8. WHAT IS LOGIC? Today we begin the second of the four main parts of this course. In the first part we learned something about the roots of the tree of philosophy-- i.e., about metaphysics. The most important lesson we learned, first from Socrates, but mainly from Kant, was that, just as the roots of a tree are almost entirely buried in the soil so that we cannot see them as they are (at least, not without uprooting the tree), so also the metaphysical underpinning of our knowledge consists of something essentially unknowable to the human mind. Starting in this lecture, we will be turning our attention towards a part of the tree that allows itself to be seen much more readily: the trunk of the philosophical tree--i.e., logic. In a few minutes I would like you to tell me the answer to the question "What is logic?" But first, in view of how difficult Kant's philosophy is, let's review what it has taught us about metaphysics. Kant's Critical approach to metaphysics can be summarized in terms of the following four fundamental tenets: (1) Ultimate reality--i.e., reality apart from the limiting conditions through which we learn about it--is an unknowable "thing in itself". (2) The particular or "empirical" aspects of our knowledge are determined by the "appearances" we experience. (3) The general or "transcendental" aspects of our knowledge are determined by the knowing subject. They are space and time as "forms of intuition", and twelve categories as "forms of thought". (4) Knowledge inevitably gives rise to ideas about what ultimate reality might be like if we could know it; but examining these ideas leads reason into self-contradiction, so they can never become items of scientific knowledge. The implications of the system which arises out of these tenets are manifold. At this point, let's just look at four of the most significant implications for metaphysics. First, if we think of Socrates as planting a "seed" in the history of western philosophy with his idea that philosophers must begin by recognizing what they do not know, then the tree which grew out of that seed first bore fruit with Kant. Kant agreed that philosophy begins with the recognition of ignorance; indeed, he even claims that the "inestimable benefit" of his first Critique is "that all objections to morality and religion will be for ever silenced, and this in Socratic fashion, namely, by the clearest proof of the ignorance of the objectors" (p.30). But he goes much further than Socrates by demarcating, once and for all, the precise boundary lines between the areas of "necessary ignorance" and "possible knowledge": we may be able to think about a concept that cannot be intuited, or feel an intuition that cannot be conceptualized; but we can know only what appears to us in a form that lends itself to both intuition and conception. Moreover, Kant distinguishes on pp.605-606 of the first Critique between two types of ignorance. Our accidental ignorance in empirical matters should motivate us to extend our knowledge, whereas our necessary ignorance in metaphysical matters should motivate us to look beyond knowledge to the practical purpose of doing philosophy--namely, to live a better life. We shall come back to this in Part Three of this course. With Kant, therefore, metaphysics has finally come of age. After two thousand years of philosophers attempting to combat necessary ignorance with metaphysical knowledge, Kant brought to a close the first major period of western philosophy, and in so doing, opened up a whole new set of problems. For the next implication of Kant's system is that we must now find a way to cope with our necessary ignorance. How can we do philosophy without having any knowledge of ultimate reality? The last two hundred years of philosophy has been a series of different suggestions as to how this can best be accomplished. Kant's own solutions, such as his "Copernican" theory that the subject reads the transcendental conditions of knowledge onto the object, have been rejected by most subsequent philosophers. However, I don't think we should be too quick to reject this rather strange sounding theory. For just as Descartes' "cogito" paved the way for Newtonian physics, I believe Kant's Copernican revolution paved the way for today's relativity physics, which is based on a very similar notion of the observer participating in all scientific knowledge. Because Kant defined such a clear-cut set of limits for human knowledge, we can say philosophy becomes more complete with Kant than ever before. Kant himself was well aware of this aspect of his system: I have made completeness my chief aim, and I venture to assert that there is not a single metaphysical problem which has not been solved, or for the solution of which the key at least has not been supplied. (Critique of Pure Reason, p.10) Interestingly, if you think back to our discussion of myths towards the beginning of the first part of this course, you might recall that a myth is also something which is enclosed in limits. So I think it would be right to say that with Kant western philosophy has experienced such a major "paradigm shift" that we can say Kant gives philosophy a new "myth"--the myth of the thing in itself. Of course, as long as this is, as it were, an "enlightened" myth--i.e., as long as we always remember it is a myth, and so treat it not as an absolute truth, but as a basic assumption, freely adopted on faith--we can avoid many of the pitfalls which "living in a myth" would otherwise have. One final implication of Kant's philosophy is that its insistence on an area of necessary human ignorance keeps the philosopher humble. This might seem surprising, especially for those of you who have read some of Kant's own writing, since Kant was certainly not ignorant about the greatness of his own achievement! For on several occasions he proudly explained why his system is superior to those of all past philosophers. But my point here is that, whereas most philosophers' ideas are based on the assumption that philosophers have access to some kind of special knowledge to which the man on the street is blind, Kant's philosophy puts philosophers in general on an even par with non- philosophers when it comes to their ability to gain knowledge about the most basic metaphysical issues. Because Kant used such complicated terminology to express his ideas, this implication of his philosophy is often overlooked, even by those who spend years studying his writings. Yet Kant stated this "humiliating" aspect of his Critical system clearly enough on several occasions. One of the best examples, near the end of the first Critique (pp. 651-2), is worth quoting in