Is the law of non-contradiction the foundational and inviolable law of reality?

[This is a post for the more philosophically-minded.]

Is the law of non-contradiction the foundational and inviolable law of reality? The law of non-contradiction states that something cannot be both Y and non-Y at the same time and in the same sense. Many Christian thinkers believe this to be the foundational law of reality. But this law of logic is never directly stated in Scripture. It cannot be elevated to the same level as the direct statements of the inspired Word of God.

 

Many would say that the law of non-contradiction is a basic assumption underlying all of the other statements of Scripture. Any truth-claim of Scripture – especially the exclusivist truth-claims – must assume the law of non-contradiction.

 

But even if we grant that there are no stated contradictions in Scripture, the most we can say is that the Bible assumes the law of non-contradiction in the areas in which it makes direct statements. Because the Bible never comes out and says that the law of non-contradiction is true in all places, at all times, in all circumstances, all we can do is observe whether or not the Bible assumes the law of non-contradiction in the statements it does make.

 

Many Christian thinkers would say that God himself does not violate the law of non-contradiction. I have often heard or read this stated in such a way that makes God subordinate to the law of non-contradiction. It is said that even God cannot do or be the logically impossible. I am not entirely comfortable with this, since it seems to me that if God must bow to the law of non-contradiction, then the law of non-contradiction is God. By this understanding, there is something more fundamental to reality than God himself.

 

Many Christian thinkers would be a little more moderate by embedding the law of non-contradiction within the nature of God. God cannot violate the law of non-contradiction in the same way that God cannot sin. It is not that God is incapable of sin. It is that God will not sin. It would go against God’s very nature to sin. In the same way, God is non-contradictory, and since it is an essential part of his character, it radiates out into the rest of reality.

 

This way of thinking makes a lot more sense, but is it correct? Is the law of non-contradiction an essential part of God’s character? Many find support for this understanding in the biblical statements to the effect that God cannot lie. The thought is that if God were to speak a contradiction, or be a contradiction, or act in a contradictory way, then God would be guilty of lying or being untruthful.

 

I find this argument to be less than compelling. If there existed a contradiction in the universe, how would God be lying by telling us about it? If God were contradictory in his nature and if he were entirely open and honest about it, how would that be deceitful? If God were to act in contradictory ways but if he were not seeking to fool anyone by doing so, how would that be untruthful? As long as God is faithful to his promises, as long as he has been truthful in the statements he has made, does it really matter if there is a contradiction somewhere in the hidden, mysterious recesses of his being?

 

By this point, any proponent of the law of non-contradiction who has read this far has long since popped a blood vessel. To them the law of non-contradiction matters a great deal. The universe cannot make sense without it. There would be no way for us to understand or live in the universe if the law of non-contradiction were false. There would be no way to carry on rational discourse without it. In fact, many people would be quick to point out that my own discussion of the law of non-contradiction has assumed the truth of the law of non-contradiction.

 

And that raises what is to me the basic question: is it that the law of non-contradiction is the fundamental law of reality, or is it that the law of non-contradiction is the fundamental law of technical rational discourse? This strikes at one of the basic conundrums of philosophy. Can philosophy actual discover truth about reality, or can philosophy only express and explain truth?

 

For instance, what does it mean for something to be logically impossible? Are we saying that the laws of logic dictate reality? Are we saying that logic is some all-powerful force that prevents things from becoming contradictory?

 

Personally, I find that way of expressing it hard to swallow. It is more palatable to say that the law of non-contradiction is a formulation of a principle that we have observed to be true throughout the entirety of our experience. (We find it to be self-evident, and it appears to hold true throughout our normal experience.) I take the view that philosophy and logic are a reflection of reality, not a determiner of reality.

 

Really, when you boil it all down, the real reason that Christian philosophers are so insistent that we accept the law of non-contradiction is actually not because they have observed it to be true in reality, but rather that they have a hard time conceiving of reality without it. In order for a philosopher to be able to comprehend, communicate, and discuss a truth, it has to conform to the law of non-contradiction. Without the law of non-contradiction, all technical rational discussion breaks down and dissolves into nonsense. If something can be both X and non-X, then how can it be fit into any rational system of thought?

 

Christian philosophers will also point out that the universe would be unlivable without the law of non-contradiction. The only way we can live our lives is on the basis of the assumption that the law of non-contradiction holds true in all circumstances.

 

But this is an overstatement of the case. I can imagine a point X which is the point in the universe that is furthest from me. I can imagine that point X is at the very center of a black hole. I can also imagine at that point that there is a thing Y. Thing Y is so miniscule and insignificant that at such a great distance within that black hole there is nothing about thing Y that could possibly impact my life in any way. If thing Y were both Y and non-Y, would it matter? If thing Y was the only thing in all of reality that violated the law of non-contradiction, would it matter?

