The Practical Side of Heaven: Chapter Two, Part Eight: The Three “Basic” Laws of Logic and How They Affect Reasoning

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Chapter Two, Part Eight: The Three “Basic” Laws of Logic and How They Affect Reasoning

The three basic laws of logic are:
. The Law of Identity.
. The Law of Non-Contradiction.
. The Law of Excluded Middle.

The law of identity institutionalizes the prevailing theory of nature stating that every member of a class, say class X, has the same nature as every other member of that class. From this we can conclude that every member of that class is, by nature, X, and only X. In symbolic terms, this simply means that X is X.

As obvious as X is X may appear, its consequences are not. The law of identity justifies generalizations, and therefore, the concept that reasoning in terms of absolutes and certainty is logical. If everyone agrees that X is X and only X, it is reasonable to generalize, and be absolutely certain, that every X is X.

Generalizations that describe single nature classes are necessary and good. How could scientists conduct experiments if they could not be certain of weights and measures?

Problems arise when we try to generalize about classes with more than one nature. Light, for example, is problematic in terms of the law of identity. According to this law, light is either a wave or a particle. Yet the new sciences demonstrate that light is both a wave and a particle.

Even greater problems arise when we think it reasonable to generalize that one standard of human nature applies to all humans. This leads to judgmental reasoning that can be destructive. For example, if one generalizes that the standard of human nature is a white, heterosexual, Protestant, male, and some do, then one can reason that blacks, homosexuals, Catholics, and women are inferior or even nonhumans. It is exactly this kind of judgmental reasoning that justified the genocide of American Indians, Jews, and Albanians; racism and bigotry in all its forms; and persecution by any name.

The law of identity also supports generalizations like there is only one best idea, belief or standard that correctly describes every class. This concept justifies those who think that their religion, country or economic system is the best. Most of us have felt threatened, and some have even been put in concentration camps, by those who reason that their beliefs and standards are best for everyone.

Language Problems Created by the Law of Identity

A wise man once said, “language exists on the surface of our consciousness. The great human struggles are played out in silence and in the inability to express ourselves.” Let us now explore why this may be so.

The law of identity makes it logically impossible to communicate the idea that some classes can be more than one thing at the same time. For example, we can say that light is both a wave and a particle, or humanity is both human and godlike, but our language cannot convey what this means. According to the law of identity, X is X. Therefore, the plural form of X implies more than one X. This excludes being able to communicate the idea that light (X) is both wave (X) and particle (Y), or that humanity is both black and white. According to the law of identity, light is either a wave or a particle, and humans are either black or white.

It is difficulty to use the term ‘humans’ because our language cannot convey the idea of more than one human nature. When X is X, the plural form of human—humans—implies many human beings that share a common nature, not many humans with diverse natures. This excludes being able to logically communicate the idea that human diversity is natural because the law of identity allows for only one definition of human nature. The uncomfortable feeling that occurs when trying to say human natureS or humanitieS demonstrates that our present system of logic does not have the capacity to encompass diversity within classes.

How the Law of Identity Undermines Free Will

The law of identity makes free will impossible to practice when free will is defined as freely choosing between rational alternatives.

The noted psychologist, Erich Fromm, believed that free will is contingent on freely choosing between rational alternatives. According to Fromm, “man’s freedom lies in his potential to choose between the real existing possibilities. Freedom, in this sense, can be defined not as acting in the awareness of necessity [animals do that], but acting on the bases of alternatives and their consequences.”

Free will, then, cannot exist as long as the law of identity is applied to all classes. According to this law, there can be only one correct choice in every category of choices. This makes free will an exercise in finding that one correct choice, not choosing between rational alternatives.

In classes with one nature, like the shortest distance between two points, for example, only one rational option exists, a straight line between the two points. Because this answer, and only this answer, describes the class, we can claim to have found the correct answer, but not to have practiced free will. To practice free will, we need rational alternatives. The law of identity denies us these alternatives by limiting each class to one definition.

