“One swallow does not make a summer.”
Many aspects of American education are “hit or miss” in terms of producing positive results. One area especially likely to slip through cracks in our various systems is logic. Though it is no more complex at its core than algebra, symbolic logic is often regarded as a high level discipline reserved only for electronic engineers (as it explains the fundamentals of circuit design for information technology applications) and a particularly rigorous subset of philosophers. Though it also is a vital skill applied to the reading of non-fiction, it is rarely given any place at all in coursework intended to cultivate verbal skills.
Actually, logic has useful applications in almost any discipline. It goes to the heart of sound methodology in science. It yields tremendous dividends of insight when applied coldly to questions of civics, economics, foreign relations, etc. It can even inform efforts based on any systematic approach to creative arts. Yet in being vital to so many basic human pursuits, it seems to have been excluded from training for almost all of them. It is as if the “somebody else’s problem” phenomenon has educators of all specialties convinced that it would be a distraction from their mission to give students a proper education in logical deduction.
I was fortunate enough to be exposed to the works of Aristotle, and the significance of the categorical syllogism, in a high school course on adversarial debate. Though I continued readings on logic out of my own interest in philosophy, it would not be until my final semester of college, sharing a small class with a few math-focused engineering students, that the subject would be revisited in any formal way. In my own informal way, here’s the phenomenon in a nutshell.
Many forms of reasoning can produce novel error. By that I mean that normal methods of inference and argumentation tend to be complex processes that do not involve verifying every new thought follows with certainty from prior givens. The categorical syllogism is the fundamental unit of deductive reasoning. Following the proper form, deductive reasoning is a “garbage in, garbage out” process. What this means is that falsehoods can still be deduced, but only if falsehoods are included in the assumptions made at the start of the process. If only true statements serve as the premises for a categorical syllogism, then it will produce a new true statement as its conclusion.
Take the classic example . . .
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
If everyone agrees with the first two statements, the third becomes an inescapable logical conclusion. It simply must be true if the premises on which it rests are also true. The mechanism for this involves categories, though in modern parlance “sets and subsets” may have more resonance. Thus the abstract form is . . .
All As are Bs.
All Bs are Cs.
Therefore all As are Cs.
In terms of the example with Socrates, the man himself becomes a category of one. Socrates is a subset of “men.” Thus the form remains valid when applied to individual subjects of study as well as groups.
Some people find it helpful to diagram this sort of logical relationship. Others may reduce things to the most succinct meaningful symbols. That may open up an entire realm of computational logic in which complex forms may still benefit from the absolute reliability of pure deduction. That sort of thing is crucial to understanding how computing technology works at its most basic level, though in a modern context it is a fairly esoteric speciality.
By contrast, basic logic is a vital tool in both reading comprehension and structured argumentation. Most people, most of the time, do not think in purely logical forms. Yet understanding purely logical forms provides a method through which the messy complexities of real world discourse can be broken down into basic units. Sometimes sensible advocacy is simply a matter of being able to go further toward the goal of distilling reason from argument than contrary advocates do. Of course, this is only an avenue worth pursuing if your overall reasoning is sound to begin with. Then again, if you raise your voice in support of unsound reasoning, just what could you hope to accomplish in the first place?
Those who champion unpopular causes are often right to point out the flaws of inductive reasoning. This is a fallible process by which conclusions are reached based on a preponderance of evidence. Yet dwelling on such flaws can create problems of its own. Scholars discussing the philosophy of science may refer to “black swans.” Centuries upon centuries of familiarity with swans led to the widespread belief that mature unpainted swans could not be black. Thus it was surprising when naturally occurring black swans were discovered in Australia. The story of the black swan illustrates the dangers of reasoning by means of sampling.
Yet in some ways this can be a powerfully misleading argument. Given the definition of swans along with what is known about biology and evolution, it is a reasonable assertion to claim that there are no swans with the natural ability to fire deadly laser beams from their eyes. A victim of what I call “the skeptics’ infinite regress” might argue that this assertion cannot be accepted as factual until each and every swan in the universe has been observed with enough detail to verify that its gaze could never produce a lethal concentration of coherent light. Personally, I believe that the black swan tale illustrates an excessively narrow definition of swans existed prior to the 17th century, but in doing so it does not render any efforts to define swans as futile. To the contrary, the term retains meaning and value even if it defines laser-blasting swans as an implausibility unworthy of consideration.
This is an important concern even with deductive logic, because ultimately anything useful and practical we might say about the world must go beyond work with purely abstract terms. To reach concrete conclusions, we must work with concrete premises. Those can only be obtained through observation and induction (at least, to the degree they are not a function of speculation or outright fabrication.) Thus, no matter how well-deduced your own conclusions might be, convincing others to follow your train of thought must begin by getting those others to accept your initial point of departure.
This explains much of why the application of reason has been so problematic in modern political discussions. Our culture abounds with false narratives popularized by appeals to the worst in human nature. Demonizing political adversaries, discrediting large groups by focus on the worst individuals within, substituting catchy sloganeering for substantive analysis — it all serves to establish a strong foundation of lies on which great structures of misinformation can be constructed.
With many sources of “news and information” neglecting much of what is newsworthy while freely echoing popular misinformation, many people with the best of intentions still find themselves standing firmly in the wrong. The quagmire traps of the propaganda past have given way to rock solid bulwarks from which powerful bursts of reason can be resisted. This makes it all the more important to become versed in logical forms so as to better isolate and undermine the bedrock of nonsense propping up legions of the happily misinformed. Until common ground, ideally constrained by underlying factually accurate claims, can be achieved; any clash of ideas, no matter how formal or thoughtful, is unlikely to lead to common conclusions.