Introduction

In today's busy world, we are barraged by messages of all types: information, questions, jokes, requests, demands, enticements, even threats.  The messages come from all quarters: our family and friends, our coworkers and clients, our recreational and social groups, our preachers and teachers, store clerks and traffic cops.  And those are just the people we meet personally!  In addition, there are advertisers, business and union leaders, churches, educators, journalists, politicians, scientists, and many others bidding for our attention.  There are advocates and opponents of civil rights, consumer rights, gay rights, gun rights, litigation rights, privacy rights, religious rights, and women's rights.  Ideas by the hundreds and thousands, some of them agreeing, more of them conflicting, many of them from people with something to peddle or something to hide, a cause to promote or an ax to grind.

Whom should we believe?  What's true and what isn't?  How can we possibly make sense of it all?

The first thing most of us do is to latch onto what's immediately important to us—our health, our family, our job, our neighborhood.  From what's left, we pick out what's generally important beyond our own personal sphere, and anything else that seems interesting; then we filter out whatever is of no concern to us.  Now, from the topics we've selected, we weed out material from what we've come to consider unreliable sources—Faux News, Irrational Enquirer—unless, of course, we find them amusing or appealing in some other way.  Once we have the task trimmed to a manageable size, we can consider opposing viewpoints, check facts, and thus verify that we're working with adequate and reliable information.  What then?  That depends a lot on each of us, personally.

If we're the sort who prefer to deal with stuff mostly on an emotional level, we can just "go with the flow."  We can choose the cereal in the prettiest box, drive the truck with the macho grille, watch the video or play the game with the most spectacular hype, believe whatever makes us feel happy.  We can let others tell us what we ought to buy, what to eat, what to read, which team to root for, which candidate to vote for, whom to trust, whom to love, whom to hate.  And what to think?  Well, that's the beauty of it: If we let others make our choices for us, we don't really need to think, do we?  As long as we fit in, we're happy, and we can declare everyone else "losers."  Case closed!

However, if we're the type who fancy ourselves in of control of our own lives to some degree (or if we'd like to become that kind of person), if we have a strong sense of personal responsibility, if an important part of what we do is solving problems and making decisions, and if we or others must depend on our solutions' and decisions' being right most of the time, then we need a reliable tool to get at what's real.  We have to sift through the heaps of nonsense and pick out the kernels of truth, and then we must properly nurture and cultivate those kernels to yield useful information.  What tool can do that?  Logic!

We all know what logic is, right?  Logic is using reason to make an idea sound reasonable—or something like that.

Well, if that's what we think logic is, then we're thinking in circles, and that's decidedly illogical!  So we need to think again, because making something sound reasonable doesn't make it reasonable, any more than believing something actually makes it come true.  To illustrate, let's look at some arguments.  No, not the confrontational dispute kind of argument, but rather the evidence-reason-conclusion kind.  The following arguments are fairly familiar to most people, and at various points in time many have found one or more of them convincing.

1. "SUVs are safer than cars, because when an SUV and a car collide, the driver of the car is five times more likely to be killed than the driver of the SUV."
   
   

2. "The Bible makes clear that the earth is stationary, and that the sun, moon, planets, and stars all revolve around it.  Therefore, any theory that the earth moves is false, a heresy punishable by imprisonment or torture."
   
   

3. "Most drug addicts start out smoking marijuana, so obviously using marijuana leads to drug addiction."
   

What these arguments have in common is that...

• they sound logical to most people, in that each uses premises to justify a conclusion; and

• they are not logical because of faulty reasoning—regardless of whether the conclusions are true or false.  We'll see why later.*

But figuring stuff out sounds like too much work.  Why can't we just use common sense?

For one thing, what we curiously call "common sense" has little or nothing to do with our senses, and mostly to do with hunches and gut feelings—which, if we are brutally honest with ourselves, turn out to be wrong about as often as right.  Common sense tells us the world is flat.  Common sense tells us we can't fly.  Common sense tells us we can never run out of clean air and water.  At least that's what it told countless generations before our own.  And today common sense seems to tell many people that we can have a free and peaceful world, if only we can imprison or kill everyone who disagrees.

