1.6: Critical Thinking

As humans, we need to recognize that we are fallible. No matter how good our intentions, we make mistakes and can be fooled. The first step toward reducing and ultimately eliminating these sources of error is to understand them. We will lump these into two broad categories: cognitive bias and logical fallacies. Understanding these will enhance our ability to think critically and avoid being fooled (or fooling ourselves).

Cognitive Bias

A cognitive bias is an inclination toward looking at a situation in an unbalanced or unfair manner. Generally, people are not aware of these biases. One example is confirmation bias (AKA, confirmation of expected outcomes). That is, we expect (or hope) to see a certain result and thus we tend to overvalue evidence that confirms it while discounting evidence that contradicts it. One way to avoid this is through the use of a double-blind test. Suppose we wish to test a new drug to see if it is effective and safe. As we may have invested a lot of time and money developing the drug, it is only natural that we want it to work, and this may skew our analysis (unintentionally, of course). What we do is have a third party create two sets of pills; one is the drug under test and the other is a placebo (it looks like the other pill but does nothing). These sets are identified using codes known only to the third party. The sets are then given to the researchers who, in turn, give them to the patients. The important thing is that neither the patients nor the researchers know which pills are which. When the trial has run its course, the researchers (us) analyze the data to determine if any set of pills was successful. Only after the analysis is completed does the third party tell the researchers which set was real and which set was the placebo.

Another cognitive bias is the Dunning-Kruger effect, named after the two social psychologists who studied it. This states that the knowledge needed to determine if someone is competent in a certain field is competence in that same field. Thus, individuals who have low competence are not in a position to accurately evaluate their own level of competence. Consequently, these individuals often over estimate their competence. This is known as illusory superiority. To put it crudely, these individuals are too ignorant of the subject to understand just how ignorant they are. Among the highly competent, two other effects may be seen. First, the advanced individual may be keenly aware of any shortcomings or gaps in their competence and may undervalue their level as a result. Second, they may assume that their level of competence is typical, and that most people are therefore “at their level”.

It is useful to remember that in our complex and interdependent society, no one can be an expert at everything, or even at most things. Instead, it is likely that we are all largely ignorant of a majority of subjects and/or incompetent at a variety of skills.

Logical Fallacies

Logical fallacies represent faulty reasoning. They are “thinking traps” that people sometimes fall into. Familiarity with them will help reduce their occurrence. There are dozens of logical fallacies but we shall only investigate a representative few.

To help explain the process, we'll begin with a syllogism. This is, in essence, a simple argument. It starts with a major premise (a generalization) which is followed by a minor premise (a more specific statement). From these, we derive a conclusion. For example:

\[\text{All humans breathe air. (major premise) } \nonumber \]

\[\text{Alice is a human. (minor premise) } \nonumber \]

\[\text{Therefore, Alice breathes air. (conclusion)} \nonumber \]

Errors can occur when either premise is false or when the conclusion does not follow (the latter being referred to as a non-sequitur). For example:

\[\text{All fish live in water.} \nonumber \]

\[\text{Lobsters live in water.} \nonumber \]

\[\text{Therefore, lobsters are fish.} \nonumber \]

The problem with this is the linkage between the major and minor premises. Saying “all fish live in water” does not preclude something else (like a lobster or a sea snake or kelp) from living in water. Compare the prior example to this version:

\[\text{All fish live in water.} \nonumber \]

\[\text{Trout are fish.} \nonumber \]

\[\text{Therefore, trout live in water.} \nonumber \]

While these examples may seem obvious, there are trickier versions. For example:

\[\text{I am made of nothing but atoms.} \nonumber \]

\[\text{Atoms are not alive.} \nonumber \]

\[\text{Therefore, I am not alive.} \nonumber \]

Nope. Doesn't work. This error is called the fallacy of composition. Basically, it says that what is true of the parts must be true of the whole, and vice versa. It ignores the concept of emergent properties (consider the behavior of a single bird to a flock, or a single fish to a school).

The fallacy of composition can be illustrated without using a syllogism. Suppose you are in a crowded movie theater. If you stand up, you will have a better view of the screen. In contrast, it is not true that if everyone stands up, everyone will have a better view. In fact, everyone will most likely have a worse view. If one person stands, they are unique. That unique character is lost when everyone stands.

Turning to a different fallacy, the Latin phrase post hoc ergo propter hoc can be translated as “Before this, therefore because of this”. This fallacy is sometimes referred to as the post hoc fallacy or the causation fallacy. It is an error regarding causality; the assumption being that because event A occurred before event B, then event A must have caused event B. On the surface, it seems logical enough. For example, you might see a lightning strike and then hear a clap of thunder. It seems reasonable to assume that the lightning caused the thunder (generally speaking, that is the case). On the other hand, you might wake up some morning when it's dark outside. Shortly thereafter, the sun rises. Obviously, your waking did not cause the sun to rise.

Another error involves proportional contribution to an outcome. Relative size is mistakenly seen as a determiner. That is, the error assumes that only large contributors have any sway in the outcome. Basically, this fallacy proposes that if something makes up only a small percentage of the total, then its effect must be minimal. This is easily proven wrong. As an example, the atmosphere of the Earth is comprised largely of nitrogen (78%) and oxygen (21%) along with a number of trace gases such as argon, carbon dioxide and so forth. If the atmosphere was suddenly altered so that it included just 0.1% hydrogen sulfide, every human likely would be dead after their first breath of this new combination.

Along with size, there is a similar issue regarding linearity of effect. A linear function is one that can be plotted as a straight line. More to the point, if we have a linear system, then doubling an input to that system doubles its effect. To wit, if you order two pieces of pie for dessert, it will cost twice as much as one piece. The reality is that many systems do not behave in a linear fashion. Systems or relationships can be logarithmic, square law, cubic, or follow some other characteristic. For instance, the braking distance of a car does not vary linearly with its speed, it varies in accordance with the square of its speed. Therefore, if you're traveling twice as fast, it doesn't take twice as far to come to a stop, it takes four (two squared) times farther to stop. Remember this the next time you're speeding down a highway.

The next two items sometimes appear in arguments for or against a proposition. They are the excluded middle and the ad hominem. The excluded middle presents a false set of choices. Essentially, it falsely reduces the set of possible outcomes and then proceeds to disprove all but one of them. By process of elimination, the remaining outcome should be true. For example, someone might complain that a particular politician would only support a particular bill if said politician was either stupid or a communist (or a fascist, take your pick). They then show that the politician is not stupid, so by their logic the politician must be a communist. Of course, there are any number of other possible scenarios that have been excluded; for instance, the politician might have taken a hefty bribe to vote for the bill or the analysis of the bill by the complainer might be faulty.

Finally, ad hominem is a Latin term meaning “to the person”. The ad hominem attempts to disprove a point by arguing against the person making a claim, not the claim itself. For example, suppose Doug makes a claim in favor of a new theory of gravity. Fran's counterargument is that Doug is an evil person because he likes to spray paint foul words on other people's pet cats, and therefore he can't be trusted. The reality is that, in spite of his proclivity for penning feline profanity, Doug's ideas regarding gravity might be spot on. Those ideas need to be addressed directly.