Law of Knowledge


by Walter R. Dolen


The Law of Knowledge is the general method through which we obtain information or knowledge.

Herein I put the Law of Knowledge in a word-equation form that represents the general way in which we gain knowledge. I have reduced the wording of the law to its simplest form because the simplest declaration in most cases is the best explanation of a phenomenon according to the principle called the ‘Ockham’s razor’ or the ‘law of economy,’ which is a rule of thumb that guides scientists and philosophers when they develop models or theories. The rule can be stated: "a simpler explanation is better than a more complex one."

The law of knowledge is axiomatic and may seem so self-evident one wonders why anyone would even bother to put it into words. But sometimes the obvious is hidden in plain view and needs to be pointed out and elucidated upon in order for us to comprehend its importance. The same could be said about other self-evident laws such as the law of contradiction[1] or the law of supply and demand. The law of contradiction was explained by the famous philosopher Aristotle over 2300 years ago in book 4 and 11 of his Metaphysics:

"It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect… this is the most certain of all principles." [Book 4: p. 10005b]

"There is a principle in existing things about which we cannot make a mistake; of which, on the contrary, we must always realize the truth—viz. that the same thing cannot at one and the same time be and not be, nor admit of any other similar pair of opposites. Of such axioms although there is a proof ad hominem, there is no absolute proof; because there is no principle more convincing than the axiom itself on which to base an argument, whereas there must be such a principle if there is to be absolute proof. But he who wants to convince an opponent who makes opposite statements that he is wrong must obtain from him an admission which shall be identical with the proposition that the same thing cannot at one and the same time be and not be, but shall seem not to be identical with it. This is the only method of proof which can be used against one who maintains that opposite statements can be truly made about the same subject. Now those who intend to join in discussion must understand one another to some extent; for without this how can there be any common discussion between them? Therefore each of the terms which they use must be intelligible and signify something; not several things, but one only; or if it signifies more than one thing, it must be made clear to which of these the term is applied. Now he who says that A is and is not denies what he asserts, and therefore denies that the term signifies what it does signify. But this is impossible. Therefore if ‘to be so-and-so’ has a definite meaning, the opposite statement about the same subject cannot be true." [Book 11: pp. 1061b-1062a]

Even though the law of contradiction is a maxim of logic, Aristotle said "there is no absolute proof" of its validity except through the ad hominem method, yet "there is no principle more convincing than the axiom itself on which to base an argument, whereas there must be such a principle if there is to be absolute proof." Even though ordinary people and the elite used the law of contradiction to argue, reason and prove the truthfulness of their words and deeds in their daily lives and in their law courts before Aristotle’s time, Aristotle still felt the need to explain the law as clearly as possible to not only offset those few among him who argued contrary (to be argumentative, it seems) to the obvious truth of the principle of contradiction, but to also to affirm the axiomatic nature of the law: the law must be "if there is to be absolute proof" at all. For different reasons I also think it is important to elucidate and affirm the law of knowledge.

The reason I think it is important to understand fully the law of knowledge and its implications is because it leads to logical answers for the theological problem of evil[2] and subsequently the meaning of life. It also may lead to better teaching methods, better understanding in science, philosophy and other disciples. The law also demonstrates the difficulty in ascertaining the truth: you need to know a great deal of correct information in order to correctly find the truth and this is one good reason for each of us to be slow to judge one another.

Can I or anyone else ‘prove’ the law of knowledge? Such proof would depend on one’s definition of proof and one’s understanding of the law. Inductive logic and examples of learning help to prove the law of knowledge in a similar way that Aristotle’s reasoning and examples helped to prove the law of contradiction. I believe if one carefully reads through my examples and compares them with other examples in their life, one may well find that this law works in all situations pertaining to learning without contradiction and thus should be in the realm of ‘law’ as is the ‘law of contradiction.’ I believe, as I have written about in other papers, that the full cognizant understanding and the usage of both the law of knowledge and the law of contradiction are the only sure pathway to the truth, and this is what makes both of these laws so important and is one reason I wrote this paper.

More on the Law of Contradiction (aka: Law of Non-Contradiction) can be found here.