How the Law of Identity Pits Science Against Religion

The seemingly irreconcilable conflict between science and religion is rooted in the law of identity. For if every class is limited to one best definition, we are limited to thinking that truth has only one description. And because science recognizes only those truths based on objective facts that are universally accepted, and religion accepts truths based on personal and subjective experience, we cannot expect that truth will be described by both in the same way. We cannot, therefore, expect science to be compatible with religion as long as the law of identity limits truth to one definition. The conflict between creationists and evolutionists exemplify one of many seemingly irreconcilable conflicts between subjective and objective truths.

We can go so far as to say that the law of identity generates almost every irreconcilable conflict. We can, for example, recognize that this law underlies the conflict between mind and heart, left and right brain, flesh and spirit, yang and yin, Adam and Eve, maleness and femaleness, and science and religion. For here, again, the first term in each category relies on objective facts, and the second, subjective facts. Therefore, we cannot expect both to define truth, wisdom, or reality in the one way that the law of identity requires.

In effect, irreconcilable conflicts are, in principle, a manifestation of the law of identity because it allows only one standard or definition of truth for every category or class of truth. This excludes any real possibility of reconciling two sides of any conflict that measure truth by different standards. Compromises may be reached between members of each of these categories, but never one solution that is totally right for both. Conflict resolution will never be equitable as long as what we believe is reasonable is limited to the law of identity.

Law of Non-Contradiction

What justifies the dualistic reasoning that divides and separates us from others, the world, and God? What justifies the dogmatic reasoning of radicals? What justified the beliefs of Nazis or the actions of Serbian Christians and Muslims towards each other? It is the law of non-contradiction, for it makes the concept of relating “all” ideas/reasoning in terms of either/or, yes/no, us/them, and I/it appear logical.

The law of non-contradiction states that each member of a class is not only identical to every other member in that class, or that X is X, as the law of identity states, but also that the nature of a class cannot be what it is not, say X and non-X. Symbolically, the law of non-contradiction states that X is not non-X.

According to the law of non-contradiction, it is reasonable to assert that a given quality either belongs, or does not belong, to a given class. For if there is a single nature that represents a class, everything in that class must exemplify that one nature. In effect, the law of non-contradiction divides everything into two categories. One category that encompasses that which exemplifies the nature of the class, and a second category that does not.

Dividing the world into these two categories lays the foundation for dualistic reasoning—relating ideas in terms of either/or, yes/no, us/them, black/white, right/wrong, and I/it.

Dualistic reasoning can be good. Computer technology relies on yes/no thinking. And science in the traditional sense relies on either/or reasoning. For instance, either 16 ounces is a pound or it is not.

Dualistic reasoning can, however, be problematic. It justifies the concept that we are separate and distinct from all else by teaching us to reason that we are either individuals or nature — not that we can be both individuals and one with others and nature. This undermines the concept of new thought teachers that both individuality and universal oneness are irreducible principles.

It is true that the feeling of separation at times vanishes and we experience oneness. Our concept of separation blurs, for example, when we are in love or empathize with others or nature. Nonetheless, the law of non-contradiction, and the either/or reasoning it demands, so dominates us that even these flashes of oneness quickly fade and we soon feel separation again.

Some Aborigines, it seems, think of themselves as one with nature. The reason why this may be true is that they do not relate ideas according to the law of non-contradiction. They perceive themselves to be both individuals and one with nature.

The fact that some Aborigines feel one with nature, whereas we feel separate, implies that how we relate to others and the world is learned and is not an innate quality of human nature. As long as we accept the law of non-contradiction, separation will dominate our thoughts, and oneness will be limited to moments of love and occasional experiences of bliss.

