With respect to the nature of understanding, for example, we might take the view that what cannot be understood is that which has no other. This notion of other is taken in two ways, and each way ushers in its own particular problem. The first problem is this: to understand something there must be at least something else against which that something can be compared and contrasted, against which there can be some standard of judgment, and, if there is no other something, then there is no yardstick by means of which to judge the first something. The second, considerably more cantankerous, problem has to do with language: to make something intelligible in words implies that there is in the very least words in addition to that something that is to be put into words, and that some sort of correspondence can be had between words and that something. Without words, the something must remain unintelligible. Without words, there’s not much of worth to be known——this, at least, is the customary time-honored view.

Yes, words. Proud words, bearers of all that is worth knowing.  They are signs that link up to that with which they are interdependently, interrelatedly, interactive by way of cultural conventions. The problem is that during the past century, words became the spoiled offspring of more basic nonverbal signs. After the so-called ‘linguistic turn’ in the humanities and social sciences, we have come to consider language not merely the culmination of human expression, but the heart and soul of all thought and communication. Language now predominates to the extent that we take virtually all signs of sight, sound, smell, taste, and tactile sensations basically in terms of language, language as mediator and revelator of concrete experience. Sensations must pass through the language filter before they can become adequately understood. And mind is the grand adjudicator deriving understanding from language. Mind is the knower of what is to be known, and body, processor of sensations conveyed to mind, is no more than at best a willing servant. Consequently we tend rather contemptfully to relegate the more basic semiotic forms of communication directly emerging out of concrete sensations received by body to the category of relative unimportance, or we attempt conveniently to ignore them, while rendering homage to mind.

It is quite comfortable to assume that if something is intelligible it must require language, and that by and large European languages are chiefly dualist——bivalent——in nature, following traditional logical tenets. This puts everything into neat sets of pigeon-holes. But what if reality is fundamentally nondualistic? What if certain aspects of the world resist either/or imperatives? What if the world itself is of contradictory, inconsistent nature? In such case, the world must be made unintelligible, according to the imperatives of classical logic. We might tend to rebel against the very thought. We want crisp, clear-cut words and meanings. In order that reality may be made intelligible, for every concept or word there needs be something against which it stands. Here the word, there the thing. Here the word, there the maker or taker of the word. Here the word, there the meaning. Quite comfortable, all this.

The Christian edifice also enjoys its root beginning with the dualism of good and evil. After all, Christianity——along with Greek philosophy, which is also injected with a massive dose of bivalency——is where much of Western thought begins. Everything else emerges from there. Adam and Eve knew neither happiness nor sadness, neither joy nor sorrow, neither pleasure nor pain, until they partook of the fruit of the tree of knowledge, of good and evil. And, of course, it had to be a slithering, formless, nonbinary and unstructured serpent that was instrumental in bringing about this original sin.

Unintelligibility can be considerably less mundane than metaphysical thought and ancient religious accounts. Concepts that incorporate falsehoods as if they were true may actually be unintelligible. The ancient notion that the earth rests on an elephant’s back and the elephant is standing on a turtle’s back is in a manner of speaking unintelligible. It is so unintelligible that we tend to take it as simply child-like. Do the elephant and turtle live forever? Where did two beasts of such magnitude come from? And most perplexing of all, if the elephant stands on the turtle, then what does the turtle stand on? When the story of the earth, the elephant, and the turtle was narrated by a Buddhist monk and he was asked this last question, he is reported to have responded: ‘It’s turtles all the way down.’ The response is in a manner of speaking also unintelligible, because the idea of infinity is implied, and an actual infinity of existent objects is inconceivable.

But, then, one may wish to retort that the elephant-turtle account is mere myth, and should not really be taken seriously. Actually, this account is of mytho-scientific origin; it stems from an attempt to describe and explain the universe. Surprising as it may seem, concepts that incorporate apparent falsehoods as if they were true are also found in many scientific theories, and some of them have even come to be taken as unintelligible. As an example, allowed me to put a certain aspect of quantum theory in a nutshell, if you will, since here, we have an account that could well be for generations of the distant future considered mytho-scientific as well. Is the wave interpretation or the particle interpretation most appropriate for the quantum world? This posed a virtually irresolvable problem for almost two decades. Then Niels Bohr suggested that quantum events can be conceived as either waves or particles, depending on the context. But the catch is that they cannot be waves and particles at the same instant. In the classical, atemporal sense, then, it can be said that quantum events are both of wave and particle nature, or that they are neither of wave nor of particle nature. This quandary remains, at least for classical thinking. The term ‘wavicles’ was proposed for quantum events, but that doesn’t quite cut the cake. It only gives the quandary a convenient label.

John von Neumann developed an alternative logic, ‘quantum logic’, in an attempt to account for the strange world of quanta. Basically, quantum logic does away with the classical Excluded-Middle Principle, though it still holds true to the Principle of Non-Contradiction. If we embrace quantum logic, then classical logic loses face (Heelan 1970, 1971, Putnam 1969, 1971). So we must toss binary values as we know them in the trash can, for nothing would necessarily be true or false, good or bad; rather, some act of mind would be sufficient to make it so. How could this possibly occur? Would not the consequences be devastating for our Western cultural life as we know it? How could we begin to cope in a world the very ground of which has been ripped from underneath us?

Perhaps the problem is not as dire as we might expect, however.