full: But, it will be said, is this all that pure reason achieves in opening up prospects beyond the limits of experience? .... Surely the common understanding could have achieved as much, without appealing to philosophers for counsel in the matter. I shall not dwell here upon the service which philosophy has done to human reason through the laborious efforts of its criticism, granting even that in the end it should turn out to be merely negative ... But I may at once reply: Do you really require that a mode of knowledge which concerns all men should transcend the common understanding, and should only be revealed to you by philosophers? Precisely what you find fault with is the best confirmation of the correctness of the [Critical philosophy]. For we have thereby revealed to us, what could not at the start have been foreseen, namely, that in matters which concern all men without distinction nature is not guilty of any partial distribution of her gifts, and that in regard to the essential ends of human nature the highest philosophy cannot advance further than is possible under the guidance which nature has bestowed even upon the most ordinary understanding. In other words, philosophy is special not because it allows us proudly to claim a higher level of knowledge than ordinary people, but because it humbles us by showing us the limitations of all our knowledge. I hope this review of Kant's contribution to metaphysics has given you all ample time to think about what logic is. I would guess that, before you started this course, most of you had more ideas about logic than about the nature of philosophy in general. So I hope this discussion question will be a bit easier than the one we had in the first session. Who would like to make the first suggestion? What is logic? Student H. "I think logic is like science: it's supposed to teach us about the facts in the world, so we don't have to rely only on our own opinion." Logic certainly does have something to do with helping us to see beyond our own opinion. But I'm afraid I can't agree with you when you relate logic so closely to scientific facts. Nevertheless, I'm glad you spoke up, because this is a mistaken idea about logic which many beginning philosophy students have. Logic actually has nothing to do with teaching us new facts! In fact, it's more like metaphysics than physics when it comes to the issue of teaching us new facts. Metaphysics, at least for Kant, does not extend knowledge at all, but prevents errors, just as the roots of a tree do not bear fruit, but need to be cared for in order to insure the fruit will be healthy. And the same is true for the trunk, logic. The reason for studying metaphysics and logic is not so we can know more, but rather so we can learn to express more clearly and accurately the knowledge we gain from elsewhere. Otherwise we might find ourselves cultivating knowledge which looks good on the outside, but is rotten when we "bite into it". So what is logic? Student I. "Logic is step by step thinking, like the kind scientists always use." I think you're right to suggest that scientific thinking must be logical. And "step by step" thinking, assuming the steps follow according to some definite order, is certainly one of the main characteristics of anything logical. The word "order" implies that there is a definite relationship between the different steps we follow in our thinking. I assume that's what you mean by saying "step by step". But your answer shows that you have misunderstood my question. Can anyone see how? If a beginning history student asks me "What is history?", would it be adequate for me to answer him by saying "History is something important about the past"? Can any of you who are studying history right now tell me whether or not this accurately describes what you are learning about? Student J. "We do learn a lot about significant events that happened in the past." But is that all you learn about? I suppose students in all subjects learn important things about the past without actually studying history. For example, in the last few lectures we've been learning about metaphysics by studying the ideas of past philosophers; but taking an historical approach does not mean we were studying history as such. What else have you been learning about? Student J. "Some of my history teachers have presented different theories about how historical change actually takes place, such as the debates over whether history is like a line or a circle. Also, we are supposed to be learning not just the facts about the past, but why they were significant, and how we can interpret them in the best way." Very good! Now, just as all academic disciplines teach us something about the past without necessarily teaching us history, so also all academic disciplines are, or at least, should be, logical, yet do not teach logic. Not just science subjects, but history, economics, politics, religion, even music and art, are also normally taught in an orderly, logical way (provided we recognize that there are different types of order). So what I am asking you now is to tell me what makes logic itself different as an academic discipline? As we turn our attention to logic, what is it that we will be studying? Student K. "The principles of orderly thinking?" Yes! This could even be used as the basis for a general definition of logic. Logic as an academic discipline is distinguished from other disciplines by the fact that logicians do not simply use orderly thinking; they think in an orderly way about orderly thinking. Probably the most common definition for logic is to regard it as "the science of the laws of thinking". This definition reminds me of a special word Kant had for describing the patterns built in to human reason. He compared good philosophers to architects who construct systems (conceptual "buildings") according to a predetermined plan. Reason's own "architectonic" structure provides a set of ready-made patterns, which Kant believed philosophers should use as the basis for making their presentation of philosophical ideas more orderly. Kant himself never spent much time explaining just what these patterns are; but in this second part of our course, quite a lot of our attention will be devoted to this task. As we shall see, it is through logic that we can best recognize an idea and an ordering of its parts, which Kant regarded as a prerequisite for understanding a philosophical system. Of course, giving a simple definition of logic is not the only way of answering our question. Who else has an idea about what logic is? Student L. "I remember in one of the first lectures you talked about the Greek word logos. Does that