The Jewish mystic, Martin Buber, in his book, I And Thou, recognizes that we perceive our relationships to others in terms of separation, rather than in terms of oneness, or in terms of “I-It,” rather than “I-Thou..” Buber says, “There is no ‘I’ taken in itself, but only the ‘I’ of the primary word, I-Thou, and the I of the primary word, I-IT. When a man says I, he refers to one or the other of these…. When a primary word is spoken, the speaker enters the world and takes his stand in it.” (14)

This sensitive mystic understood that each individual relates to others in one of two ways. Either he “meets” others and loses his sense of separation in relationship with them, in which they are no longer an “other,” but rather a “Thou.” Or he is aware of his and their difference and their separateness, in which case they are experienced as an “It.” To be a “Thou” is to be accepted nonjudgmentally, with affection, care, even love, for a “Thou” is embraced by the “I” as one with itself. To be an “It” on the other hand, is to be perceived as a separate thing, rather than one with the self. In the “I” – “It” – relationship, the other becomes an object rather than a subject; an “It” rather than a “Thou.” According to Buber, there are only two ways to be in the world: in a relationship of “I-Thou” or in a relationship of “I-It.” There can be no “I” apart from one of these relationships. Either the “I” is relating to a person, an object, an animal, a tree, a car, or a sunset and is aware that the “I” is separate from whom or what it is engaged with (I-It), or the “I” is lost in the wonder of oneness with whatever or whomever it is engaged with (I-Thou).

Martin Buber is suggesting something very profound. Subconsciously our reasoning leads us to think of the “I” as separate and distinct from the person or object encountered. What he doesn’t say is what causes our reasoning to separate us. I propose that it is our acceptance of the law of non-contradiction that justifies our relating to others in terms of I/it.

The law of non-contradiction covertly supports the separation of spiritually and intellectually dominant individuals and organizations. Stereotypically, those of us with intellectual personalities value facts and experience over the intuitions and subjectivity of those with a spiritual or artistic personality. Intellectuals, for example, consider reason the path to a better world. Some spiritual groups, however, teach that the mind must be quieted before one can grasp the truth. The result is that the intellectually dominant individuals and organizations separate themselves from spiritual individuals and organizations. In effect, the law of non-contradiction supports those who minimize views and beliefs that differ from their own.

Not only does the law of non-contradiction separate us from one another, it comes between many religious people and their God. Jesus, in John (17:21), for example, teaches that we are meant to be “one with the father.” When we read this, we may feel we understand what Jesus means, but our minds cannot truly comprehend it. The reason is that by simply saying the word God, we separate ourselves from God, because the law of non-contradiction has trained the mind to reason that we are either humans or Gods, not capable of being both individuals and one with God. All one needs to do to experience this ingrained training is to say the word God, and the image that comes to mind is one of God out there, and we, here, i.e. separate and distinct entities. As long as the law of non-contradiction dominates our reasoning—except for occasional flashes of bliss, love and empathy—the acknowledgement of oneness with God, nature, and others will be the exception, and the feeling of separation will be the rule.

When applying the law of non-contradiction to human beings, we can also recognize that this law is the major source of personal and social problems. This law, and the reasoning it produces, was behind the persecution of “communist sympathizers” by the Committee on un-American Activities. It was the either/or reasoning of that committee which led to labeling everyone as either communist or noncommunist. This same dogmatic either/or reasoning is what justified the burning of heretics in the Inquisition and witches at Salem.

When applied to human beings, the law of non-contradiction also provides justification for intolerance to those who are different. In other words, when we use either/or categories to identify ourselves in terms of gender, nationality, race, religion, political preference, sexual orientation or economic status, we place ourselves in opposition to others. It is important to note that merely differentiating ourselves from others would not create a problem if we did not also believe that there was just one right or best way for human beings to be. If we accepted differences as natural, and did not add the negative judgment that one’s own group was the right one, or at least better than all others, then we would not find ourselves in conflict with each other. But we do. Why we do is the legacy of reasoning according to the law of non-contradiction.

The Law of Non-contradiction and Language Problems

The law of non-contradiction limits our ability to communicate in caring ways because it allows only one correct definition for each class of words. This “tends to pit classes of words, like ‘cooperation,’ against other classes, like ‘individuality,’ so that they clash like swords.”

We see the consequences of these clashes when a friendly conversation turns into a shouting match. For when a listeners’ ideas differ from what is being said, he or she often feels challenged. This challenge, however, does not necessarily come from the speaker. Rather, it more often comes from a third source – the subliminal notion of the listener that he can be right only if the speaker is wrong. This notion is the product of the either/or reasoning that is justified by the law of non-contradiction.

