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.