Logic vs. Logical Fundamentalism (Part 2)

Logical Mastery

A master of logic knows both its power and its limits. As we saw in the last part, to assume that logic alone is sufficient for forming all our beliefs is absurd, because then we would need no other techniques.  On the contrary, it is manifest that a true master of logic would have many diverse forms of knowledge, in order to use the techniques and premises most useful for the question at hand. And since no human has the time to learn all disciplines, a true master of logic must be acquainted with the most general and important disciplines.

In other words, the best logicians are more than logicians. The domain of logic itself is rather narrow. It consists of simple-yet-thorny problems, which would confuse if they were not laid out explicitly. Some of these problems are more central than others. What is 12 times 15? Most of us don't know this immediately. Even people who can do it quickly in their heads reason something like this: 4 times 15 is 60. Since 12 divided by 4 is 3, this is the same as 3 times 60, which is 180. This is how I personally do the problem, and in most cases I can do it in about 3 or 4 seconds. But I haven't been entirely logical yet, and perhaps you didn't follow. To clarify, let me use arithmetic which is essentially the logical formalism of numbers:

12 x 15 = A

(3 x 4) x 15 = A           factorization of 12

3 x (4 x 15) = A           associativity

3 x 60 = A                   4 x 15 = 60

180 = A

It's probably taken you more time to understand my reasoning here than it would have to simply use a calculator, or to use long-multiplication as you learned in school. In fact, you might wonder why I chose to do it this way when I could have used the usual way of writing multiplication problems. I was attempting to explain a mental trick I use in multiplying numbers. In most cases it helps me calculate much quicker, and I've been using it for so many years it often happens largely beneath my consciousness. Where did I get the trick? Why is it faster? You should also wonder: why is it important?

This example has shown several uses of logic, as well as weaknesses. Logic is useful for well-defined problems. It is useful for explaining our thoughts more clearly. It is also useful for analyzing and teaching methods of thought that can speed up thinking. Logic is not useful for vaguely-defined problems. The question of how to find good tricks for doing math in your head is not a question of logic, but of experimentation and play. Logic can clarify, but only at the cost of using more words and symbols to explain. I could have stopped with "12 times 15 is obviously the same as 3 times 60, which is 180," because that's normally how I think about it. But it is not a fully logical argument because it might not be obvious to you why it is the case.

Humans only rarely use pure logic. When a lot of pure logic must be done, we give it to computers, which are much faster at it. Among scientists and philosophers, sometimes the use of logic is considered to bestow a greater deal of certainty and authority. This is often unwarranted – even professional papers in physics usually contain more verbal passages than they do mathematical equations. Putting more equations in a paper does not necessarily make the paper as a whole more certain. Logical or mathematical reasoning is always based on assumptions, and these assumptions, along with the fidelity of the reasoning, will generally determine the soundness of the conclusion. Rather than comparing the number of mathematical symbols being used, it is best to treat each written argument on its own terms. The practice of judging a subject based on how logical it appears is a major source of our bias against the humanities and in favor of physics and mathematics.

Logic is fidelity. By making our reasoning explicit, we make sure that nothing is lost or misunderstood. Mathematical knowledge is precise, so it requires a precise symbolism. Learning to use this symbolism carefully and with fidelity helps us to express ourselves clearly. Fidelity is also important when using the English language. The vast majority of our reasoning is in our native tongue. There is no master mathematics that can encompass everything we must say, therefore it is a special challenge to express logical arguments in words. How do you explain your logic fully when you are bound to use words that do not have perfectly precise meanings? In the universities, this is known as "informal logic," but it is taught so narrowly as to be inadequate to what we need it for.

Logic itself is easy. If it is raining, there are clouds. It is raining. Therefore, there are clouds. When you have rules and you know how to apply them, there is no problem. When you're given a set of math problems and all you have to do is follow a mechanical set of rules, it quickly becomes tedious. What is hard is expressing complex logic informally, in words. It is difficult to take a tough new problem and express it logically when you have no formalism. And this is the way it is with most real-life logical problems we run into. Is abortion right or wrong? Two novices can easily spend hours debating whether this question can even be parsed into logic.

Logic is a tool. That something is a logical question does not automatically make it important. The question of how to multiply 12 and 15 was merely an example, and we did not go as deeply into it as we might have. A true master of logic does not get caught up in less relevant details. On the contrary, a master of logic knows what is relevant and develops tools for thinking about the most relevant details.