For another, "common sense" isn't all that common.  It tells different people different things, based on a slew of different factors.  Common sense tells us we need a longer lunch break, while it tells our boss we need to work harder.  Common sense tells men to leave the potty seat up, while it tells women to leave it down.  Common sense tells Christians and Muslims they'll go to Paradise when they die, while it tells Hindus they must go through life again and again until they get it right, even while it tells atheists that dead is dead, end of story.

Well, maybe we would be better off to think things through now and then.  Certainly if we use false information to begin with, we're bound to arrive at conclusions that are questionable at best.  But if we scrupulously base our reasoning on nothing but clear and undisputed facts, how could we possibly go wrong?

Very easily, it turns out.  For one thing, absolutely clear and undisputed facts are much rarer than many people suppose; thus the bulk of evidence and theory upon which people necessarily base most of their opinions and decisions remains the subject of continuing scrutiny, evaluation, qualification, and not infrequently disagreement.  But more importantly, if we do not clearly understand how (or even if) our facts are related, and if we are careless about how we use them in our arguments, then our beautiful fabric of reason, so intricately woven from durable threads of fact, will likely unravel under the first light of critical scrutiny.

An often used example of perfectly good facts leading to an erroneous conclusion goes like this:

• Fact: When it is raining, the ground gets wet.

• Fact: The ground is getting wet.

• Conclusion: It is raining.

The obvious problem with such a conclusion is that the ground might very well get wet for a variety of plausible reasons other than rain—a natural spring, an operating sprinkler system, or a burst water main, for instance.  What this example demonstrates is the all-too-common reasoning error of confusing cause and effect.  A simple way to straighten out our thinking in this particular case is to remember that, while rain always gives us wet ground, wet ground does not give us rain.  However, we'll be happy to learn that there are simple rules of logic that not only reflect this reality, but also govern sound reasoning in all similar situations.  So we needn't get bogged down relearning everything if the terminology changes from "when it is raining" to "if it is raining," or if the subject changes to "when / if something else."

We'll delve further into this in another section.  What's important to remember for now is that the rules of logic contribute to clear thinking, not only by showing us how we can legitimately use existing information to develop sound conclusions, but also by helping us avoid turning good ideas into nonsense (and ourselves into fools) through faulty reasoning.  Clear thinking in turn leads to better decisions and fewer mistakes, and fewer mistakes (in general, and excepting occasional fortuitous slips) lead to less misery and waste, and to that extent a more enjoyable existence.  Does this mean we ought to formulate all of our opinions strictly on the basis of strict and impersonal logic?  No, not at all.  We don't need logic to savor a delicious meal, appreciate a bouquet of roses, or delight in a glorious sunset.  But we should consider competence in logic a powerful tool for finding truth, whenever we desire or need it.

Many people seem under the impression that if an argument can be made to sound logical, then it must be logical.  Perhaps they try a few times to use some form of pseudo-logic in this way (as we did in our "rain" example earlier), and achieve disappointing results.  Or perhaps on various occasions they've been "burned" by others using pseudo-logic to fool them.  As a result, they might "conclude" that anything resembling systematic thinking is worthless at best and diabolical at worst, and develop a strong distrust of it.  However, real logic is as different from pseudo-logic as a real dog is from a stuffed toy, despite the superficial resemblance.  Whereas pseudo-logic relies on the way it sounds, real logic derives instead from the soundness of the reasoning process and its parallel to reality.

Logic is not simply an artful way of creating a comforting illusion that things make some kind of sense.  Rather, it is a systematic way to ensure that a group of ideas are consistent with each other.  The system is governed by strict rules, which ensure the consistency of ideas to which they are applied, and which rule out inconsistent patterns.  But although the rules of logic are strict, the basic ones are quite simple, easy to understand and apply.  Moreover, they are a practical necessity in any job or lifestyle requiring the ability to solve problems and make decisions, not to mention to be a wise parent, a thoughtful consumer, and a responsible citizen.  This is particularly true if anything very important—such as someone's life or livelihood—depends on having his or her solutions and decisions turn out to be right on more than an occasional and accidental basis.