What is knowledge? The definition of knowledge has a board meaning among the general population and even its philosophical meaning is still being debated among philosophers. This paper will emphasize true knowledge about things and objects, processes and techniques, being (what is), etc. False knowledge is about what is not real (rumors, fictitious ideas, fiction, etc.).

knowledge —


• is the intelligent-nonrandom information held by our mind’s memory

• true knowledge (that reflects the actually state of reality as perceived through rational beings)

Law of Knowledge


The mind gains information through a series of processes that can be generalized by the equation called the "law of knowledge."


Basic Definition of the Law of Knowledge:


Knowledge of A is equal to and dependent on the knowledge of non-A.


• Where A can be any particular object, technique or belief;

non-A is anything but that particular object, technique or belief.


It follows —


The depth of one’s knowledge of A (and it truthfulness) is contingent upon the depth of one’s knowledge of non-A; particularly, in the case of opposite qualities (light and darkness), you must know both qualities to know either; you must compare each with the other to know either.


In other words:

• To know A you must also know something to everything about non-A;

• The knowledge of A presupposes at least some knowledge of non-A;

• In order to know A you must compare A with non-A;

• the knowledge of A (and its truthfulness) is proportional to the knowledge of non-A.


True Knowledge through the law of knowledge:


The continuum from incorrect knowledge to absolute true knowledge:

• The less one knows about non-A, the less one knows about the truthfulness of A and the more likely one’s knowledge is incorrect.

• The more one knows about non-A, the more certain one knows the truthfulness of A.

• If one knows all that is non-A, one knows absolutely the truthfulness of A.

• An omniscient being would know the full truth about A because the being would know the full truth about non-A; less than an omniscient being would not know the full truth about A because he would not have the full truth about non-A.





Knowledge of Opposite Values

Light and Darkness: A way to explain the law of knowledge is to manifest how it works with opposite qualities. To begin we will use the example of a totally blind person (from birth). Try to empathize with a person that was totally blind from birth. Light is the quality that allows one’s eyes to see objects. Without light no one would see even if they had perfect eyes. Light is the quality that the totally blind person cannot perceive or comprehend and is clinically recorded as NLP — "no light perception."

If one has never seen light, how would you explain light to that person? What choice words would describe light to someone who has never seen light? To explain anything to someone who has never seen it, you have to use comparison, and say it is like this or like that. But there is no comparative quality in the universe that compares with light. It would be impossible for someone to explain light to another, let alone sight, if that person had never seen light.

Yet at the same time one truly doesn’t know what darkness is until one has seen light. The very definition of dark is: "without light." Darkness means without light as light means "without darkness." Each definition is dependent on its opposite quality. A definition of something is a statement of the knowledge of that thing. To know light or darkness by their very definition presupposes knowledge of each other. A totally blind person in order to know what darkness is, would have to see light. He knows darkness only if he sees light, for it is only then that he will understand what people were talking about when they spoke of darkness. The only reason that anyone can close their eyes, and call the result darkness, is because they have seen light. One cannot know darkness or light unless one has seen both and compared both qualities with each other. Specifically in the case of opposite qualities, one’s knowledge of light (A) is dependent upon and equal to one’s knowledge of darkness (non-A), and vice versa.

The ability to see light and darkness does not bring sight. We are blind if we do not see light and we are blind if we only see light. There is more to sight than just knowing both extremes. Real knowledge does not dwell in extremes, it dwells in-between: we only have sight because we see in shades of light (colored) and varying luminance.

Sound and Silence: The same applies to sound and silence. If one has never heard sound, how would he know what is silence? Sound and silence are opposite qualities as light and darkness are opposite qualities. You must know both to know either, and you must compare each with the other to know either. Since these two qualities are interrelated, one has to know both to know either. The very basic definition of sound ("without silence") and silence ("without sound") need the opposite quality to define it. To know sound or silence by their very basic definition presupposes knowledge of each other.