Aristotle, the ancient Greek philosopher, is perhaps the most all-round capable logician who has ever written a book. Everything he wrote was in Greek, not in equations (as modern logicians strive to do), yet it is so clearly and carefully thought-out and argued, that even where he is mistaken you can tell exactly where his error crept in. Ultimately, this is why logic is important. If we can lay out our ideas clearly and explicitly, then we have done something useful for future generations even if it is wrong. Let's take a look at his discussion of it means to be wise:

[W]e must inquire of what kind are the causes and the principles, the knowledge of which is Wisdom. If one were to take the notions we have about the wise man, this might perhaps make the answer more evident. We suppose first, then, that the wise man knows all things, as far as possible, although he has not knowledge of each of them in detail; secondly, that he who can learn things that are difficult, and not easy for a man to know, is wise (sense-perception is common to all, and therefore easy and no mark of Wisdom); again, that he who is more exact and more capable of teaching the causes is wiser, in every branch of knowledge; and that of the sciences, also, that which is desirable on its own account and for the sake of knowing it is more of the nature of Wisdom than that which is desirable on account of its results, and the superior science in more of the nature of Wisdom than the ancillary; for the wise man must not obey another, but the less wise must obey him. (Aristotle, Metaphysics 2, 982a, W.D. Ross translation).

The context for Aristotle's discussion is an introduction to the principles of metaphysics, which for him are the first principles of what exists, applicable in all fields of knowledge. He equates knowledge of metaphysics with Wisdom itself, which is the broadest and most divine science. As he does at the beginning of all his books, Aristotle clearly and succinctly lays out the goal of his work and his method of approach. The first task, then, is to determine what "causes and principles" the wise man must understand to be wise. This passage is only preliminary, but it begins with "what notions we have about the wise man," including (1) that he has general (if not detailed) knowledge about every field, (2) that he has knowledge about difficult subjects, (3) he is a capable teacher, (4) he knows subjects which are more theoretical and primary.

Just in stating these aspects of wisdom, which are generally taken for granted and left as unconscious assumptions, even today, Aristotle has given an explicit, logical definition of philosophy that is as perfect as can be desired. (Incidentally, the art of making definitions is an essential branch of logic that is nevertheless neglected in most modern courses on the subject.) The relevance of his definition today can be seen simply by asking who we moderns consider wise and determine whether they satisfy it. Scientists are usually called the wisests among us, and among scientists, physicists, such as Albert Einstein, are held in the highest esteem. Other people, who oppose putting mathematics on a pedestal, most commonly name novelists like James Joyce or perhaps analytic philosophers, like Wittgenstein, or postmodern philosophers, like Derrida, as the wisest. So let's consider these four categories of modern thinkers – physicists, novelists, analytic philosophers, and postmodern philosophers – in terms of Aristotle's criteria.

Physicists fail, in general, to satisfy criterion (1). They do not have knowledge of every field, but are relatively untrained in philosophy, the humanities, and "soft sciences" such as the humanities. Most modern physicists are encouraged to specialize even further in a particular field, such as astrophysics, solid state physics, quantum field theory, etc. They are far indeed from being trained in politics, ethics, or mysticism. Physicists do, however, often satisfy criterion (2). Their subject involves extremely difficult mathematics, so difficult that professional physicists tend to score better on mathematical aptitude tests than mathematicians themselves. Some physicists do satisfy criterion (3), being good teachers. My experience as an undergrad at Caltech was that most physicists, however, prefer to focus on research. Physicists are rarely excited about teaching their theories to those outside their field, and when they are good at making their ideas accessible, the way Stephen Hawking or Brian Greene are, their books fail to address the broadest range of human concerns, however excellent they are in other respects. Theoretical physicists satisfy criterion (4), knowledge of what is theoretical and primary, but experimental and applied physicists do not. Therefore, even theoretical physicists only satisfy 2 out 4 of Aristotle's criteria, and are thus not Wise under his definition. This conclusion holds up when compared to the role physics plays in practice – physics is indeed too specialized and too insular to provide people with what you would call wisdom, and is usually more useful in technical engineering contexts.

Novelists often do satisfy criterion (1). Science fiction authors, especially, often display an impressive range of knowledge, including moral, aesthetic, social, and scientific aspects of human life. Writing good, publishable fiction is indeed difficult, so we can give them criterion (2) as well. Are novelists capable teachers? In a few ways they are, because they can inspire people to think and question. But on a person-to-person basis, you wouldn't generally go to novel or novelist to learn a particular subject. Aristotle's criterion, more specifically, is that "he who is more exact and more capable of teaching the causes is wiser." Novelists can't be exact in novel writing, because their stories become boring. Nor do they focus on causes, but on human drama. So they do not sastisfy criterion (3). Do they know subjects which are more theoretical? Often they do, but this is not essential to being a novelist, so we cannot say they satisfy criterion (4) either. Once again, we have a class of thinkers that satisfy only 2 out of 4 criteria.

