10. SYNTHETIC LOGIC At the end of the previous lecture I asked you to go away and think about two questions: What should we call the opposite of traditional, "analytic" logic? and On what law would such logic be based? Any of you who have read the lecture outline for this course (see above, p.vii) will have easily guessed that the term I think best describes the kind of logic governing functions like induction and synthetic propositions is "synthetic logic". But I imagine you've had a bit more trouble thinking of a law that we can set alongside Aristotle's "law of noncontradiction". So let's begin today by determining what such a law would be. Finding the basic law of synthetic logic need not be a difficult task. Since analytic and synthetic logic always function in opposite ways, all we really have to do is to determine the opposite of Aristotle's famous "A=-A". There are, in fact, two ways of doing this. We can either change the "=" to "=" or we can change the "-A" to "A". In this way, we derive the following two laws: "A=-A" and "A=A" My suggestion is that we call the first new law the "law of contradiction", since it shows us the inherently contradictory form followed by anything which truly functions in a "synthetic" way. The second is actually the opposite of a rather boring law of analytic logic, usually called the "law of identity" (A=A); so we can refer to "A=A" as the "law of nonidentity". This gives us a complete set of four basic laws of logic: [Figure 10.1: The Four Fundamental Laws of Logic] Obviously, the laws of synthetic logic require some explanation. For how could contradiction or even nonidentity be the basis for constructing any meaningful proposition? A computer, for example, could never work if it were programmed using synthetic logic rather than analytic logic. To attempt this would be like trying to operate the computer while it is submerged in water: the whole thing would short-circuit! What then is the point of talking about synthetic logic at all? What sense could it ever make to say, for instance, "Black is not black"? Fortunately, in spite of the tremendous advances we have seen lately in computer technology, human thinking still surpasses that of the best computer. This is because, even though even a small computer can out- think the most highly developed human brain in analytic operations, computers are completely incapable of performing synthetic operations. In order to see how synthetic logic can have meaningful applications, let's look at some examples. Next to Confucius, one of the most influential ancient Chinese philosophers was Chuang Tzu (369?-286? B.C.). As far as we know, he didn't write much; but what he did write is well preserved in a collection of thirty-three short essays. One of the most interesting of these utilizes synthetic logic on virtually every page. Even the title, "Discussion on Making All Things Equal", suggests that one of Chuang Tzu's main goals was to encourage us to break out of our ordinary, "black and white" way of thinking, by giving us a glimpse of what the world will look like if we learn to synthesize ("make equal") such opposites. One passage in particular (pp.34-35) is worth quoting at length: Everything has its "that", everything has its "this". From the point of view of "that" you cannot see it, but through understanding you can know it. So I say, "that" comes out of "this" and "this" depends on "that"--which is to say that "this" and "that" give birth to each other. But where there is birth there must be death; where there is death there must be birth. Where there is acceptability there must be unacceptability. Where there is recognition of right there must be recognition of wrong; where there is recognition of wrong there must be recognition of right. So far, Chuang Tzu has merely pointed out the universal need of human beings to think analytically. He notes, quite rightly, that in such cases, the opposites actually depend on each other for their existence. But he then continues (p.35): Therefore the sage does not proceed in such a way, but illuminates all in the light of heaven. He too recognizes a "this", but a "this" which is also a "that", a "that" which is also a "this". His "that" has both a right and a wrong in it; his "this" too has both a right and a wrong in it. So, in fact, does he still have a "this" and a "that"? Or does he in fact no longer have a "this" and a "that"? A state in which "this" and "that" no longer find their opposites is called the hinge of the Way [i.e., of Tao]. When the hinge is fitted into the socket, it can respond endlessly. Its right then is a single endlessness and its wrong too is a single endlessness. So I say, the best thing to use is clarity. Here Chuang Tzu explains that the way of the sage is to follow the Tao (the "Way" of heaven), and that this Way can be expressed in words only by using the contradictory language of synthesized opposites: "this" and "that" (Chuang Tzu's equivalent of "A" and "-A") must be identified with each other; moreover, each must be regarded as itself containing what we would normally regard as a contradiction: e.g., both right and wrong; both birth and death, etc. Do you think Chuang Tzu was being serious when he wrote this, or did he intend it all to be a joke? Why did he end this rather confusing paragraph by stressing the need for clarity? Later (pp.37-38) he says: "The torch of chaos and doubt ... is what the sage steers by.... This is what it means to use clarity." He then announces he will "make a statement" which "fits into some category", though he's not sure which. What follows is a series of blatant contradictions, such as: "There is nothing in the world bigger than the tip of an autumn hair, and Mount T'ai is little. No one has lived longer than a dead child, and P'eng-tsu [the Chinese Methuselah] died young." Can he really be aiming at clarity when he makes such statements? I don't think Chuang Tzu was joking at all--though the truth can often be funny. He reveals his intentions more fully when he says (pp.39-40): The Great Way is not named; Great Discriminations are not spoken; Great