Where our dualism got us
In classical logic, two statements each of which is presented as true, yet they contradict each other, are considered inconsistent. Falsified scientific theories have been so falsified because contradictory statements that were incorporated within the same theory were revealed, and the theory was thereby disproved.
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We find an example of this in Newtonian mechanics. It held the reins of scientific knowledge for about two and a half centuries. Classical physics was a success story the likes of which have occurred few times in human history, if at all. However, a thorn in the side of Newtonian mechanics remained in the form of Mercury’s perihelion. The planet should move in smooth ellipses like the other planets. But it didn’t. It wobbled slightly, creating an unbalancing effect. Thus predictions regarding Mercury’s behavior were less than satisfactorily accurate. And science was stuck with a contradiction. Einstein’s relativity seemed to resolve the issue. At least it resolved this particular issue. But others quandaries remained. For instance, within Einstein’s universe we have the ‘twin paradox.’ One of the twins enjoys a trip around the universe at a velocity approaching the speed of light, while the other twin stays home. When the adventurer returns, many years have transpired on Earth, but as far as she is concerned, her trip lasted only a few weeks. She has aged little, but to her consternation, her sister is now old and infirm. So to the question ‘Can our scientific theories be entirely free of contradictions and hence inconsistencies?’ an ultimate answer can hardly be forthcoming, at least in terms of classical logical terms.

Aristotle is often considered the father of classical logic. Aristotle set out the Identity Principle according to which something is what it is and nothing else, for if it were something else it would not be what it is, hence nothing else can be what that something is either. The Principle of Non-Contradiction is dependent upon the Identity Principle. It says that if something is what it is, then it cannot be anything else. Then there is the Principle of the Excluded-Middle according to which if A is what it is and nothing else, then whatever there is must be A, or it must be Not-A, and there can’t be anything else. There can be no third option between something and that which it isn’t. In a nutshell, that’s about it. Rather disappointing, one might think. Nevertheless, it guided much Western thought for a little over a couple of millennia.

Actually, the condition of classical logic is not as severe as it might appear. When we look at the fine points, we come to understand that A cannot be Not-A at the same time and in the same respect. This greases the wheel a little so it can move in one direction or the other and even make a few wide turns when it must in order to avoid catastrophe. It confines the Principles of Identity and Non-Contradiction to legitimate identities and contradictions and excludes the apparent ones. There is no identity, contradiction, falsity, or unintelligibility in a statement about something that holds at one time and place and in one respect but not at another time and place. To say ‘All people are mortal’ is apparently unquestionable. To say ‘The earth rests on an elephant’s back’ might appear patently absurd, and perhaps even unintelligible for today’s worldly inhabitants. Yet according to certain accounts it was found acceptable by a certain group of people from a past culture. The idea that ‘The universe is (like a) a machine’ predominated Western scientific thinking for a few centuries and came to pervade its general mind-set for generation after generation. Today, however, it has by and large fallen from grace——though there are some well-meaning citizens of the world who apparently don’t know it yet. A sentence is considered contradictory in the strict logical sense only in the event that it is simultaneously subject to affirmation and negation. In such case it is inconsistent, and one might wish to say, unintelligible——though children, poets, and mystics would likely disagree on this point.

In this sense ‘A and not Not-A’ might appear as the sole survivor with respect to iron-clad contradictory sentences. Even such apparently deductive sentences as ‘1 + 1 = 2’ and ‘All people are mortal’ are not absolutely immune to revision under certain circumstances (philosopher Charles S. Peirce himself has said as much). In quantum theory the addition of certain subnuclear particles does not yield a product equal to ordinary arithmetic addition. Rather, it leaves us with less of what we started with. In this manner we might conjecture that we have the equivalent of ‘1 + 1 = 1’. In Boolean logic also, as well as Spencer-Brown’s (1979) ‘Laws of Forms’, if an annotation is made, and then made again, it is the same as if it were made once. Hence also ‘1 + 1 = 1’. Disconcerting.

Even more disconcerting, in quantum theory and relativity, enigmatic numbers called ‘imaginary numbers’ (or √√-1) occasionally pop up. How can we rationalize these numbers? If we say ‘*√-1 = +1’, it’s a strike against us. If we say ‘*√-1 = -1’, we’re victims of another strike. One more strike and we’re out. What are we to do? Say the answer’s both of the possibilities, and it’s neither of the possibilities, which leaves us with a paradoxical situation? There seems to be no rational answer to the problem. Nonetheless, scientists and computer engineers customarily use ‘imaginary numbers’ in their mathematical description of what is presumably ‘real’. Biologist and physicist Howard H. Pattee (1969, 1972, 1979, 1986) goes so far as to speculate that the equivalent of ‘imaginary numbers’ exists at the heart of life processes.

In our age when prosthesis, transplants, and cloning are coming into their own, who knows how and to what extent life can be prolonged a century from now——if by that time we haven’t all destroyed ourselves and our planet Earth to boot. With respect to presumably inductive truths, the sentence ‘All crows are black’ is not absolutely fool proof. We can have no absolute proof, inductively speaking that is, until we have observed each and every crow, past, present, and future, which is to say that we have to be well nigh immortal, thus refuting the deductively or synthetically derived sentence ‘All people are mortal’.

Pouring more salt in our inductive wounds, Carl Hempel’s once demonstrated that in order to obtain absolute proof that ‘All crows are black’, we have to confirm the contrapositive sentence, ‘All nonblack things are noncrows’. This for sure lands us in interminable task. After all, if we spot a nonblack thing, how do we know it is not a crow until we have verified its noncrowness? For all we know it could be an orange crow we overlooked when we were obsessed with our premise that ‘All crows are black’ and we overlook that white thing that happened to be a bird that happened to be a crow. One could perhaps say that by deduction we can try our damnedest to demonstrate that a sentence is not inconsistent, and that by induction we can try our damnedest to demonstrate that a sentence is not consistent, and in both cases we will either end up with an inconsistency, or our search will suffer from incompleteness, given our finite capacities.