Yet lest we get the impression that logic is always starkly and stuffily serious, we should reflect that it also allows us to "get" jokes, by identifying the ironies, parallels, and inconsistencies that are the crux of much humor.  For much of simple logic is so intuitive that we use it without even realizing it.  Learning to use it well requires merely paying a little extra attention to detail, understanding how it works, and expanding upon that.

There is no reason the fundamentals of logic cannot be learned at the high-school level; any student who can comprehend geometry or algebra can certainly master basic logic with only a little effort.  Indeed, a compelling case can be made that logic is as important as reading, writing, and mathematics, and that demonstrated competence in it ought to be a high school graduation requirement.

There are different ways to learn logic:

• First, there is the hard way: being conditioned slowly by the results of many mistakes, by being bamboozled by every salesman, politician, and faith-healer, and perhaps even by regularly ending up in hospital or jail along the way.  For the most part, such a clueless existence amounts to little more than a blind stumble from one crisis to the next.  It's not the way most of us choose, but some folks seem to gravitate to it.

• Next, there is the way most people do it: learning through the often hit-and-miss practical experience of having to figure things out.  In human society, this is a necessary part of staying alive, healthy, and out of trouble, not to mention fun stuff like designing, creating, using, and fixing things.  So anyone who earnestly aspires to become part of this picture can't help but pick up at least a smattering of logic in the normal course of daily life.

• Finally, there is the easy way: reading a book or taking a course on logic.  While the adage that there's no substitute for experience certainly rings true, my own preference is to use the easy way as much as possible.  Not only does it minimize the pain and expense that often plague other methods, but it is also more thorough in many respects, preparing one to apply similar processes to a variety of disciplines.

But even if someone is not inclined to read a book or enroll in a course on logic, I believe it is not only possible, not only desirable, but actually easy, for anyone of average intelligence to learn logic—the basics of it, anyway—on his or her own, and moreover "on the cheap," right here on the web.

Thus I'm posting some information about logical thinking, starting with simple ideas, and eventually advancing to concepts that might take a few moments to digest and a little practice to master.  Don't let the terminology intimidate you; logicians have a jargon of their own, but we'll translate it into normal English.  There are no overpowering concepts here, just enough to get the average person's mental gears meshed and turning smoothly.  Those who find the experience beneficial or even enjoyable might decide to go ahead and buy that book or enroll in that course after all.  I'd be interested in any feedback.

Subjects we should expect to touch upon, in approximate order of increasing difficulty, are:

The earlier segments are devoted mostly to concepts the average person can immediately apply in daily life, whether in solving problems at home or work, or in evaluating claims of advertisers, politicians, and others.  The later ones are to give those who are curious a closer look at the abstract nuts and bolts of logic.  This is intended to offer insight into how and why logic works so consistently, and therefore applies to a broad spectrum of human endeavor that demands reliable support.  In the process, it might also provide some further clues on how to tune up and expand one's own reasoning skills.

Among the many things with which we will not deal here are the history of logic, complex proofs, set theory, and Venn diagrams.  If you're curious about any of these, then you can congratulate yourself on being somewhat above the mainstream, and you really do need to visit a bookstore or a university (or a more advanced web site).

It will be a project of mine to create tutorial and informational files, a project I will work on as I have the opportunity, and which I will revise as the evolving situation and guest feedback suggest advisable.  By no means will this work constitute a complete and comprehensive course in logic; rather, it should be viewed as a layman's guide to the process of methodical thinking, and of applying that process to enhance quality of life (however one chooses to define it).  Perhaps most important, it should allay anyone's fears of tackling, and deriving practical benefit from, a subject customarily seen as the exclusive province of programmers, professors, philosophers, and scientists.  For to prosper in today's demanding world, there is no question that one needs logic—the only option being whether to learn it the hard way or the easy way.  You, the esteemed guest, are invited to make whatever use of these files you will (subject, of course, to any copyright provisions), as they become available.  I would very much appreciate your feedback, should you care to offer it.

