Ontological Argument. David Banach, Department of Philosophy, St. Anselm's College. Retrieved on 12 September 2004 from http://www.anselm.edu/homepage/dbanach/anselm.html.

[4] Penrose, R. (New Edition, 1995). Shadows of the Mind: A Search for the Missing Science of Consciousness. London: Vintage. Chapter 1.9, pp26-33. (Originally published:1994. Oxford: Oxford University Press)