Benevolence is not benevolent; Great Modesty is not humble; Great Daring does not attack. If the Way is made clear, it is not the Way. If discriminations are put into words, they do not suffice.... This suggests that the purpose of speaking in an intentionally unclear (or contradictory) way is to point our hearts and minds beyond the realm of ordinary distinctions, in which analytic logic suffices, to a deeper and far more important realm--to a reality which cannot be spoken about clearly and truthfully at the same time. In other words, Chuang Tzu teaches us that the unclarity of synthetic logic is the clearest way of expressing ourselves if we must use words to describe the indescribable. Life, real life, does not actually come in the neat little boxes that our minds create. Hence, the authentic life is the one which sees beyond these artificial boundaries (p.44): Right is not right; so is not so. If right were really right, it would differ so clearly from not right that there would be no need for argument. If so were really so, it would differ so clearly from not so that there would be no need for argument. Forget the years; forget distinctions. Leap into the boundless and make it your home! If we try to force Chuang Tzu into the straight-jacket of analytic logic, we will have little choice but to declare him insane. However, once we recognize that his goal is to give us a glimpse of something beyond the boundaries of analytic logic, his words begin to take on a new kind of meaning. The "clarity" he recommends is not the clarity of thought (i.e., thinking about what we know), but the clarity of vision (i.e., seeing what remains mysterious). The irony is that he is using words to point us to this vision. In so doing, he recognizes that he is, in a sense, falsifying the true Way--at least, for anyone who focuses on his words as a literal description of his meaning, instead of focusing on that to which his words are pointing. And what we discover when we examine his words is that the tool he uses most frequently to do the pointing is intentional contradiction. "Right is not right." What better example could their be of the law of nonidentity (A=A) at work? "'This' is 'that'." What better example could there be of the law of contradiction (A=- A) at work? Whereas analytic logic offers us the clarity of eyesight (i.e., thorough knowledge), synthetic logic offers us the clarity of insight (i.e., deeper understanding). When used properly, these two kinds of logic need not be viewed as competitors, but ought to be regarded as complementing each other, just as deduction and induction can be used effectively as complementary methods of argumentation. One of the best ways to picture their complementary relationship is to relate them to the distinction we learned from Kant, between the areas of possible knowledge and necessary ignorance, as in Figure 10.2. Analytic logic can be used to produce knowledge any time we are describing something that falls within the boundary of possible knowledge (e.g., anything we can see). But once we use words to describe what lies beyond this boundary, analytic logic not only loses its explanatory power, but can actually mislead us into making false conclusions. Instead, as Chuang Tzu has shown us in describing the Tao, for those cases in which we are necessarily ignorant, we can discover what we should believe only by using synthetic logic to gain the insight needed to support such beliefs. It is no accident that Chuang Tzu regarded a "leap into the boundless" as the best way of understanding the truths of synthetic logic. This leap, which others have called the "leap of faith" is essentially the leap from mere thinking about ultimate reality to actually experiencing it. But "experience" here refers not to knowledge, but to what Kant calls "intuition". For Kant, our power of intuition is a power of "receptivity", as opposed to "conception", which is a power of "spontaneity" (see the first Critique, p.92). [Figure 10.2: The Analytic and Synthetic Domains] So also, Chuang Tzu's "leap" is actually a leap into the Tao, into the intentional passivity of silence. This aspect of the "boundless" will be the focus of our attention in the fourth part of this course. For now, it is enough to point out that analytic and synthetic logic provide us with two complementary perspectives: using the former, we actively impose onto the world strict conceptual divisions; using the latter, we passively receive from the world the power of its intuitive unity. Since this unity cannot be expressed literally in words, synthetic logic can be talked about only by viewing it as a parasite on analytic logic, based on the negation of the analytic laws. What other way would there be to express the inexpressible than to negate the laws of correct expression? In the absence of any alternative, synthetic logic could not completely destroy analytic logic without destroying itself! This is why good philosophers recognize both kinds of logic as legitimate philosophical perspectives, and attempt to develop both as integral aspects of their philosophy. The western tradition has relatively few good examples of how synthetic logic can be employed to help us cope with our ignorance of ultimate reality. One ancient Greek philosopher, Heraclitus, touched upon synthetic logic with his insightful principle that "Opposites are the same" (i.e., "A=-A"). However, the little that remains of his writing does not provide much help as to how to apply this principle. Others have developed forms of synthetic logic into much more elaborate systems. The best example, undoubtedly, is Hegel (1770-1831), who constructed his entire "dialectical" philosophy on the principle that historical development takes place according to a synthetic pattern of "thesis", "antithesis", and "synthesis" (see Figure 10.3). This version of synthetic logic has had its greatest influence in this century in the form of "dialectical materialism"--the political ideology of Karl Marx (1818-1883), who, as we shall see in Part Three of this course, turned Hegel's synthetic pattern upside