The cliché, “never discuss politics and religion with relatives,” illustrates that the either/or characteristics that the law of non-contradiction breeds into our language play a determining role in how we are understood. Having to explain that we didn’t mean what others thought we said illustrates that the law of non-contradiction adds meanings to what we say that are foreign to what we mean. It can be said that the law of non-contradiction puts our language system in control of how we are understood.

The Law of Excluded Middle

The third law that institutionalized the prevailing principle is the law of excluded middle. This law states that not only is X, X, and that X is not non-X, it adds that X is X and nothing in between. For example, we cannot say that the flying horse, Pegasus, is a horse, because Pegasus is in between a horse and a bird.

According to this law, every quality either belongs, or does not belong, to a given nature. There is no logical compromise, or exception, and no middle alternative. It is this law which accounts for Aristotelian logic’s hierarchical nature. For if there is a single nature for every class, that which has more of that essential quality will be judged superior to that which possesses less. Based on the law of excluded middle, the concept of the hierarchy of values is established.

Like the laws of identity and non-contradiction, the law of excluded middle is appropriate to apply to single nature classes. For example, it would be confusing to call unicorns horses. Even though they do have similar characteristics, unicorns are different from horses.

As long as a class is considered uniform, no particular problems arise with regard to what we observe of it. But we human beings typically define ourselves in terms of sexual, political, national, religious, economic, racial, and social differences. If human nature is defined in one exclusive way—which is precisely what happens when we identify in hierarchical terms—the implication is drawn that if those who are different from us are wrong, bad, or somehow inferior, then we must be right, good, and superior.

Hierarchical reasoning leads us to conclude that there is but one “best” in every category, which divides and alienates us from our fellow human beings. In practice, this concept justifies reasoning that “bigger is better,” “my religion is the true religion;” and “if America isn’t No. 1, who is;” and most every other claim that something is superior to all others.

Low self-esteem is also rooted in hierarchical reasoning. When we judge ourselves in relation to others, we may feel inferior to them because we are heavier or not wearing designer clothes. The whole idea of judging ourselves as inferior to others is created by the concept that one quality in every class is superior to all others.

Pride, negativity, social status, prestige, and elitist thinking, like low self-esteem, are also the result of hierarchical thinking. Ideas such as “keeping up with the Joneses” and “you can never have too much money;” and eminent domain, privilege, super heroes, super markets, and even heaven (as commonly interpreted) would be nonsensical without the concept of superiority. All hierarchical reasoning is justified by the law of excluded middle.

The Law of Excluded Middle and Language Problems

The law of excluded middle, like the law of identity and non-contradiction, also limits our ability to communicate nonjudgmentally.

Most words are meaningless unless they can be related to another term. Up, for example, is meaningless unless we can relate it to its counterpart, down. Recognizing this opens us to the real possibility that the law of excluded middle covertly adds hierarchical characteristics to the words we use. When we use words like males, capitalists, or straights, for example, many of us subliminally relate these terms to their unspoken counterparts according the law of excluded middle. Consequently, some males may feel superior to women, some straights superior to gays, some Christians superior to non-believers, some capitalists superior to communists, and vice versa. The point is that the law of excluded middle subliminally leads us to relate to others in hierarchical ways. There is no natural reason for such hierarchical thinking. It is the law of excluded middle that makes relating ideas in terms of hierarchies reasonable.

In principle, then, bigotry in all its forms is the manifestation of the law of excluded middle. Said another way, the law of excluded middle is the prerequisite of the concept of superiority, which in turn, makes difference a problem when, in reality, difference is simply difference.

Evidence of the Inadequacy of the Prevailing Theory of Nature

There is much debate that new systems of logic are needed because of discoveries made in the new sciences. The basic argument is that civilized laws of logic are true only if the assumed principle, namely that all classes have a single essence or nature, is true.

Simply said, the new sciences demonstrate that some classes do have more than one nature. Light, for example, has the nature of both a wave and a particle. Such classes warrant the new principle that some classes have more than one nature. This principle justifies the need for an additional system of logic that Gnostic Christians call nonjudgmental logic. In practice it would be appropriate to use the traditional system of logic when considering single nature classes, and nonjudgmental logic when multiple nature classes are concerned.