The inconsistency or incompleteness of all sufficiently sophisticated formal systems is due to the enterprising work of mathematical logician Kurt Göödel (Nagel and Newman 1964). His two incompleteness theorems reveal the impossibility of our deciding on the truth of a logical system from within that selfsame system. Some scholars have suggested basically the same with respect to ordinary language use, and indeed, with respect to all sign making and taking. The layperson’s example of Göödelian undecidability is a variation of the infamous Cretan paradox in the form of ‘This sentence is not true’. Is it true or is it false? If we say it’s true, then it says of itself that it is not true, so it is false. O.K. So we assume it is false. But that is what it says of itself anyway, so what it says of itself is true, so it is true. We simply can’t win. The sentence refers to itself, it contradicts itself in its self-reference, and thus it sets up an infinite regress. We might wish to say that the Cretan sentence is not true and false simultaneously. We read the sentence, pretty much like we read most sentences, by charitably suspending disbelief and giving it its say. Then, after the fact, we think about what it says of itself, and we balk. Why, the sentence is absurd, nonsensical, and perhaps unintelligible! And we are in a certain sense correct: the sentence actually doesn’t affirm and deny itself in the same breath, in the same instant.

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Willard V. O. Quine (1969) points out that in natural language we can get closest to a Göödelian undecidable sentence with something I have simplified for the sake of the present argument as: ‘‘Is an inconsistent sentence’ is an inconsistent sentence’. The phrase inside the inner quotes is a mirror image of the sentence outside the inner quotes; the first phrase acts as the subject half of the sentence and the second phrase is the predicate half. The problem is that subject and predicate are identical. Now we might say that time enters the picture once again. We read the first phrase. Then, upon reading the same phrase again, our sense of the first phrase undergoes an alteration. Gertrude Stein’s ‘A rose is a rose is a rose’ suggests that it is not only a matter of a rose by some other name being either different or the same. It is also a matter of time. Saying ‘A rose’ and then saying it again alters the context of the first saying and the second saying and it alters the combination of both sayings such that meaning is also altered.

This might all appear fine and dandy. However, the previous couple of paragraphs deal chiefly with logically formulated sentences and genuine paradoxes. What we usually tend to call contradictions are only pseudo-contradictions. For example, assume Charlton Heston, once President of the National Rifle Association, were to declare, ‘The question of our right to bear arms is not negotiable’. Then he is asked: ‘Do you mean to say, Sir, that you are absolutely unwilling to discuss the issue?’ To this he replies: ‘Of course not. I will discuss the issue until I am blue in the face. The fact remains, however, that our right to bear arms is not negotiable’. Then: ‘But with all due respect, are you not contradicting yourself?’ The disgruntled reply: ‘It seems a contradiction, but it is not. I cannot refuse an offer to discuss this problem, but my mind is settled on the topic’.

Marxist intellectuals often adopt some version of Hegel’s view according to which the Principle of Non-Contradiction is not valid. Yet they do not in fact accept two statements that contradict each other as both true in all respects. In a well-known essay, Mao Ze-Dong distinguished two types of contradictions. There are contradictions that exist among the people———right-minded comrades, that is. These are benign contradictions, and hence ‘nonantagonistic’. There are also contradictions between what the people believe and what the enemy believes. These are malignant, antagonistic contradictions, and must be eradicated at all cost, even by disappearing the enemy if there is no other way. Neither type of contradiction is considered inconsistent with the Principle of Non-Contradiction. On the contrary. In either case, two contradictory positions cannot both be true. Ultimately, there must be a choice of either one pole or the other of the contradictory premises. As far as Mao is concerned, both types of contradictions must be solved. The difference is that one type must be solved by war, and the other type can perhaps be solved by going to the discussion table (in Schurmann 1968: 55).

Where is all this taking us anyway? What does it have to do with our learning from life, from living? The implication of this section, I would suggest, has a bearing on traditional notions of reasonable and logical knowing and how it is that we can acquire this knowing.

Whose logic?, What kind of logic?
To begin, if we are not content with what conventionally goes as rational argumentation, then why should we flee from whatever our convention tells us is contradictory with the fear that if we do not free ourselves of the contradiction we will surely remain in the dark back alley of ignorance? Yet, should we not reject as irrational any body of knowledge that can rest content with a few contradictions lying around here and there?

If one’s knowledge can include contradictions, then is not the whole of that body of knowledge flawed? Is it perhaps not even nonsensical and virtually unintelligible? On the other hand, if we are satisfied with nothing less than clear and distinct, and consistent and complete, accounts of the world and ourselves and of our knowledge of those accounts, will we not ultimately become like Buridan’s proverbial ass that, suffering from hunger and thirst, couldn’t decide whether to turn left to the water or right to the food that was offered him, and finally dropped dead right there in the same spot? Will we be able to decide at all? Will we not eventually suffer from cognitive combustion and burn out?

Our Eurocentric prejudice has customarily had it that the West is rational, while many other cultures engage in mushy, irrational thinking, and somewhat childish behavior. Actually, if we toss Western biases to the winds and look at the West and the rest somewhat more dispassionately, we find a complex situation. The West, it is now well known, does not have a monopoly on science, even Western science. Joseph Needham’s massive Science and Civilization in China (1954) was one of the first thoroughgoing studies to address this problem. It is becoming increasingly evident that the West is split between what is considered the rational tradition, mathematics and science, and the irrational tradition, that is, the tradition based on faith rather than reason, culture-laden ethics rather than logic, and gratuitous aesthetics rather than purposeful rhetoric. Take religion, for example. Witness the controversy surrounding feminist movements, abortion, prayer in the schools, gay and lesbian rights, Aids and stem-cell research, and especially, evolutionary theory and creationism. There is in the Christian West a season and an irreason for all things. Maintain a critical and even skeptical demeanor during the week, but be sure you are willing to espouse the most irrational brand of blind faith in the incomprehensible on Sunday, at least while in church.

