6 Minutes Of Logical Catastrophes
Tags: Reasoning, Judgement, Critical Thinking, Logic, Logical Thinking

Pseudo-Reasoning Is Everywhere

‘Pseudo-reasoning’ sounds like some mysterious tricks used in a room crowded with rows of sophisticated men, but they are really not something distant from us — they are everywhere. In fact, probably more common than logical reasoning.

What determines whether an argument is valid or not? Reasoning is the process of deriving a conclusion from premises or postulates, like the deductive geometry problems you did back in the days in school. Reasoning can be as simple as this:

Alice likes sweet food and apples are sweet. Thus, Alice likes apples.

This is valid reasoning: if the assumptions are true, the conclusion can’t be wrong. Based on the two assumptions (Alice likes sweet food and apples are sweet), it is unquestionable that Alice likes apples.

The path from premises, postulates, or assumptions to the conclusion is usually not as straightforward as the case with Alice and her apples; this is why pseudo-reasoning exists — the arguer, as well as the audience, are not always aware of the flaws in certain stages of the reasoning.

And here we go — you will be presented with a series of invalid arguments that look true at the first glance.

The Logical Catastrophes

The Most Out of The Most

Most students in this school play an instrument, and most of them play the violin. Thus, most students in this school play the violin.

There is nothing wrong at the first glance, but think again — ‘most students’ means over half of the students, let’s say 60% — that’s over half. Among that 60% of the students, over half of them(which we will assume to be 60% again) play the violin. By simple calculations, there are a total of 60%×60% = 36% of all students playing the violin, which is far less than half.

Most out of most no longer have to be the most. Find this disturbing? This is a trick public figures love, whether they are aware of the deceiving nature of this or not.

Correlation And Relation

A higher level of chemical Y in the blood is correlated with a higher chance of getting heart disease. Chemical Y must cause heart disease in some way or others.

Whether it seems obvious or not, chemical Y may no effect at all on the health of the heart. There may be another factor that increases the level of chemical Y and causes heart disease at the same time, for instance, smoking. We find that almost everyone with a high amount of chemical Y in their blood has heart disease, but that is because smoking always causes both at the same time.

If you extract the excessive chemical Y in the blood, the probability of the person getting heart disease may not change — because the real cause may still be present.

Let’s take a look at a more obvious example. Animals that live in the urban area are more obedient than those that do not. There is a correlation, but it would be ridiculous for us to say that the concrete buildings cause animals not to bite everything and excrete everywhere. It is the existence of humans that causes both.

Two Correlation

Using drug X is correlated with higher level of chemical Y in the body; higher level of chemical Y is correlated with higher chance of getting a heart disease. The use of drug X is correlated to higher chance of getting a heart disease.

Wait, why? A relation is not involved here, how is it still wrong?

Let’s take a look at another example: doing more exercise is correlated with a healthier body, and healthiness is correlated with better pay at work; does that mean a correlation exists between doing exercise and the salary? Obviously no!

Better payment may make one afford to have nutritious diets, which then results in better health. But the thing is, this has nothing to do with exercising. Correlation is intransitive — A is correlated with B, B is correlated with C, and A can have no correlation with C.

Reversing The If-Then Relationship?

People who have been using vitamin supplements have been shown to have decent health in all studies performed. Your health will be inferior if you don’t take the supplements.

Good health is probable if you take vitamin supplements, but this alone doesn’t concern what happens if one doesn't take supplements — the supplements are not proven to be the only way to improve health. The argument doesn't inhibit the probability of a person being healthier than the supplements takers; the conclusion isn’t valid by any means.

If you consume a lemon, your body will get a good amount of vitamin C (together with torture on the tongue). However, it is not impossible to get vitamin C from other sources, like kiwi. There can be an array of approaches for one to get the same results.

Misleading Percentages

Most people from town A are criminals while a few people from City B commits crime. Given that John commited a crime, it is likely that he is from town A.

Let’s say town A is so unsafe that 80% of residents are criminals, and town B is much safer, only 0.1% of citizens are criminals. Is it impossible for town A to have fewer criminals than city B? No! If the population of city B is big enough relative to town A.

If there are only 1000 people in town A, the number of criminals will be 800; and if there are 1,000,000 people from city B, the number of criminals will be 1,000. If John is a resident of either place and he committed a crime, he can be more probable to be the resident of city B.

‘Most’ and ‘few’, or ‘80%’ and ‘0.5%’ do not tell you anything about the factual number; you need to have an idea on the base if you don’t want to be fooled by percentages.

Rejecting The Cause

Smartphones have been shown to aggravate one’s ability to concentrate, we can become concentrated if we don’t use them.

Why can’t we concentrate after removing the source of distraction? Because there exist other distractions! Smartphone impairs concentration, but the absence of smartphones doesn't guarantee the absence of the impairment — the noise from a construction site is distractive enough to make you headbutt your computer, isn’t it?

X causes Y; the absence of X does not necessarily cause the absence of Y. A simpler example: going to Disney costs you money, but you will still have to spend money even when Mickey is not around.

So What?

There goes invalid reasoning, but why should we concern? We can live our life without being that sharp, and it may even be easier — why do we need to care whether the reasoning is valid or not?

The simple answer is that your beliefs and decisions are affected by words from other people. It is easy to act upon what we perceive rather than what is the case, seriously, ‘something sounds true’ underlies most decisions we make. The lack of logical thinking plants the seeds of bad decisions: buying and taking a drug you don’t need, taking wrong suggestions and mistreat your children, voting for glib politicians.

Speaking of politicians, they are heavy users of unsound arguments; the reason is simple, people don’t really think that much — they are heavily affected by emotions, all it takes to give them an opinion is an (or a few) emotional speech together with sheets of false or falsely interpreted statistics.

Making bad decisions is fun until the consequences come — a thinner wallet, an impaired child, or getting ruled by an unscrupulous person. How to avoid them?

Recognize the logical catastrophes.