=SAJ=

*By the way, remember those arguments at the beginning of this page?  Here they are again, along with what's wrong with them.

1. Argument: "SUVs are safer than cars, because when an SUV and a car collide, the driver of the car is five times more likely to be killed than the driver of the SUV."
   
   Error: This argument turns on the fallacy of "contradictory premises," curiously equating greater safety with greater harm.
   
   Fact: Studies of SUV and car accidents reveal that SUVs are actually more prone to crash in the first place (due to a higher center of gravity and greater tendency to roll over). Furthermore, SUVs are only recently catching up with cars in occupant survivability in crashes with stationary objects. It turns out that the greater hazard to car drivers in car-SUV crashes is the SUV's inordinately high bumpers. While these do not make the SUV any safer to its own occupants, they pose a much greater hazard to anyone that the SUV happens to run into—say, at window level instead of at normal bumper level. Thus the marketers' attempt to portray a lethal hazard as a "safety feature" fizzles!
   
   

2. Argument: "The Bible makes clear that the earth is stationary, and that the sun, moon, planets, and stars all revolve around it.  Therefore, any theory that the earth moves is false, a heresy punishable by imprisonment or torture."  [This argument commits two errors.]
   
   Error #1: "Appeal to dubious authority" (ad verecundiam) here ascribes full knowledge of the natural universe to the Bible's authors.
   
   Fact: In light of many independently confirmed scientific discoveries, religious scripture—whatever other merits it retains—has been discredited as a reliable authority on the workings of the natural universe!
   
   Error #2: "Appeal to force" (ad baculum) threatens harm to anyone who dares disagree.
   
   Fact: No amount of punishment can confirm or refute whether the earth, in fact, moves!
   
   

3. Argument: "Most drug addicts start out smoking marijuana, so obviously using marijuana leads to drug addiction."
   
   Error: The problem with this is the "false cause fallacy"—more specifically, a version known as post hoc ergo propter hoc (or just post hoc for short). As the English translation, "after this, so because of this," indicates, in this case post hoc supposes because drug addiction is often preceded by marijuana use, that the one causes the other—ignoring that a host of other common factors might as well be plausible causes.
   
   Fact: We need only observe, that millions of marijuana users—the vast majority—remain content with "pot" over many years and never escalate to more addictive drugs, to demonstrate that the argument is not borne out in reality!

So why do people make such absurd arguments?  The general reason is simply "because they can get away with it."  Whether or not the arguer himself understands logic, he can be fairly certain that most of his audience doesn't.  Most of us pick up a little logic as necessary, to apply specifically to what we do for a living, to balance the checkbook, and maybe to fix the car; but we fail to absorb the general principles behind it.  Consequently, when the topic shifts to something less familiar, we can easily be fooled into accepting a conclusion on the basis of dubious assumptions and faulty reasoning—whether our own or someone else's.

In addition to the general reason, "because they can get away with it," in each particular case there is usually a specific motivation.  Regarding our particular examples, the motivations appear to be, respectively:

1. Someone has something to peddle.

2. Someone has a cause to promote and something to hide.

3. Someone has an ax to grind.

Apparently unable to find good ways to argue their cases, they've settled for bad ways.  But as long as no one notices the errors and points them out, it's all the same to them.  They've baited their hook and it's been swallowed.  They've sold another SUV; they've promoted their belief and hidden its weakness; they've ground their ax.  They've once again hauled in the suckers, so let the truth be damned!

(Bear in mind that showing an argument invalid or unsound does not in itself prove its conclusion false.  It merely shows that the conclusion is not adequately supported by the argument as it stands.)

On the other hand, it is not infrequently the case (especially during a political campaign) that an exuberant but inattentive debater is publicly hoist on the petard of his own illogic, and that can be a merry spectacle indeed to behold!  But of course, only those with some grasp of logic get the "joke" without having it explained to them.

Curiosity piqued?  Want to be one of those who "get it"?  Then click a link!