Westerners tend to approach Eastern philosophy as a religion, hence more often than not the assumption has it that they are dealing with blind faith and irrationality. However, this comfortable notion by means of which we can decry the East and revel in our science and technology is the other side of the Eastern coin, which enables them to critique Western materialism and consumerism. The West takes reason as the way to go about life in the physical world and leave subjective, intuitive, contemplative concerns to the spirit. The East cannot steer clear of subjective, intuitive, contemplative concerns, and embraces them along with spiritual life and everyday life in the physical world of joy and pain and pushes and pulls. Which is to say that the East maintains a critical, rational posture regarding everyday as well as religious life, while the West tends to maintain a shrift between the two, relegating religious to the irrational while coveting objective, empirical, and rational life to the maximum. In this sense at least, one can justifiably assert that the West is irrational, as a result of the split, while he East wishes to exercise rationalism with respect to unified life’s experiences.

What are the implications of the West’s chasm between religion and faith on the one hand and science and reason on the other with respect to the East’s union of everyday affairs with religious affairs? They are far-reaching. The West has generally confined reason to the study of the natural sciences and the human sciences, with the assumption that the two areas of scientific endeavor belong to distinct modes of theory making and methods of research———although that assumption has changed in some circles since the turn of the last century. To a limited degree, scientific concerns were at times extended into philosophy, especially during the heyday of logical positivism. But the applications were severely restricted, and so it did not much benefit the humanities at large. The human soul was considered the subject of religion, in that hazy area where irrationalism and faith rather than tough-minded reason and hard evidence were embraced without qualms. The sciences did not touch a person’s soul or the subjective side of her mind, and when they made the attempt, more often than not they used a ‘pseudo-positivistic’ methodology resulting from an impoverished notion of what the natural sciences were imagined to do.

The idea that linguistics is an area of rational investigation, for example, is a relatively recent discovery in Western civilization. The concept was pioneered by Ferdinand de Saussure and brought to a screaming pitch with Noam Chomsky’s transformational and generative grammar. Linguistics as a positivist or rational area of inquiry, however, has seen its better days. In fact, over the past three decades the study of languages has been in the process of taking a softer ‘cultural-political turn’, as witnessed explicitly through George Lakoff’s studies (for example, 1987, 2004, Lakoff and Johnson 1980), and implicitly in Chomsky’s seething critiques of U.S. policies (for example, 1988, 2002, 2006).

The notion that religion and mysticism can and should be explored rationally has been tried and found lacking. During the glory days of logical positivism, attempts by philosophers and theologians to ape positivist methods in religious studies made little headway. A skeptical jury of scientists still heatedly debates forays into scientific studies of paranormal experience. The assumption amongst one group of true believers in the paranormal and supernatural, outside wild-eyed New Age and religious cults, is that the irrational is as real as what usually goes by the name of reason. If this is so, then the apparently most irrational, most extraordinary, and least accessible manifestations of the soul——its mystical properties——must be amenable to rational analysis. ‘Foul!’ cries another group of true believers. The view that religion and mysticism are irrational, they claim, is a myth. This myth has stifled the progress of our understanding, and it should be abandoned, modified, or at least scrutinized. In order to see clearly to what extent this is possible, it is instructive to look more closely at its historical background, and contrast it with other approaches (Mansfield 1995, Wilber 1982, 1983).
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However, comparable splits are common in our everyday life practices. To mention a random smattering of apparently mundane examples, a child may believe in Santa Claus, yet asks the parents about the price of the Christmas gifts she receives; she believes, yet she engages in language practices within customary consumerist practices. High school football teams pray to God before a game to help them to victory, as if the Christian deity were of a nature to take sides in the contest. New Age esoteric practices and beliefs in the occult are on the rise in the United States, in spite of the logicizing age of information.

In fact, in a poll reported in the Religious News Service, June 8, 2005, 42 percent of U.S. citizens described themselves as ‘born again’——perhaps in part following the role model of their venerable president, George W. Bush. Kevin Phillips goes so far as to write that never before ‘has a U.S. political coalition [the Republican Party] been so dominated by an array of outsider religious denominations caught up in biblical morality, distrust of science, and a global imperative of political and religious evangelicalism’ (2006: 393). Even the DOW Jones Industrial Average has over the years taken on practices that border on fetishism. If Alan Greenspan developed a strange cough, the market would take a dip; a blemish was once found on Ronald Reagan’s nose, and, you guessed it, the market responded; these days, under the watchful eye of Ben Bernanke, wild market mood swings following what appear to be inconsequential events are notorious.

In non-Western and marginally Western societies, certain Ethiopians believe leopards, considered ‘Christian animals’, will never attack their domestic beasts on a day of fasting, yet they do not fail to secure their animals’ enclosures on such days. The Romans believed in the divinity of their rulers; yet on important family occasions they always turned to their traditional gods. Ask many Afro-Brazilians if they are Catholics, and they will give you a positive response; yet they may often engage in African based candomblé, macumba, or umbanda ceremonies. Or, take the cases of the bigoted Southerner who swears that some of his best friends are ‘colored folks’, Bill Clinton who ‘never had sex with “that woman”’, Reagan and Bush Senior who apparently could not fully cope with the contradictions that emerged regarding the Iran-Contra affair, and so they conveniently forgot about it altogether. Or Bush Junior, who all but forgot about Bin Laden and Al Queda for the purpose of focusing on chimerical weapons of mass destruction in oil rich Iraq obviously in order to secure the second largest oil reserves for gas guzzling SUVs and other instruments of mass consumption in the U.S. These days the sentiment among the religious right is: if we will soon be running out of oil, God will provide a way; if terrorism is on the increase, it’s God’s punishment for our wicked ways; if there is global warming it’s not our doing, God makes the climate, and besides, is all this not prophesied in the Bible? Indeed, White House accounts of Iraq since 2001 square with a struggle between Good and Evil.

