Chapter 3 – Elementary Logic

One of the traditional functions of a mage is that of seer. According to the fairy tales, the goodly mage is expected to see things that others do not, and to share this insight with the monarch for the benefit of the kingdom. It is a useless mage who sees something important in a crystal ball and then misinterprets what is seen. In other words, in order to see clearly, we must first be able to think clearly. In place of crystal balls, most of us use the Internet as well as other news media and receive tons of information. However, interpreting that data correctly, and identifying the skewed and the deceptive information, require sound use of logic. This chapter will provide an overview of the basics of logic, which you can then use to evaluate the following chapters more clearly.

Order and logic are closely intertwined, and logic is home territory for any order mage. But what is logic, exactly? We can often recognize bad logic when we see it but defining it is not so easy. So I will defer to  Merriam-Webster and quote that logic is: “a science that deals with the principles and criteria of validity of inference and demonstration : the science of the formal principles of reasoning.”[1]

I confess I don’t find that definition very helpful. Nevertheless, let us dive into the principles of logic and let the term stand as is.

The clearest example of logic is known as deductive reasoning. Here is an example of deduction:

• All spheres are round,
• A crystal ball is a sphere,
• Therefore, a crystal ball is round.

Deduction occurs when two or more known facts are seen together and force an additional conclusion. The first two lines are called premises, and the third line is, in this case, a valid conclusion. As long as we don’t nit-pick over whether micro-scratches on the surface of a crystal ball render it non-spherical, we are good. 

For every sound use of logic, there are, sadly, faulty uses as well. Consider the following:

• All eyeballs have pupils,
• My teacher has pupils,
• Therefore, my teacher is an eyeball.

This line of reasoning fails on two points. The first is that the premise, “all eyeballs have pupils,” does not imply that there cannot be other things in the universe with pupils. Secondly, we are dealing with two distinct definitions of the word “pupil,” and deduction cannot cross multiple definitions.

Deduction, as bulletproof as it is when properly used, is very limited in its scope. The number of premises that can be proven, in a strict sense, are relatively few. It is far more common for us to use induction in our everyday lives than deduction. As Merriam-Webster tells us, induction is “inference of a generalized conclusion from particular instances.”[2] Let’s look at an example of inductive reasoning.

• My car always starts when I turn the ignition,
• I’m going to turn the ignition in a minute,
• Therefore, my car will start in a minute.

This is not deductive reasoning because the first premise is based on historical observation, not on an absolute fact. The provable fact statement would actually read, “as I recall, my car has always started every time I have turned the ignition.” That may be a true statement, but it is different from an assertion that every time the ignition is turned, the engine will start. It is quite possible, of course, that the ignition is worn out or it is -20 degrees outside and the engine might not, in fact, start. However, we go through our lives making hundreds of assumptions based on past experience. If you ever get the chance to take a course in Philosophy, you will be surprised to discover how few assertions can actually be proven with certainty. Still, without inductive reasoning we could not live our lives. Picture someone who refuses to take a drink because there is always the remote possibility that it has been poisoned. That person would soon die of thirst, but at least they would not get poisoned!

Now let us look at some of the common fallacies. One common logical error to avoid is called the Genetic Fallacy. This line of thinking attributes trust or mistrust based on the source of a statement. Formally, the argument goes like this:

• Miss X is an honest person,
• Miss X said statement Y,
• Therefore, statement Y must be true.

Logically, the truth value of a statement has no relation to the character of the speaker. However, this error is very common based on human nature. It derives from all our prejudices and biases. When you watch a political debate, consider how you feel when a member of the party opposed to yours takes the stand. Think about the skepticism with which you listen to their statements. Conversely, try to recall the emotions you experienced while listening to a candidate you supported. Now, apply this to your reactions to salespersons, editorials, preachers, bosses, children and teenagers, minorities, men and women and non-binary persons. We all have biases which color our perceptions of statements in light of the sources. I am not recommending an attempt at purging our feelings; I am merely suggesting that we become acutely aware of them as a key step toward clear thinking.