Postmodern philosophy does not stress ability in mathematics or science, though it does encourage its students to investigate a broad range of fields. At their best, postmodern philosophers do have broad-enough knowledge to satisfy (1). Being a successful postmodern writer is certainly not easy (any kind of writing career is difficult), so we can say that they have knowledge of difficult subjects (2). When it comes to causes and exactness, postmodern philosophers are not trained to teach clearly (3). It is unclear whether postmodern philosophy is properly theoretical, or simply claims to be, but even if we give it the benefit of the doubt on (4), it still only scores 3/4.

	Physics	Literature	Postmodern Philosophy	Analytic Philosophy
1) Broad?	No	Yes	Yes	No
2) Difficult?	Yes	Yes	Yes	Yes
3) Teach causes well?	No	No	No	Yes
4) Primary?	Yes	No	Yes	Yes

Analytic philosophers generally do not satisfy condition (1). They are often untrained in literature, religion, and aesthetics, though most respected ones have at least some knowledge in these fields. They do satisfy condition (2), since analytic philosophy is a very difficult subject, in terms of the complexity of the language and logical reasoning used. They generally score even higher than English professors on language aptitude tests. The best analytic philosophers are good teachers and mentors, and write clear popular accounts of their philosophy. They treat causation and reason as exactly as can be expected, so they satisfy (3). Analytic philosophy is also entirely theoretical, which means they satisfy (4) and score 3/4 on Aristotle's test.

In other blog posts (for example this series) I have argued that analytic philosophy is too narrow to be considered the heir to classical Western philosophy. Aristotle would have agreed that analytic philosophers are not philosophers in the truest sense. Let's take a look at the passage almost immediately following his definition of wisdom:

"[T]he science which knows to what end each thing must be done is the most authoritative of the sciences, and more authoritative than any ancillary science; and this end is the good of that thing, and in general the supreme good in the whole of nature. Judged by all the tests we have mentioned, then, the name in question falls to the same science [metaphysics]; this must be a science that investigates the first principles and causes; for the good, i.e. the end, is one of the causes." (Metaphysics 2, 982b)

Why is the study of the supreme good or end necessarily the most authoritative science, according to Aristotle? He states the reason at the end of his definition of Wisdom: "for the wise man must not obey another, but the less wise must obey him." Whatever knowledge deals with the supreme good, or the ultimate goal, is necessarily the one that determines how the rest of our knowledge is organized or applied. Whatever project one works on, the first question is always, "to what end?" If a project does not have a goal it is not a project at all but mere play. Modern analytic philosophy is mere play because it does not have a supreme goal or aim, which is Aristotle's first requirement for a science to be central. So let us augment Aristotle's definition of Wisdom to take into account the other assumptions that he originally left implicit. (Making them explicit is, once again, a practice in verbal logic):

1.      A wise person has general knowledge of all major fields and their ends.

2.      A wise person can learn difficult and important subjects.

3.      A wise person is more exact and capable of teaching causes and purposes in every major branch of knowledge.

4.      A wise person is more knowledgeable about fields that are primary in the sense of being more theoretical and which concern central or superior ends or purposes.

According to this more exact definition, which is closer to what Aristotle really meant, analytic philosophy fails to satisfy any of these criteria because the ends or purposes of its abstract linguistic systems are rarely made explicit, nor are they stressed in university courses. It is generally assumed – usually implicitly – that because science drives societal progress, and analytic philosophy is the study of science, analytic philosophy is directed toward the ultimate goal of civilization. However, as I argue in my recent book, it is far from obvious that progress is occurring at all, nor does it appear that the so-called "advances" of Western civilization are sustainable. At the very least, these bedrock assumptions warrant investigation. No field of study can be called "wise" which ignores the open question of the ultimate goal of civilization.

Aristotle is the master of logic, and it is thanks to his fidelity – which, again, is the essence of logic – that the modern world is acquainted with the views of his opponents. Even Plato's system of metaphysics is made clearer in Aristotle's writings than they are in Plato's own dialogues. The strength of a philosophical tradition lies in the fidelity of its logic. Without clear explanation, the basic ideas of a system of thought cannot be transmitted faithfully to future generations. Nor can the weaknesses of a way of thought be uncovered, analyzed, or overcome.