In these and other such cases it is often unclear whether we are dealing with different modalities of belief, or with separate beliefs that guide different spheres of life. On neither interpretation is there any need to postulate a split self. Nor do we need to make this strong assumption in cases where the formation of one belief, for which we have good evidence, is blocked by a strong a priori conviction incompatible with it. The television program, Candid Camera, once recorded people sitting on a bench in Central Park who suddenly saw a tree on the edge of their visual field walking toward them. Many of the subjects reacted by shaking their head as if waking from a bad dream, and then went back to whatever they were doing. What they saw simply couldn’t happen, so it didn’t happen.

And so on. The tales, of course, are virtually unlimited.

Illogical logic, logical illogic
To reiterate, according to a common Western assumption, Eastern mystical doctrines are groundless, while we God-fearing people have our feet firmly planted on terra firma. This, quite obviously, is a problematic issue. Some strains of Buddhism in the beginning stressed the rational and logical features of their doctrine, and continue to do so. The Mahayana form of Buddhism, principally of Tibet, China, and Japan, is by far the most widely known, especially in the United States where it has usually been imported simply as ‘Zen’, whether in pop or genuine interpretation.

Mahayana Buddhism and Christianity share a few characteristics. Yet they are at odds with one another on many important issues, as pointed out by a noteworthy Japanese scholar:

The relationship between faith and reason is an important consideration in comparing Christianity and Buddhism. There is a strong emphasis on reason within the traditions of Buddhism. The relationship between faith and reason is more problematical in Christianity. Gotama is often pictured as instructing his disciples in Socratic manner. Jesus is not. His teachings are more picturesque than argumentative. Many strains within Christianity downgrade reason as an appropriate approach to salvation. However, there is a tradition of Christian thought which holds reason in high regard. The tradition has been influenced by the contact between Christianity and Greek philosophy. (Nakamura 1973: 30)

The central philosophy of Mahayana Buddhism is the Mādhyamika. Nāgārjuna, one of India’s most profound thinkers who lived around 200 AD, is often regarded as the father of Mādhyamika and the great-grandfather of Zen. He is also considered a proponent of all that is irrational in Buddhism.

Some scholars, however, R. H. Robinson (1967) to name one, argue that Nāgārjuna always stuck close to the Principle of Non-Contradiction. His adherence to the principle stems from his insistence on nonsimultaneity. He believed that a thing cannot at the same time exist and not exit, be both black and not black, real and not real, good and evil, at precisely the same moment. In other words, the existence or nonexistence of something, its legitimacy as a member of the real or the irreal, and one of its attributes and the opposite of that attribute, are complementary. They cannot exist, at the same instant in time. (This is roughly comparable to the Bohr or Copenhagen interpretation of quantum theory, where an event can be either of wave characteristics or particle characteristics, depending on the context, but it can’t be both in simultaneity.)

Yet, things are not so clear-cut as we might like them with respect to Nāgārjuna and Buddhism. If we consider the whole of Nāgārjuna’s interpretation of Buddhist doctrine, we realize that two contradictory terms can become quite convenient bed partners. But to do so, each term must remain in its proper place, and on different levels in sort-of bunk-bed fashion. If the upper level term is that of everyday experience and the lower level has been reserved for ‘emptiness’ (Sunyātā), then they are there, now, above and below. Though they are incompatible, or mutually exclusive, nonetheless, they can sit next to each other with quite handily. There is the world of appearances, the world we experience during our coming and going in everyday life, the world of Maya. But this world is actually ‘irreal’ from the other view, from the perspective of ‘emptiness’, even thought we might take it quite ‘real’ with respect to our daily affairs. We take the one view to be ‘real’ because it is part of our concrete world of living and breathing, though it is ‘irreal’. We consider the other view ‘irreal’ because it is ‘emptiness’. We simply cannot fathom it, cannot articulate it, cannot cope with it. Yet it is the ‘really real’.

Here, one might expect, we have a blatant violation of the Principle of Non-Contradiction. We might take the one ‘reality’, Maya, on the basis of what our sensory faculties tell us. Therefore it is what must be rational. At the same time we might take the other ‘reality’, Sunyātā, on faith, since we cannot otherwise account for it. So it must be irrational. In this sense we seem to embrace a double truth, and Buddhism would seem to share some commonality with Christianity. Troubling.
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An unlikely alternative?
Yet, we might also say that there is really no problem at all. If on a dark summer night we take a long curled object to be a snake when actually it is our garden hose, we have no more than error and false appearance. We saw something as a snake.

But it was no snake; it was a garden hose. Both the ‘irreal’ snake and the ‘real’ hose mutually arose from ‘emptiness’: one was considered ‘real’ and the other was not. So the contradiction between them is no more than appearance, for there is no snake. We saw a snake but there was no snake. We didn’t see a hose but there was a hose. So there was what we saw not and there was not what we saw. Now, in order to see what there was, it would have been imperative that we see the hose as a hose. On so doing, we would have seen a hose, and that’s the end of the story, we might suppose.

But that’s not the end of the story. If we saw hose and hose is what there was, then we would have been correct. There was a hose. But there was also an undefined and indeterminate number of other things we might have seen and that might have been but we did not see them and they were not. Instead of a hose there might have actually been a snake. Or there might have been a long curled strip of paper or a piece of thick rope. By a long stretch of the imagination, there might have been a carefully preserved tape worm recently extracted from its deceased host, or whatever else that might have been conjured up. But it was a hose. Upon becoming a hose, the image canceled out all the other possibilities without any of them having happened to pop up so we could take a gander at them. But, alas, we are left with appearances. To the person engaged in everyday real life experiences, the appearances, Maya, are ‘real’; to the logician they are the product of a maniacal stream of sensations; yet, by logical principles, they should be knowable, and in principle they are; to the adherent of the Mādhyamika, appearances are ‘irreal’, and the only reality we are left with is the nonreality of ‘emptiness’.