Another common Fallacy is called the Slippery Slope. This is usually invoked as an argument against a course of action that contains risk when taken to extremes. Here is an example:

• Marijuana is a gateway drug.
• Gateway drug use leads to more dangerous drug use.
• Legalization of a drug leads to increased use of it.
• If we legalize marijuana, thousands more youth will overdose on other drugs and die.
• Therefore, we must not legalize marijuana.

Tying the proposition that we consider legalizing marijuana to the worst-case scenario of thousands of street-drug related deaths is an example of a Slippery Slope argument. This does not necessarily mean that the conclusion is untrue. The point is that the conclusion is not proven by this kind of fallacy.

A very common question that comes with a slippery slope argument is “where do we draw the line?” Whenever a controversial course of action is proposed, a natural fear is that once we take a step in that direction, we might take a second and a third and so on until we reach a disaster point. The question itself is valid and important. But the answer is that a line can be drawn at any point in a progression. The principle here is that step five being a disaster is not a logical reason to run screaming from step one.

Another common error is to confuse correlation, which is when one event follows another closely, with causation. It is easy to suspect that two events that happened in rapid succession are related, although that thinking ignores coincidence. This can be seen every time an election is pending. Let’s suppose that a president is running for re-election. We hear the following from the opposing side of the political spectrum:

• Groucho was president the past four years,
• During the past four years, gas prices have doubled,
• Therefore, Groucho’s policies caused the spike.

The fact is, the spike may have been caused by reasons that had nothing to do with any of his policies. I hear this kind of thinking every time there is a national election and voters from both sides seem to be equally guilty of this sort of rhetoric. I am grateful that I have not heard a president blamed for a hurricane or earthquake yet!

Another error in logic occurs as a result of something called groupthink. It is difficult to contradict a majority, especially when the feelings of the social circle are important to the individual. In college classrooms, I recall few students willing to challenge the assertions of the teachers. Also, in closely knit communities, the words of the pastor carried many followers along with them.

The final example I will discuss here is called confirmation bias. I’m going to refer to Wikipedia on this one because I want my readers to reflect on this one carefully. The definition here is, “Confirmation bias, a phrase coined by English psychologist Peter Wason, is the tendency of people to favor information that confirms or strengthens their beliefs or values and is difficult to dislodge once affirmed.”[3] The psychological tendency at play here is the desire to be proven right. In elementary school, we were all rewarded when we answered questions correctly, and penalized or even shamed when we were incorrect. Being perceived as right or wrong affects our place in the pecking order of our social circles.

I believe the most compelling instance of confirmation bias can be found in dogmatic religious circles. I spent many years in right-wing christian circles where it was taught, to my discomfiture, that those with wrong beliefs were to be condemned to an eternity in Hell. I cannot imagine a more binding psychological “need to be right” than a mindset which punishes error to the ultimate extreme. I have always found the concept itself to be deplorable. If it is true that “unbelief” may be motivated by pride or hostility, then condemn the pride and the hostility, not the sincere beliefs themselves. Anyway, it seems clear how the need to be right can be fueled by upbringing and cultural context. I concede that liberal and scientific biases exist as well. Note the dogmatic posture of some who refer to science as “disproving” either the supernatural, or the possibility of alien species among us.

A thorough exploration of even the basics of logic would require an entire book by itself. I encourage you to continue your rational development on your own. We can see here how emotions like fear and bigotry can skew our logical thinking processes. Therefore, as you progress with this book and make plans for your future, consider your emotions carefully. Are there avenues you fear to explore? Conversely, is there a future opportunity that you want desperately enough to pursue without wisdom? Shakespeare suggested, “to thine own self be true.” Looking at yourself honestly and understanding your desires, strengths and weaknesses can give you a great advantage toward choosing logical goals and attaining them. In the same way, I hope that when you refine and develop your societal and political beliefs, you will allow clear logic, as well as awareness of the unknowns, to inform your citizenship.