 

I am sure that most Christian philosophers would say that it does matter. If the law of non-contradiction can be violated by thing Y, then all of rationality dissolves into nonsense. I, however, would say that it is no harm, no foul. If thing Y is an exception that does not impact my life, then I am free to live by the law of non-contradiction as if it were an inviolable law. It will have no impact even on my rational discourse, since all that I will need to discuss still falls in line with the law of non-contradiction.

 

This illustration demonstrates an even deeper issue: an intellectual egocentrism. Could it be that the reason thing Y might get a philosopher’s dander up is that they cannot bear to think that there might be something in reality beyond their ability to comprehend it? Could it be that the philosopher demands that reality must fit into their neat logical boxes?

 

This becomes a very serious problem when a philosopher turns his attention to ponder the deep mysteries of God. A philosopher who believes the words of God in Scripture must agree that God is by his very nature incomprehensible. We can know him truly, but we cannot know him fully. Yet, a philosopher boldly asserts that God does not violate the law of non-contradiction.

 

The revealing question for the philosopher is whether or not he could believe in God if thing Y was a part of God’s nature. If there was known to be a contradiction within the deep recesses of the mystery of God’s being such that thing Y was also non-Y, would the philosopher be able to continue to believe in God? Probably most Christian philosophers would say that they would not be able to believe in such a God, since, they would say, such a God would be logically impossible.

 

This is odd, since a biblical view of God affords many opportunities for seeing contradictions in God. Any time you try to introduce the idea of the infinite into a finite system of thought, you run into problems. Hence the old question, “If God is omnipotent, then can he make a rock that is too heavy for him to lift?” Christian philosophers would say that of course God cannot make such a rock because such a rock is logically impossible. They would also say that the problem is not with God but rather with the question.

 

I would contend that the question merely exposes the issues encountered when you try to speak of the infinite in logical ways. The problem is not with the question. The problem is with trying to understand the idea of limitless power within a finite reasoning system. If you play with the idea of the infinite long enough, eventually you run into many such conundrums. (For more on the contradictions of infinity, research how mathematical set theory proposes numbers greater than infinity, or the paradoxes noted by Zeno.)

 

For other contradictions within the nature of God, a lot of non-philosopher Christians turn to both the doctrine of the Trinity and the doctrine of the incarnation. How is it that God can be both 1 and 3? How is it that Christ can be both God and man?

 

But Christian philosophers would be quick to explain that the Trinity and the incarnation are not inherently contradictory. God is 1 in a different way than God is 3. Christ is 1 in a different way than Christ is 2. And then they work at carefully defining the oneness and threeness of God and the oneness and twoness of Christ. For instance they might say that God is one being in three persons, and Christ is one person with two natures. And they carefully define what they mean by “being,” “person,” and “nature.”

 

Even still, many times the average Christian will read such explanations and be able to make little sense of them. Even if average Christians understand such explanations, they still might see such explanations as self-contradictory. Not only are they not able to reconcile these concepts in their minds, but they have a gut feeling that these concepts are just not quite right.

 

At this point the philosopher has to either admit that these rank-and-file Christians could be seeing something intuitively that the philosopher has missed, or the philosopher has to say that these rank-and-file Christians are stupid, deceived, and/or ignorant. Most Christian philosophers opt for the latter – writing off the uneducated masses as being too unenlightened to plumb the depths of theology proper, whereas the philosophers are of a higher echelon of intellectual knowledge and ability.

 

The formulations of the doctrines of the Trinity and the incarnation reveal at least three great limitations of the use of the law of non-contradiction in theological/philosophical thought. Even if you accept the law of non-contradiction as the self-evident foundational principle of rational reality, you still have to admit that the law of non-contradiction has at least three crippling limitations.

 

First, making use of the law of non-contradiction usually requires a very strict and technical definition of terms. This is clearly illustrated by the discussions surrounding the Trinity and the incarnation. The problem here is multifaceted. Often it is extremely difficult (impossible?) to define the terms in a satisfactory way. Even when a satisfactory solution is achieved, often it is by defining terms so technically that the resulting philosophical picture bears little resemblance to the idea it is trying to represent. This is how a lot of people feel with the doctrines of the Trinity and the incarnation. The philosophical formulations of these doctrines lack the beauty and luster of the God and God-Man described in Scripture. And finally, the process of defining one’s terms can feel relatively arbitrary. The philosopher denies the possibility of a contradiction, and then he proceeds to define his terms in whatever way he deems necessary to avoid the contradiction.

 

Second, the conclusions that the philosopher makes based on the law of non-contradiction can be false due to the philosopher’s own staggering ignorance. Since the mind of the philosopher is very finite, the amount that the philosopher does not know and understand far exceeds the amount that the philosopher does know and understand. The danger here is that conclusions made based on the law of non-contradiction can appear so black and white, but can still be terribly wrong.

 

One of my favorite examples of this is a basketball. If I were to convert a basketball into a philosophical/logical/mathematical description, I am certain I could demonstrate that it is impossible to turn a basketball inside out without cutting or ripping it. But a physicist will tell you that the feat is easily accomplished in four spatial dimensions. The physicist will also tell you that he is pretty certain that such a fourth spatial dimension does exist, so it is completely logically possible to turn a basketball inside out without cutting or ripping it. So my original seemingly-certain (slam-dunk?) conclusion turned out to be wrong due to my ignorance.