At the same time, with respect to the Mādhyamika, and contrary to the opinion of some Buddhist scholars, we have what at least at the outset appears to be a most violent rape of the Non-Contradiction Principle. I have the ‘Tetralemma’ in mind, once again, for which Nāgārjuna is most notable. The Tetralemma consists of a tetrad of propositions set out much as one would expect to find in Western logic. But the similarity ends immediately after the first proposition, for the Tetralemma will have no truck with clean-cut bivalent categories of Western logical sort. In replay, it goes like this:

          (1) A exists.
          (2) A does not exist.
          (3) A both exists and it does not exist.
          (4) A neither exists nor does it not exist.

We should have no problem with (1) and (2), that is, if they are not taken in simultaneity but within different timespace contexts. In other words A can exist, with its own particular Identity, within timespace context x, and within another timespace context y, its existence, and hence its Identity, has transmuted into something else. That won’t give orthodox, straight-laced logicians much comfort, but it can accommodate Aristotelian thinking, and it allows for change. In contrast, (3) obviously gives a stiff uppercut to the Principle of Non-Contradiction, that is, assuming that A exists and it does not exist within the same timespace context, and (4) does the same with the Principle of Excluded-Middle, for traditional bivalent logic will have nothing to do with more than a dyad of values (Conze 1970: 219, Murti 1955: 146-48). However, since common sense as well as reason tell us that (3) simply cannot be the case in any coherent world, the implications of (4) are not so ghastly. In fact, even such mainstream North American philosophers of mathematics and logic as Quine (1953) and Hilary Putnam (1983) speculate on the possibility of conducting our affairs without the need of having to pay strict homage to the Excluded-Middle.

In a manner of speaking the Excluded-Middle reformulated as the Included-Middle, of three-values and more, gives rise to the possibility of change over time. According to the Included-Middle principle, something must be either ‘green’ or ‘not-green’. If it is ‘green’, it is ‘green’ and that’s that. If it is ‘not-green’ then it cannot be ‘green’, but at some other time and place and according to the mind of a particular beholder, it might possibly be some other color, say ‘yellow’. O. K., so it’s ‘yellow’. But perhaps it could have been something other than ‘yellow’ at some other time and still be ‘not-green’, say, ‘blue’ or ‘brown’. A leaf is ‘green’ in the summertime, ‘yellow’ during a short period of time in the fall, and ‘brown’ thereafter and just before it falls to the ground. We would ordinarily consider the possibility of the leaf turning ‘blue’ out of the question, or at least remote, though not an absolute impossibility, given some strange setting or some zany perceiver. So over time it has manifested several of its possible attributes. All this, and the Excluded-Middle remains pretty much intact, that is, if consideration remains atemporal.

However, one might wish to assume that to say the leaves of a certain tree are ‘Either green or not-green’ should imply the idea of double negation, ‘Not-not-green implies green’. In this sense, if a leaf is ‘not-not-green’, then it must be ‘green’, and not ‘yellow’ or ‘brown’ or some other color from the spectrum that could possibly fit leaves at some particular time of the year. The Principle of Excluded-Middle has not in this manner been salvaged so much as it has been expanded: it has given way to the Principle of Included-Middle. This is easy enough. It is so much as to say that the leaf is ‘Either not-not-green or not-green’. However, one may then expand the meaning of the equation by assuming that the sentence ‘Either not-not-green or not-green’ gives us a choice between green, and what is neither green (not-not-green) nor not-green, but some other color unbecoming of proper leaf behavior. This other color might be what, at some point in time as a result of some new experience on the part of an interested—or perhaps confused—onlooker receiving strange sensations, might happen to emerge from the gap between green and not-green leaves, namely, blue, pink, mauve, or some other possible color. When taking process and the emergence within time and from the perspective of some sentient subject into consideration, perhaps the Excluded-Middle is not as iron-clad as we would like it.

In contrast, Western logic usually contends that the strictly defined Aristotelian Principle of Non-Contradiction is an unvarying law of all valid thought. The difficulty is not, however, in knowing how to get along without Aristotle’s ban against any and all contradictions. The difficulty rests in comprehending the function of negation, of the use of ‘not’. We can say of something that ‘It is A and it is Not-A’, but on so doing we eventually come to understand that when saying ‘A’, what we mean is the we aren’t saying ‘Not-A’, for we are denying it while we assert ‘A’. Moreover, when asserting ‘Not-A’, we are by the very nature of our assertion denying ‘A’. That is to say, we do all this if we assume we are living in a world of pure simultaneities, timeless simultaneities.

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However, we can assert one thing, explicitly, while at the same time we deny some other thing, implicitly. The explicitly asserted thing remains at the focal level of direct attention while we relegate the other to the subsidiary (or peripheral) level of indirect or peripheral attention. The focal level is there for consciousness while the subsidiary level is not, though what is subsidiary can become focal and vice versa in the blink of an eye. Nothing can be both focal and subsidiary, in consciousness, at the same instant; yet scintillating, rippling, oscillating to and fro switches between something that is now focal, now subsidiary, and now back again, is common in everyday perception and conception.