have anything to do with what we will learn about when we study logic?" You probably also remember that, when I mentioned logos in the third lecture, I was trying to shed some light on the significance of myths for philosophy. The term logos can sometimes refer to the myth itself, or to some unknown, hidden meaning. However, I think it is best to regard it as referring to the first attempt to express this meaning in words. Since "logos" means "word", we could say that in this sense the term "logical" refers to a use of words whereby the words carry some meaning. As we shall see in the next few lectures, there are two types of logic: one type virtually ignores any hidden (i.e., mythical) meanings, while the other type focuses almost entirely on bringing just such meanings out into the light. Words generally carry a meaning when they are used in combination with some other words. The special term used in logic to denote a sentence that puts forward a meaningful relation between two or more words is the term "proposition". For example, our discovery in the fifth lecture that for Aristotle "substance is form plus matter" could be regarded as a simple proposition, showing the definite relationship between the three concepts "substance", "form", and "matter". In the next lecture I will introduce some special terms that will help us to refer to the most important types of relations by name. Why is it important to learn how words get their meaning? If we know what a word means, why do we need to go further and learn the laws that determine how that meaning arises? This should be an easy question to answer, since I've already mentioned the reason at the beginning of today's session. Student M. "If we don't know the rules, we might make errors without knowing it. Learning the rules will help us to think and speak truthfully. A logical person can avoid saying anything that is false." Avoiding errors is indeed the answer I was thinking of. But we have to be careful not to think something we say is always true just because it is logical. It might surprise you to find out that logic is not really concerned about the truth of the words we use, but only about their truth value. As we shall see, it is possible to say something which is utterly false, but to say it in a logically correct (or "valid") way, or to say something which is very true, but to state that truth in a logically incorrect way. The kind of errors logic helps us to avoid are not called "falsehoods", but "fallacies". A fallacy is a mistake in the structure of the argument we use to draw a conclusion based on some evidence. For example, if I say "History and philosophy have nothing in common with each other; you are an historian and I am a philosopher; therefore we have no common interests", then my argument is fallacious. Even if the first two statements (called "premises") are both true, they do not necessarily imply the third statement, because you and I might have something in common that has nothing to do with history or philosophy. On the other hand, even if the first two statements were false, the conclusion might be true: history and philosophy might be closely related in certain respects, and you might be studying chemistry, not history; but we might have no common interests. Logic is incapable of telling us whether or not either of these two scenarios is true; all it can do is tell us that in either case we cannot demonstrate its truth by constructing an argument in this form. Logicians sometimes make this point by saying logic is concerned with "formal truth" rather than "material truth". The material truth of a proposition is the particular external fact that makes the proposition true or false. Thus, if we want to demonstrate the material truth of the statement, "This chalk is white", the best way is for me simply to hold it up like this where you can all see that it is white. The proposition is true if it turns out that the chalk in my hand really is white. The formal truth of a proposition, by contrast, is the general internal way it is expressed. By "internal" I mean that, without going outside of the proposition itself, we can determine its formal truth value. As an example let's take the complex proposition, "If this chalk is completely white, then it is not blue." In this case, we can say that, without looking at the chalk at all, we know that if the first part of the proposition is true, then so is the second. A proposition's formal truth does not depend at all on the specific meanings of the words used within the proposition. All that matters is that we know the truth value of each of its parts. For that reason, logicians often find it is helpful to substitute the words in a proposition with symbols. Because the symbols represent only the general or formal properties of each word, they make it easier to look beyond the particular content and see the proposition's underlying logical structure. Thus, the ideal goal of some logicians is to develop a complete symbolic logic which can function, rather ironically, as a language without words (i.e., logic without logoi). For example, the above "If ... then ..." proposition can be expressed by replacing "this chalk" with "a", "all white" with "w", "not" with "-", and "blue" with "- w" (i.e., "not white"), so that the formal structure of the proposition becomes clear: "If a is w, then a is -(-w)" is always a true proposition, no matter what words we use to replace these symbols. The proliferation of symbols in logic texts is, perhaps more than anything else, what scares beginning philosophy students away from logic. But like any new language, once we learn how to use these symbols, the initial awkwardness and confusion goes away. In this course I will only introduce you to a very small number of logical symbols; but I hope some of you will be interested enough to do some further reading on your own in the area of symbolic logic. My main interest in the next six lectures will be to help you to deepen your insight into what logic itself actually is. QUESTIONS FOR FURTHER THOUGHT 1. What was the old myth that Kant's system replaced? 2. What is "humility", and is it ever possible to be completely humble? 3. Is logic always logical? 4. Is truth always true? RECOMMENDED READINGS 1. Morris Cohen, A Preface to Logic (London: George Routledge & Sons, 1946), especially Chapter One, "The Subject Matter of Formal Logic", pp.1-22. 2. Susan K. Langer, An Introduction to Symbolic Logic3 (New York: Dover Publications, 1967[1953]). 3. Susan Stebbing, A Modern Elementary Logic2 (London: Methuen, 1946[1943]). 4. Wilfred Hodges, Logic (Harmondsworth, Middlesex: Penguin Books, 1977).