 

Probably the most well-known examples of the problem of ignorance are non-Euclidian geometries. In Euclidian geometry parallel lines do not cross – a concept that would seem either self-evident or true by definition. However, some mathematicians have proposed alternative geometries in which parallel lines do cross. To most people this would immediately appear to be nonsensical and even self-contradictory. However, when applying the rules of geometry to the surface of a sphere (such as the earth), one quickly discovers that parallel lines do cross. In fact, probably there are more curved surfaces than flat surfaces in nature. The seemingly self-contradictory idea of crossing parallel lines is probably the more commonly applicable idea and therefore more commonly representative of reality.

 

Third, the law of non-contradiction is always trembling in the looming shadow of the apparent contradiction. Philosophers like to make a distinction between an apparent contradiction and an actual contradiction. They would deny the possibility of actual contradictions, but they will admit that some things appear to us to be contradictions. Apparent contradictions are just unresolved problems. They are non-contradictions that are not yet fully understood. Once all the facts are known, once all of the terms are properly defined, the apparent contradiction will be clearly seen to not be a contradiction at all.

 

The problem here is the theoretical (or not-so-theoretical) existence of apparent contradiction Z. Let us imagine the existence of apparent contradiction Z. Apparent contradiction Z is a problem that is so immense and so complex and so detailed that no human being will ever be able to resolve it. In fact, no matter how far computer technology and genetic engineering advance, no matter how many human beings work on the problem, no matter how long the lifespan of those humans is extended, the apparent contradiction Z will never be resolved.

 

Perhaps the more arrogant philosophers would deny the possibility of apparent contradiction Z, but probably the majority of the more realistic philosophers would acknowledge the possibility of such a conundrum. Some philosophers may feel they have already discovered apparent contradiction Z. Others may feel that apparent contradiction Z is out there just waiting to be found.

 

Now, there is certainly a theoretical difference between my apparent contradiction Z and my thing Y. Y is in reality a contradiction, whereas Z is in reality not a contradiction. However, in practical terms there is no difference whatsoever. How would a philosopher be able to prove that apparent contradiction Z is not a thing Y? If the philosopher cannot resolve the apparent contradiction of Z, then for all intents and purposes Z looks and acts exactly like Y.

 

When the philosopher encounters Z he will just have to live with the real existence of something that looks to him and will always look to him as if it is a contradiction. He can console himself with the thought that Z is only an apparent contradiction, but he will never be able to prove it. He can only take it on blind faith that Z is not a thing Y.

 

Many Christian philosophers are aware of the problem of apparent contradiction Z, and this is why they find it so important to embed logic within the nature of God. A human philosopher may never be able to resolve apparent contradiction Z, but the all-knowing, all-wise God is able to fully understand Z. He is able to see it as non-contradictory. So when faced with apparent contradiction Z, the humble Christian philosopher is able to say with relief, “I may not understand this, but God does.”

 

Strangely enough this sounds exactly like the folk wisdom of the many rank-and-file Christians who deny the applicability of the law of non-contradiction to the infinite God. The rank-and-file Christian says, “This is a contradiction, but it makes sense to God.” The philosopher says, “This is an apparent contradiction, but it makes sense to God.” In practice there is basically no difference between the two.

 

The major practical difference between the philosopher and the rank-and-file Christian is one of extremes. The rank-and-file Christian is probably too quick to give up trying to understand what appears to be a contradiction, whereas the philosopher is too quick to resolve it at the cost of losing much of the richness of true reality.

 

Much can be learned from the example of the book of Job. Job and his friends spend the majority of the book struggling with what appears to be a contradiction: the problem of pain. How can a good God allow/cause a good man to suffer? To many Christians and non-Christians this is the greatest contradiction or apparent contradiction of them all. After chapters of debate, God finally appears to Job and his friends. However, God’s speeches to Job do not actually provide an answer. Instead God says he as God does not need to provide an answer to mere humans whom he has created. In fact, the wisdom of God is far beyond the understanding of man.

 

One of the implications of the book of Job is that trusting, worshiping, relating to, and coming to know God involves grappling with actions God takes and aspects of his nature that do not fully make sense to us. Many rank-and-file Christians give up grappling and avoid thinking about such matters. Many Christian philosophers accomplish the same by taking philosophical shortcuts to resolve apparent contradictions to their own satisfaction.

 

However, I think the appropriate posture is to live a life grappling with deep spiritual matters, fully aware that many of the details are ultimately beyond our understanding. As we open our eyes to the richness of God’s truth, we are moved to our knees in humble worship. If we are too quick to avoid these issues, or if we are too quick to jump to a neat and tidy solution, God may command us to sacrifice our sons, or he may take away all that we own. Then we will be forced to admit that we cannot fully make sense of reality, and we will have to choose to trust God in spite of apparent contradiction Z (or thing Y).

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