The adjective of the second sentence tells us what the ‘wave function’ is not. It is not ‘actualized’. There is no need of denying the adjective, for the adjective already says what the subject is not. That is, the predicate, as complement of the subject, is what the adjective of the subject is not.  The predicate is an ‘actualized wave function’. In other words, if we assert ‘actualization’ of the ‘wave function’, we hold to the complementarity principle: ‘An actualized wave function is this particle’ implies that ‘An unactualized particle is a wave function’. However, it might be the case that ‘this particle’ is neither that particular ‘unactualized wave function’ nor is it not that particular ‘unactualized wave function’. Any ‘unactualized wave function’ is a ‘wave function’. That much is clear. But an ‘actualized wave function’ can take on many faces. It can be ‘this particle’ here, or it can be any one of a virtually unlimited number of other possible ‘particles’ somewhere else. So the two sentences, ‘This unactualized particle is a wave function’ and ‘An actualized wave function is this particle’, are asymmetrical. ‘This particle’ was an ‘unactualized wave function’ but an ‘unactualized wave function’ is not necessarily ‘this particle’. It could be ‘that particle’, or some ‘other particle’. This is because a particular ‘particle’ is one, while the ‘unactualized wave function’ entails many in terms of a range of possible ‘particles’. The Excluded-Middle Principle doesn’t hold with respect to the complementarity principle, since between one ‘wave function’ and a ‘particular particle’ there could have been many ‘alternate particles.

Now, all this might appear as so much word spinning. The Excluded-Middle (neither A nor Not-A) contends with the Bivalent Principle (either A or Not-A), but it virtually ignores the Non-Contradiction Principle (not both A and Not-A). In contrast, if A and Not-A are considered in simultaneity, then Non-Contradiction continues to exercise its force. A quite feasible way to abrogate both the Excluded-Middle and Non-Contradiction is Nāgārjuna’s Middle Way. In one fell swoop, it negates all four sentences of the Tetralemma. Following ‘A’, ‘Not-A’, ‘A and Not-A’, and ‘Neither A nor Not-A’, and in light of our tentative observations of Figure 1, Nāgārjuna, with a few strokes of the quill, writes ‘All of the above’, and then he caps it off with ‘None of the above’. Beautiful, and monstrous.

One might retort: ‘Monstrous, but hardly beautiful, for the only possible response is apathy or nihilism’.  But not really. There’s actually nothing to be concerned over when confronting the Tetralemma. You say you don’t like ‘Both A and Not-A’? So, negate it. And you can plod along the narrow path of two-valued classical logical thinking. You like it? Then revel in it to your heart’s desire. ‘Neither A nor Not-A’ throws a bit of fear in you? Take it in your stride or simply forget it. By all means don’t fret over it. It could give you nightmares. You take a liking to it? Kick your heels up and sing praises to the free-wheeling play of the universe. We are free to accept the Principles of Non-Contradiction and Excluded-Middle, but we don’t necessarily have to if we don’t want to. That’s the beauty of it all (Nishitani 1990).
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I do not mean what I just wrote in some frivolous way. Nor am I advocating irrationalism, and I am certainly not implying nihilism. The Mādhyamika is not really irrational, because ‘it is not irrational in that it nowhere contradicts the principle of Non-Contradiction’ (Staal 1975: 40). That is to say, it doesn’t contradict the Principle of Non-Contradiction in the event that you wish to stick to classical principles. It lets you do as you wish. Live and let live.

Actually, the logical liberty I am proposing is not as wild as it seems at the outset. Nor is it entirely unknown to Western thinking. Intuitionist mathematician L. E. J. Brouwer argued that when we are considering infinite sets—or anything else that is equally unsurveyable—it is not always the case that ‘Either A or Not-A’. There can be values other than merely the dichotomous pair. Something else can always emerge between the either and the or. With neither time nor space to go into detail, I might add that Ludwig Wittgenstein developed a controversial paradox regarding rule following along comparable lines (Baker and Hacker 1984, Shanker 1987). Putnam (1981) expounded at length on a natural language rendition of what is called the ‘Löwenheim-Skolem Paradox’ to yield comparable results. Then we have Kurt Göödel’s incompleteness theorems. Göödel demonstrated that a sufficiently rich formal systems is destined either to incompleteness— hence it must be opened and a new sentence added— or inconsistent. If it is incomplete, it must be opened for reception of some clarifying details. If it is inconsistent, it cannot pass the classical logical litmus test. So it must be amended or tossed in the circular file and replaced by something else (DeLong 1970, Goldstein 2005). If these apparently devastating consequences of tough-minded formal thought and reason apply, then what chance do the tender-minded disciplines have of getting things right once and for all time?

The moral to the story? Dilemmas of thought and reason there will always be; however, in the world of everyday life processes, the timeless iron-handed control of reason and thought wanes, for they have no direct bearing on concrete temporal process. So forget about quandaries. Keep things open by allowing for Included-Middles if you need to. Embrace the Principle of Non-Contradiction and at the same time embrace Contradiction when it becomes expedient to do so— and all other binary antagonisms for that matter. In other words, when things are a question of what can usually be considered C. S. Peirce’s bivalent category Secondness, Non-Contradiction can be our best friend. When Peirce’s unary, self-contained, self-sufficient, self-reflexive category Firstness is up for contemplation, Contradictions can exist as quite peaceful bedfellows, and our creative thoughts and we can be so much the better for it. When Peirce’s triadic, mediary category Thirdness and the necessity of new concepts, procedures, strategies, tactics, methods, and theories are up for alteration, something always stands a chance of emerging from the gap between erstwhile Excluded-Middles; consequently, what was once excluded can now be included. As the context goes, so also the affirmation or the negation of any of Nāgārjuna’s sentences.