Said another way, our present system of logic is logical only if the principle it is based on is correct. The new sciences objectively demonstrate that some classes have more than one nature. This fact not only challenges the credibility of using our present system of logic in all cases, it establishes the need for an additional system of logic to be used in cases where classes have more than one nature. This knowledge is fundamentally important.

The assumption that there is a single nature for every class has met challenges from both recent philosophy and science. Contemporary physics has made discoveries which challenge our traditional understanding of the nature of the world. These discoveries also seem to imply that it is a mistake to continue to reason that a single nature can adequately characterize every class of phenomena.

In the case of light, two different and apparently mutually exclusive forms may, under certain conditions, correctly describe the same phenomenon: light as a particle, light as a wave. Waves and particles are very different kinds of things. For example, particles have clear and sharp boundaries; they exist at one place at one time. Waves, to the contrary, are without sharp boundaries; they spread out through their medium and hence are never at one particular point or place. Particles are like balls, while waves are like ripples on a pond or ocean waves crashing against the shore. A wave ideally spreads out to infinity, whereas a particle collapses to a dimensionless point. Waves are divisible; particles are not. So a particle is not a wave, nor is a wave a particle, yet light behaves like both! “Microphenomena, as discovered in this century, have required the combination of two descriptive vocabularies which our predecessors had so defined that they were incompatible with each other.” In short, there is not a single nature of light. Both the nature of particles and waves are equally necessary to appropriately describe the phenomenon of light, according to the generally accepted view known as the “Copenhagen interpretation.” This is “the view that fundamental micro nature is indivisibly bipartite–the wave-particle duality. If in our scientific analysis one of these aspects were subordinate to the other, the result would be not only an unbalanced picture of elementary particles but also a factually false one.”

A May 1996 article in Science News reported an experiment done on a cold beryllium atom which vibrated harmonically, producing what is said to be “a superposition of two ‘coherent-state wave packets.'” In layman’s language, this means that the atom vibrates in such a way as to produce the appearance of being in two different places simultaneously. “For a brief period, the atom appears to exist in two places,” said physicist Christopher Monroe of the National Institute of Standards and Technology, in Boulder, Colorado. It exists both here and there, in two places at once. This is strange, and stranger still, if we attempt to put it into the framework of Aristotelian either/or logic.

It would seem that a similar analysis could be made of the notion of time in contemporary physics. Relativity theory suggests that, depending upon one’s relative perspective or frame of reference, an event can be said to occur before, later than, or simultaneously with another event. Logically speaking, if an event happens before another, it cannot happen at the same time or later than the event in question. Similarly, if an event happens at the same time as another event, it cannot happen before or after that event. But according to relativity theory, depending upon the framework from which one is observing, the same event may be judged to have occurred before, after, or at the same time. As in the case of light, conflicting forms of description are equally appropriate, given one’s perspective.

The important point to notice here is that we are becoming aware that it is a mistake to attempt to reduce some things to a single best description. It is clear that not everything can be correctly comprehended by one description of its nature. In contemporary physics, for example, scientists use both the traditional Newtonian as well as quantum measurements, even though the models for Newtonian physics and quantum mechanics are completely different. Their underlying assumptions may even be said to contradict one another.

Nobel Laureate in Physics, Wolfgang Pauli, used the phrase “the irrationality of reality” to indicate that reality may include a non-rational element. “Since the enlightenment, the ‘laws of nature’ have been seen as an expression of the rational features of reality. In fact, the existence of such laws is what makes the rational description of phenomenon possible. It is characteristic of Western thought to see such rationality as an indispensable property of reality; every thought that is real is supposed to be rational [i.e., fit our laws of logic]. Pauli, however, attacks this basic belief calling it the ‘repression of the irrational’ … [the] ‘lesson of atomic physics’ … forces us to abandon our fundamental belief in the rationality of reality … the irrationality of reality must be considered an essential property of reality.” Smith, as summarized by Griffin, like Pauli, “holds that a position cannot be fully accurate unless it is inconsistent, unless its doctrines are not coherently conceivable.”