Modern Confusion about
Logic
My first day as a
college-level logic instructor for gifted 7
th-10
th
graders (
read the story here), I gave my new students a questionnaire.
One of the questions was the usual “What do you hope to learn from this course?”
A surprising number of students wrote something like, “I want to learn logic so
I can apply it to big decisions, like what career to choose.” The first time a
student volunteered such an answer, I stammered something about how logic
might be slightly useful for such things, but is normally used in subjects like
science and law. By the end of the course, I had trained myself to respond to
such hopes with a carefully intoned “maybe.” But the idea stuck with me,
especially as I dipped back into the writings of Plato and Aristotle. Wasn’t
that where philosophy had
begun, with the determination of Socrates to
apply reasoning to the most important questions in life? What had happened to that
original philosophical spirit? Had we lost faith in it for any good reason? Or
was it just me that had lost faith in logic?
In one sense, modern
professors, intellectuals, skeptics, and atheists have become
too
fanatical about the importance of logic. Skeptics and atheists claim that it is
the only viable source of truth, and that we should give no quarter to
intuition, emotion, faith, or anything unscientific. Professors and
intellectuals credit logic with giving rise to
modern technology, science, industry, and progress. This reverence for logic, and mathematics in
particular, has made scientists and mathematicians perhaps overly revered, and
overly arrogant. Scientists are now expected to be experts even in fields where
the relevance of mathematics is slight, such as human psychology, sociology,
and political science. A pre-occupation with statistics – which is virtually
the only branch of mathematics that is widely applicable in these fields – has
plagued us with countless quantitative studies that rarely give us a deeper or
broader view of human nature.
Philosophy itself, once a
fertile discipline that connected art, science, practical living, ethics, and
religion, has become divided into two camps: those who believe that we should
use logic to resolve all philosophical disagreements (positivists and
philosophers of science), and those who shun logic as a mechanical,
soul-deadening, culture-destroying practice (postmodern and continental
philosophers).
Those philosophers who still
believe in logic can, for the most part, be subdivided into two main groups,
positivists and pragmatists. Positivists see logic as a set of mathematical
rules that can provide an unshakable foundation for thought, and they believe
that some day all human thinking will become mathematical. Pragmatists admit
that not all thought can be made mathematical, but claim that the rest of
thinking is based on heuristics. But
heuristics are simply imprecise logical rules. Ultimately pragmatism amounts to a form of positivism
that simply grants logic more room for imprecision. The over-emphasis on
logic remains.
Such views, which have
dominated Western philosophy for 100 years, have obscured our understanding of
what logic ideally should be.
Logic, as understood prior
to positivism, is clear, careful thinking. When you need to figure something
out, and you spend time determining all the details, that is logic. If you are
being rushed, or if the problem is too complex to be explained in all its
detail, then we are no longer talking about logic. Logic is the practice of
bringing all of your thoughts on a problem to consciousness. You can do
this using math, words, or images. If anything is left to subconscious intuition,
you are not being entirely logical.
Bringing your thoughts to
consciousness is the essential nature of logic that has been lost amidst the
pure mathematics championed by modern professors. It is the kind of logic that
you can and should apply to your major life decisions. Logic is no specific
set of rules, as taught in a university logic class. There are an infinite
number of rules you might choose, and none of them are correct by default. What
rules you use depends on what you are thinking about. “Logic” is simply making
things clear, whether by means of rules, calculations, pictures, or any other
form of expression. When you tell someone they are being illogical or need to
use logic, all you mean is that you want them to clarify what they are thinking
so they can see what is wrong with it.
We all use logic every day.
When we draw up a schedule or written plan, that’s logic. Any sort of in-depth
discussion, where you hammer out contradictions or disagreements, is logic.
Counting is a kind of logic. All mathematics is logic. Any time you consciously use a rule,
whether moral or scientific, it is logic.
Just as you can train your
bodily movements in fine motor skills and precise hand-eye-coordination, you
can train your mind to reason clearly and precisely. Practicing mathematics is
a great way to do this. However, mathematics alone does not give one a broader
view of how logic fits in to the rest of human thought and living.
Logical Fundamentalism
Postmodern philosophers
often criticize scientific philosophers for “logo-centrism,” arguing that the
imperial drive to order all knowledge logically is a mirror of, and contributor
to, the imperial dominance of the West over other cultures. It is difficult to
argue with postmoderns, however, when their more lucid prose looks like this:
The annals of official philosophy are populated by “bureaucrats
of pure reason” who speak in “the shadow of the despot” and are in historical
complicity with the State. They invent a “properly spiritual . . . absolute
State that . . . effectively functions in the mind.” (Brian Massumi, “Translator’s
Foreword” to Deleuze and Guattari’s A Thousand Plateaus.”)
It seems best to follow
Ludwig Wittgenstein’s advice and pass over such claims in silence.
Nevertheless, there appear
to be a few reasons to worry that perhaps we are becoming too
logic-centric in certain ways. Arts and humanities departments are being cut
across the country, while the government continues to pour additional funds
into math, science, and economics departments. The supposed justification for
this is that literature and art are ‘just for pleasure,’ and that the true
measure of a nation’s worth is its economic strength and expertise in science.
In a time when we need less industry and more sustainability, less
wealth and more self-sufficiency, these values should be reversed. People
should be taught to treasure what is beautiful and natural again, and to
devalue the industry-building that has done so much damage to the environment.
