Exposing Fallacious Logic

What to Believe?

Right or Wrong?

We encounter a lot of arguments every day, they can be as simple as an invitation to attend a party, or persuasion to quit bad habits. Arguments are something that can affect our attitudes and actions, which means that we better handle them carefully.

An imperative component of arguments is logic: we avoid being affected by illogical fallacies and consider adopting logical ones. But a problem is that most people don’t have a systematic way to examine logic, which leaves them wide open for fallacies to attack.

The Logical Form, And Refutation by Counterexample

Before deciding whether to believe an argument or not, we should first lay out its logic and see if it makes sense; this can be done with the logical form.

Suppose a friend wants to persuade you to hang out, but you have some unfinished work, so he tries to convince you:

‘Many people suffering from mental illness overworked. If you keep toiling, you may end up becoming one of them. Have some fun!’

With a little sorting, the argument can be restructured as:

1. If a person suffers from mental illness, he probably overworked.
2. You are toiling

Conclusion: If you keep working, you will probably suffer from mental illness.

Does this look convincing? In fact, its logic — which is demonstrated below — is invalid. Even if the premises and conclusion are found to be correct, this is still an invalid argument (otherwise, you can put any two random facts together and call it a valid argument).

1. If A (suffer from mental illness), then B (having overworked) is likely
2. B (overworking)

Conclusion: A (suffer from mental illness)

This is the logical form of the argument, it still doesn’t look erroneous. But here is a thing, if the logic here is valid, you can always get a true conclusion as long as the things you plug in as A and B make sense. That means we should be able to generate a true conclusion by plugging in anything true as A and B. Let’s try:

1. If a person is an athlete, he drinks water.
2. I drink water

Conclusion: I am an athlete

So that’s how we get into the logical catastrophe.

The logic in the first argument is the same as this ludicrous one, they even share the same logical form. But we laugh and walk off when we see the previous one, yet become convinced by the latter one. We call one logical, another illogical — even though their logic is the same.

It is possible that your friend’s right — you may have mental problems if you keep toiling, but his ratiocination is flawed. An argument being invalid doesn’t guarantee its conclusion to be wrong, but you need another argument to prove it to be true or false.

Wrap-Up

This method of showing invalidity is called refutation by counterexample; which basically consists of these three steps:

• Construct an argument with the same logical form
• Ensure the premise is true
• Arrive at a false conclusion

Many seemingly strong arguments collapse when being examined, many, probably more than you realize.

Arguments, by definition, are an attempt to alter our beliefs and actions. If we do not cut the strings that control us, we will careen into unfavorable situations, or may even become a marionette of others.

Of course, though, hanging out with your friend wouldn’t be that big a deal.