Modern Confusion about Logic
My first day as a college-level logic instructor for gifted 7th-10th 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.
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.