In this light, those who follow the Mādhyamika rely on the Principle of Non-Contradiction whenever they attempt to refute their opponents. For, ‘the notion of refutation depends on the correct use of the particle “not” and makes no sense unless that principle is presupposed’ (Staal 1975: 42). The Mādhyamika method can be effective only insofar as the Contradictions they derived in their argument are considered intolerable and Non-Contradiction is deemed at least for the time and within that particular context valid. For, if the Mādhyamika can ‘harbor contradictions in their own position, they could not claim to have refuted their opponents on the ground that only they did the same’. Moreover, if the Principle of Non-Contradiction is not accepted as valid, then the Mādhymaka’s opponent’s views are ‘just as good as the negations of these views, and cannot therefore be shown to be false’ (Staal 1975: 42).

I cannot overemphasize the important point that Mādhyamika thought does not simply reject the tenets of classical Western logic. Mādhyamika scholars make best use of logic whenever they need to. For example, they use it to develop an argument between two opposite views, their’s and their opponent’s. If their opponent’s argument defends classical logic, then they use logic to trash logic. Yet they are also comfortable outside ordinary logical principles, for they are aware of logic’s limitations. Besides, if binary logic were all we had to work with, then forget about Peirce’s Firstness. Forget about creativity and novel concepts. And forget about the very idea of waves and particles too, for waves, as ‘possibility’ or ‘potentiality’ in the words of Werner Heisenberg, are a matter of Firstness. As such, they are absolutely necessary for the existence of our actualized world of things and their opposites as we know it. If we ignore Firstness, then forget about Thirdness as well. For anything and everything in the way of novel thought comes by way of emergence from the virtually infinite expanse of possibilities of Firstness.

However, I have certain truck with the Mādhyamika in regard to what might be construed as an esoteric posture. When a contradiction is dissolved by placing it in a new context, that new context invariably allows for a sense of something that is such as it is and it is not such as it is. It either is such as it is or it is not such as it is for ordinary folks. But the learned sages know better: they have been enlightened. For them, it is both such as it is and it is not such as it is and it neither is such as it is nor is it not such as it is. This move ignores the Principle of Identity. For, the assumption has it that nothing is as it is, for it is already becoming something other than what it was becoming. For example, it is often the case that what is today’s common sense and the intuitive view of popular culture was yesterday’s esotery, and occasionally what emerges from popular culture later by some quirk becomes profound philosophic, scientific or artistic insight.

After all, Picasso got his inspiration from African art. Schopenhauer’s philosophy and Bohr’s complementary principle owe a debt to Eastern philosophers. Wittgenstein’s ‘language games’ purportedly came to him when he was walking the streets near a soccer stadium during a match. Tolstoy was taken by folk culture. And Einstein was obsessed with what might appear to pedants and snobs as so many childish games. On the other side of the ledger, a few centuries were required for the Copernican-Galilean-Cartesian-Newtonian mechanical corpuscular-kinetic view, presupposing linear time and space, to become commonplace. By the beginning of the twentieth century, however, the citizens of the West had become so inculcated into that world that they could hardly perceive and conceive of their world as anything else. We are at present still struggling with the world of relativity and quantum theory. A few centuries down the line, and who knows how the world will have become according to commonplace assumptions held by ordinary folks.

This reminds one of physicist Arthur Eddington’s mentioning to an audience during the early days of relativity theory that there were only three people in the world who understood it. It was taken for granted that one of them was Einstein. The audience acknowledged that much. Then, Eddington jocularly began speculation as to who the third person might be. Considerations of relativity theory have changed drastically since that time. Now, the basics of relativity and quantum theory are taught in high school physics classes. It is remotely conceivable that at some time in the future, relativity and quantum theory may be as commonsensical as Newtonian mechanics and Euclidean geometry are today.

An other way?
If as H. H. Pattee suggests, at the very heart of life itself lies paradox, with renewed energy we can forget about quandaries, keep things open by allowing for Included-Middles if we need to, and embrace the Principle of Non-Contradiction. Perhaps in some form or another paradox at the quantum level extends upward to all levels. If this is so, then to expect the mind or consciousness to free itself of paradox is out of the question. It is more problematic to assume that enlightenment pays the paradox no mind and enters into some ethereal zone free of conflicts.

I would rather take it that, like Wittgenstein once said of logical conflicts that drive philosophers to fits, one should let go of the tension the paradox engendered, and show the fly out of the fly bottle. The fly enters the bottle, drawn by a sweet odor or some other attraction. Once inside, it rebounds at random against the inner boundaries of the container within which it is trapped. It does not fly toward the neck of the bottle, for in that direction its prison becomes more confining. So it remains within that part of the bottle of greatest circumference. If we show the fly its way out of the bottle, it is not free to roam at will. Rather, it remains oblivious of the fact that, although its world is now considerably larger, it is still caught within an existential prison. But not to worry. The parameters of this new prison are large enough for comfort. So our fly, now liberated from its erstwhile prison, is a happy fly. As far as it is concerned, its world is unlimited, infinite. It can fly in any direction it pleases, forever.

This seems to be the genuine Buddhist way, especially as incorporated within Zen Koans. The master asks the the apprentice ‘What is the sound of one hand clapping?’—&#8195from among a host of other Koans. How can she respond? She is placed in a bind. If she decides she can’t respond she fails the test, because she has exercised a mind search for a response and came up empty handed. That is the problem: she tried to solve the problem by an act of mind. If she decides the answer is ‘Silence’, she also fails. She tried, and came up with an answer, by just another mind act. So she tries gravely to try no more, and fails. For to try not to try is still the mind trying to mind the body. She decides to refrain from choosing an answer altogether, and fails. Her choice was mind motivated. What is an apprentice to do? At some point she rather mindlessly lets go of the paradox, and then she feels and senses the world anew.

This last move is not a mind act, not the product of a logico-rational process, not a selection or a choice, but a matter of the body simply doing what it does: it bodyminds, so to speak. As such,