Have you ever looked back on something and felt like banging your head against the wall? If “why did I do that???” is a motto of your life, then you need to improve on your logical thinking.

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Thinking logically involves making sound and valid arguments. A valid argument is one where one statement leads logically to another statement, eventually resulting in a conclusion. However, the conclusion may not be true if the initial condition (premise) is untrue. Only when the initial premise is true and the argument flows logically do we say the argument is sound.

Invalid argument

It takes this format: X -> Z, Y -> Z, therefore, X -> Y

It looks like this: All girls are human. All boys are human. Therefore, all girls are boys.

It sounds ridiculous, doesn’t it? However, many adults still commit this logical fallacy. Even the presidential candidate of America, Donald Trump. Here is what Donald Trump says: Illegal immigration is an illegal act. Rape and drug-dealing are illegal acts. Therefore, all illegal immigrants are rapists and drug dealers.

When nearly half of America’s 324 million people cheer on a conclusion that is as ridiculous as the “all girls are boys” conclusion, you can’t help but wonder that maybe you are not as stupid as you think you are.

Valid argument (but unsound)

It takes this format: X -> Y, Y -> Z, therefore, X -> Z, where Y -> Z is untrue

It looks like this: I am a student. All students love studying. Therefore, I love studying.

Here the premise that all students love studying is false. Some may love studying, but definitely not all. Which results in the grossly untrue conclusion that I love studying.

Valid and sound

It takes this format: X -> Y, Y -> Z, therefore, X -> Z

It looks like this: I did badly for my exam. My mum will be mad when she sees my bad result. When my mum is mad, she confiscates my phone. When I do not have my phone, I get depressed. As such, I am very sad over my bad results.

Because doctors have always been paid well, I will be paid well if I become a doctor 10 years from now

Ok, so if there are only 3 formats to logical thinking, then anyone can think logically, right? Sorry to disappoint you, but in real life, you have to come up with the premise. For instance, in the argument above, how do you know that your mother will be mad with your bad results? That is because she has, without fail, gotten mad with you over your bad results. This is inductive reasoning. Because we have always observed something, that is why we take it to be true. However, what if your mother got such a high pay raise that even your horrible results cannot dampen her mood? Instead, she brings your whole family to Din Tai Fung to celebrate. Well, in that case, our inductive reasoning has failed us.

Inductive reasoning is used frequently in all aspects of our lives, and indeed, past trends can be anchors for your future decisions. However, be careful of the reasoning that just because it has always happened, it will continue to happen.

“Because oil prices are rising every year, it will continue to rise this year.” Sorry, this year the oil price fell to its lowest since 2003.

 “Because doctors have always been paid well, I will be paid well if I become a doctor 10 years from now.” You never know, maybe the government will open the door especially wide for foreign doctors so as to lower medical costs. At that point in time, you will be thankful for the minimum wage legislation. (I swear I am not jealous. Ok, maybe not that jealous.)

Thinking logically is analysing things until you make a headway. It is recognising patterns and avoiding logical pitfalls. It also involves keeping your emotions in check so that your judgment will not become clouded. How do you improve then? Stay tuned for some brain teasers that will boggle your mind.