Yet our bureaucrats and top scientists continue to champion scientific logic
above all else. As a result of our logic-centered focus, most schools and
universities have taken on a more mechanical, almost factory-system-like
character. Opposed to these trends, a diverse and fertile home-schooling
movement has sprung up (see Homeschooling for Excellence, by David and
Micki Colfax; and A Thomas Jefferson Education, by Oliver DeMille).
The term “science” is often
used to refer to logic. This is imprecise. Science
traditionally means the same as knowledge.
Today, it more specifically means specialized knowledge. The “scientific method”
is a modern term for the logic of science, but positivism, which holds that we
can pin down a single method to be used in all sciences, has created a great
deal of confusion, and few philosophers of science agree on what, exactly, is
meant by the scientific method. If it
were acknowledged that no single method is useful in all cases, much of this
confusion could be dispelled.
The terms “reason” and “rationality”
can rightly be used as synonyms for logic. Etymologically they come from the
Latin word rationem, which meant “reckoning.”
However, as with logic, these terms have increasingly been forced into
specialized meanings. This is especially true of rationality. Scientists now frequently discuss “rational agents” or
“rational decision theory” as if we all agreed to precise and universal
definitions of these terms. But there is no universal theory of rationality.
For instance, an online
community called LessWrong
defines rationality as a two-fold art: (1) “the art of obtaining beliefs that correspond to reality,”
and (2) “the art of steering the future toward outcomes [you prefer].” Notice
that it is impossible to give a definition of any more universal art. Everything
we believe, we believe to be real. Everything we do, we do to achieve outcomes
we prefer. If we could master this kind of “rationality,” of gaining all
knowledge and reaching all aims, no other art would be necessary to human life,
which is absurd.
If we acknowledge, on the
other hand, that logic is simply the art of bringing our assumptions to awareness
for inspection and discussion, an art that is sometimes useful and sometimes
not useful or possible, then the absurdity vanishes.
Logical fundamentalism is
ultimately illogical. There are no grounds for certainty that all thought must
or should be made logical. The brain is too complex to make all thinking
completely explicit. The modern Skeptic movement is another popular example of
logical fundamentalism that tends to be over-critical of any idea that does not
wear the quantitative trappings of science.
Let’s take a look at the
article on
skeptic.com, “Motorcycle Maintenance Without the Zen,” by Chris
Edwards. He claims to be criticizing Pirsig’s
Zen and the Art of Motorcycle
Maintenance on logical grounds, which is already a questionable exercise
given that the book is a novel. In particular, Edwards criticizes this passage
from
Zen:
Phaedrus felt that […] scientific materialism was by far
the easiest to cut to ribbons. [...] He went after it […] using the reductio
ad absurdum. [...] Let’s examine, he said, what follows from the premise
that anything not composed of mass-energy is unreal or unimportant.
He showed the absurdity of trying to derive zero from
any form of mass-energy, and then asked, rhetorically, if that meant the number
zero was “unscientific.” If so, did that mean that digital computers, which
function exclusively in terms of ones and zeros, should be limited to just ones
for scientific work?
Edwards responds in this
way:
Modern mathematics, far from being a hard objective “thing”
is instead a mish-mash of concepts that arose from a process of cultural
synthesis (almost entirely in Eurasia, where cultures were easily able to intermesh
because of war and trade). The Greeks contributed geometry, the Gupta Indians
the numbers 0–9 and the decimal system, the Muslims gave us Al-Jabr, the
English gave us physics, calculus, and the Germans contributed the theory of
relativity and quantum mechanics. Each time, a culture’s language was adopted
and added not because they were “right” but because they were more descriptive
of objective phenomena and therefore a “better” language.
This response – which is
supposed to uphold logic – in fact commits the logical fallacy of missing
the point. Pirsig’s argument was supposed to show that scientific
materialism isn’t adequate to determine what concepts are useful, or even what
concepts belong in science. Pirsig’s definition of scientific materialism is
the belief that every concept must correspond to something material. He
challenged this view in order to defend his interest in “Quality” a concept
that can neither be seen nor touched. Edwards actually appears to be agreeing
with Pirsig’s conclusion, when he denies that mathematics is a “hard objective ‘thing.’” If numbers are concepts that are neither right nor wrong, but are merely a more
useful language, doesn’t that support Pirsig’s stance that Quality may be
useful despite having no material correlate? Indeed, Plato himself used
mathematics as an example of something which might be useful to think about
despite being immaterial, and in this way defended his belief in the idea of a
higher Good.
In modern times we tend to
forget three things about logic:
1.
A will or desire to be logical does not suffice
for logic. Pirsig was attempting to show the limitations of logic, yet his
argument was more logical than that of Edwards, which champions logic as the only way
to think. The LessWrong community seeks “systematic methods for obtaining truth
and winning,” yet this very definition suffers from a logically absurd
over-generality.
2.
Logic has its limitations. Because many
mathematical concepts like “zero” have no material correlate, they cannot be
derived logically. That does not prevent us from using them in a logical way
once they are established, but it does prevent us from developing a single
logical system that can encompass all truths. In fact, as Edwards admits, zero
was unknown to the Greeks despite the fact that they invented formal
mathematics.
3.
These two points together show that logic is not
the secret to truth. Sometimes people who believe they are being logical
are in fact mistaken. It is always possible that we do not possess the right
conceptual tools for the problem at hand, or that the problem is simply too
complex to be grasped in the conscious mind. For these reasons, logical
fanaticism is unwarranted and harmful to healthy thinking.
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