Life and Death: Further, one doesn’t know what life is until he has known or seen death. To have knowledge of life you must have knowledge of death. One is very aware of life only if one has seen or become aware of death. Life and death are comparative qualities and are tied to each other in our minds. We can only know what life is if we know what death is and vice versa. Real understanding of both comes from knowing what is between both extremes. One extreme is death; the other is eternal life. Between these extremes is the sickness-health continuum. It is the knowledge of the differences that lay between the extremes that gives us understanding and appreciation of life.


Knowledge of Relative Values


Hot and Cold: The law of knowledge also applies to qualities of hot and cold, except these two qualities should be called, comparative opposite qualities. One knows something is cold only so far as he has something hot to compare it with. You can place your hand into a container of water that is 90 degrees and it may feel warm to you depending on the relative temperature of the air around you. But if you place your hand into a container that is 120 degrees and keep it there for a while, and then place it again into the container of water of 90 degrees, the 90 degree water will then feel cool while before it felt warm. Your knowledge of hot or cold is obtained through contrast and comparison of both qualities. Knowledge of hot or cold presupposes knowledge of the other quality. Hot and cold are comparative qualities and are tied to each other in our minds because they are comparative qualities.

Good and Evil: It follows then that since good and evil are opposite qualities, in order to know good you must know evil, but also to know evil, you must know good. In order to "know" either quality you must compare both qualities with each other. Conceptually, good and evil are opposites, yet they are also tied to each other in the mind. Good and evil are comparative qualities.

Right and Left: The right side has no meaning unless there be a left side just as good has no meaning without evil. You don’t know what the meaning of right is until you know about left; you don’t know what left is until you know what right is. You need knowledge about both to know either. You don’t know something is "high" unless you know there is something "lower." You don’t know something is "low" unless you know something is "higher." You don’t know a "plus" quality until you know its "minus" quality. You don’t know a "minus" quality unless you know its "plus" quality.

Appreciation and Knowledge: You don’t know or realize harmony, if you have never known confusion. If one had always lived in an environment where there was no confusion, where there was only harmony, would he realize the goodness of that harmonic environment? Would harmony be appreciated or mean anything special in such an environment? Can anyone really appreciate harmony if they have never lived in confusion? Confusion and harmony are comparative qualities and one only knows either by knowing both.

Appreciation: What does it mean to appreciate something? Webster’s Dictionary says that to appreciate something one must: "recognize it gratefully; estimate its worth; estimate it rightly; be fully aware of it; and notice it with discrimination." When one comes to appreciate something, one in fact comes to know that thing and be grateful for its worthiness. One comes to know the worth of good only after he has lived in evil. There is no such thing as paradise without learning or living in its contrary; there is no such thing as harmony without living in its contrary. How can one really know what it is to be happy unless one has been sad in the past before. Both are comparative qualities and need each other to make sense out of the other?

So far we have mostly talked about opposite qualities such as light and darkness or good and evil. But the Law of Knowledge not only explains knowledge of opposite qualities, but also knowledge of everything capable of being known.


How a Child Learns What a Cow Is


Another way to understand the Law of Knowledge is to understand how a child learns. Children’s simple generalizations reflect lack of differentiation. That is, a child’s wrong generalization about a cow (A) reflects lack of knowledge of the difference between a cow and all that is not a cow (non-A), such as other four legged animals.

A child when he is first learning about four legged animals sometimes may mix up a cow and a horse, or a cow and a deer, or even a cow and a dog. This is because the child does not know what a cow is not. When parents first begin telling their child what a cow is, they point to a cow and say, "that is a cow." The child ‘sees’ this living animal with four legs. Yet he doesn’t know what a cow is very well. His knowledge is superficial because he may only have seen a few other four legged animals and thus has little to compare the four legged cow to.