down. Another interesting example comes from the The Mystical Theology of a fourth century monk who used the pseudonym "Dionysius the Areopagite". His attempt to describe the ultimate reality (which he refers to as "It") is worth quoting at length: Once more, ascending yet higher, we maintain that It is not soul or mind, or endowed with the faculty of imagination, conjecture, reason, or understanding; nor is It any act of reason or understanding; nor can It be described by the reason or perceived by the understanding, since It is not number or order or greatness or littleness or equality or inequality, and since It is not immovable nor in motion or at rest and has no power and is not power or light and does not live and is not life; nor is It personal essence or eternity or time; nor can It be grasped by the understanding, since It is not knowledge or truth; nor is It kingship or wisdom; nor is It one, nor is It unity, nor is It Godhead or [Figure 10.3: Hegel's Dialectical Method] Goodness ...; nor is It any other thing such as we or any other being can have knowledge of; nor does It belong to the category of nonexistence or to that of existence; nor do existent beings know It as it actually is, nor does It know them as they actually are; nor can the reason attain to It to name It or to know It; nor is It darkness, nor is It light or error or truth; nor can any affirmation or negation apply to It ..., inasmuch as It transcends all affirmation by being the perfect and unique Cause of all things, and transcends all negation by the preeminence of Its simple and absolute nature--free from every limitation and beyond them all. (pp.199-200) This quotation reveals a profound awareness, long before Kant, of the fact that we can know virtually nothing about ultimate reality. Yet if we insist on interpreting these words according to the laws of analytic logic, then much of it appears to be nonsense! How, for example, can something be "not immovable nor in motion or at rest"? Such claims must be rejected as blatant contradictions, until we realize they are to be interpreted in terms of synthetic logic; for in so doing the same contradictions can point us towards deeper insights about the Being whom we normally call "God". Although it is rare to find even a hint of the existence of synthetic logic in most logic textbooks, there have been a few scholars in this century who have recognized its significance and attempted to describe the way it works. No one to my knowledge has thoroughly explored the extent to which it constitutes an entirely distinct kind of logic; yet some have openly acknowledged the possibility of using alternative laws as the basis for the way we use words. For instance, some anthropologists, in their study of how people in primitive societies think, have concluded that their minds operate according to what they sometimes call the "law of participation" (which means they see concepts as participating in their opposites). Other scholars have suggested still other names for what I have called the "law of contradiction", such as the "law of paradox". This name has the advantage of making it clear that the true purpose of synthetic logic is not to utter meaningless contradictions, but to drive our imagination to the point where it discovers new perspectives, from which the apparent contradictions can be resolved. What we call this alternative kind of logic and its basic laws is not nearly as important as knowing how to use it. With this in mind, I'll discuss in lecture 12 a very practical way of using synthetic logic to gain insights. For today, let's conclude by reviewing what we have learned so far about logic, using the table given in Figure 10.5. [Figure 10.4: Three Key Logical Distinctions] There are fundamentally two different types of logic: analytic logic arises out ofthe laws of identity and noncontradiction; synthetic logic arises out of the opposite laws of nonidentity and contradiction. The former is properly used to describe anything that is possible for us to know; the latter is properly used to describe that which, by its very nature, we can never know. Analytic propositions are an expression of analytic logic, because they identify two concepts that are already known to be, in some sense, identical; synthetic propositions are an expression of synthetic logic, because they identify two essentially nonidentical things--namely, a concept and an intuition. Finally, analytic logic is most appropriately manifested in the form of a deductive argument, where the conclusion follows from the premises as a matter of mathematical (i.e., noncontradictory) certainty; synthetic logic is most appropriately manifested in the form of an inductive argument, where the conclusion always depends on some degree of guesswork (i.e., on the contradictory affirmation of what we do not know). Having now introduced to you three of the most basic distinctions in logic, I will devote the next two lectures to the task of explaining the logical basis of the various diagrams I have been using throughout this course. We will then conclude Part Two of the course by looking at two examples from this century of philosophical schools that tend to over-emphasize analytic and synthetic logic, respectively. QUESTIONS FOR FURTHER THOUGHT 1. How could a thing be both "all black" and "all white"? 2. What could it mean to say that an existing thing "does not exist"? 3. Could someone actually make the "boundless" their home? 4. What kind of logic does God use to think? RECOMMENDED READINGS 1. Chuang Tzu, Basic Writings, tr. Burton Watson (New York: Columbia University Press, 1964), Chapter Two, "Discussion on Making All Things Equal", pp.31-44. 2. Dionysius the Areopagite, The Divine Names and The Mystical Theology, tr. C.E. Rolt (London: S.P.C.K., 1920). 3. G.W.F. Hegel, The Phenomenology of Spirit, tr. A.V. Miller (Oxford: Oxford University Press, 1977), especially "Preface: On Scientific Cognition", pp.1- 45. 4. Paul Roubiczek, Thinking in Opposites: An investigation of the nature of man as revealed by the nature of thinking (London: Routledge and Kegan Paul, 1952).