Depending on how many other four legged animals are pointed out to him, he may still mix the cow up with any or all other four legged animals. After a cow is pointed out to him he may call a horse a cow, after all, to the child a horse is a four legged living animal (not a two legged animal or a toy animal or stuffed animal) just like the cow pointed out earlier by his parents. But the child is wrong. This four legged animal is a horse, not a cow. The child fails to differentiate between a cow and a horse. How does the parent correct the child? The parent says, "no, it is not a cow, it is a horse." The parent is telling the child what a cow is not. The parent by telling the child what is not a cow, is helping the child to learn what is a cow. Normally, after the child learns that a horse is not a cow, he normally doesn’t call a horse a cow again. But the child may call a deer or other four legged animals a cow. When the child does this he is again corrected, "no, it is not a cow, it is a deer." The child has learned something else is not a cow (A); he has learned one more of the non-A’s (all else besides cows). The more the child learns about other four legged animals not being cows, the better he is able to understand what a cow is. A cow is a four legged animal of a certain size (a cow is not a dog because for one thing a cow is bigger than a dog, etc.) and not any other four legged animal: it is not a dog, it is not a horse, it is not a deer, it is not an elephant, it is not a bear, etc.

But further the child from other knowledge knows a living cow is not a mountain, it is not dead (not a dead toy, not a dead stuffed animal, etc.), it is not a rock, it is not the sky, it is not a two legged animal, it is not an ant, it is not a fish, it is not fog, it is not a color, it is not a quality like "good," it is not a plant, it is not water, etc. The child knows more about what a cow is, by learning more what a cow is not. Thus, the knowledge of a cow (A) is dependent on the knowledge of what a cow is not (non-A); the more he knows what a cow is not (non-A) the more the child knows what is a cow (A).


How a Child Learns the Color Green

Let’s use another example, the color green. The more we know what the color green is not, the more one knows the uniqueness of the color green. In order to know the color green, one needs to do more than just have it pointed out, one needs to have pointed out what green is not. Since most of us know what the color green is, we will again try to understand how a child learns the color green.

First "green" is a subdivision of color. Before a child can learn what the color "green" is, he must know what is color. In order for a child to understand "color" his parents tell him, "that thing is the color green, that thing is the color red, that thing is the color blue, that thing is the color orange, that thing is the color purple, that thing is the color .…" Along with learning what color is, the child comes to understand (through comparison) what color is not: the color green on a wall is not the wall, it is not the material that makes up the wall such as wall board, or wood studs, or nails, etc., but the quality on the wall that we call "green" is the color of the wall. A child learns what the color is by understanding what color is not. So before a parent can make a child understand exactly what the "color" green is, the child has to understand what "color" is, by understanding what "color" is not. Once he understands the concept of color, this knowledge becomes acquired knowledge, and he can use this prior knowledge to build a better understanding of the color green. He comes to understand what the different colors are because each color is being named or pointed out to him by his parents or teachers. If his teacher correctly points out to him the color that is universally taught as green, then he obtains the true knowledge of green. Through comparison with past knowledge in his mind, he comes to know what green is and is not. If he is taught incorrectly what the color green is (his teachers points out red, but calls it green), he obtains false knowledge.


Green is not:


a tree, a bush, a rock, an animal, a fish, a man, the universe, the sun, the moon, our parents, a car, a road, atoms, space, form or shape, relative position in space, time, a dimension, or any other thing or quality except for a quality we call "color."


More specifically green is not:


red, blue, orange, purple, nor any other color but green


Note: The nature of green or any other color has to do with human brain and its software, and the way mind-brain interprets the electromagnetic spectrum rays reflecting off the ‘green’ object.

To summarize, green is A; green is not non-A (a rock, a shape, a concept, or red). We know green (A) because we know what green is not. Knowledge of A is equal or dependent on the knowledge of non-A.

Afterword: There are other subdivisions of this law, which are dependent on how one defines a category. The mind seems to have a need to classify things, which may be some aspect of the mind’s wiring (software). An example of a subdivision is: the knowledge of cows (A) is dependent on how we categorize cows as well as well as one’s knowledge of all the non-cows in that category (some non-A's), as well as our knowledge of all that is not in that category (the remainder of non-A's).




End Notes


1. Also known as the "law of non-contradiction" and the "principle of contradiction"


2. How or why can a good all powerful God allow evil, death and destruction in his universe



Copyright (c) 1970-2014 by Walter R. Dolen


[First published in early versions of the BeComingOne Papers and was first conceived in a college essay. This version is a 2014 updated improved version.]


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