Application of Logic in Real Life

Abstract

Most people fear encountering logic as an academic matter. The seemingly difficult vocabulary such as existential elimination, universal quantifiers, and consistency make people believe that they will never use the logic in real life. However, logic is something that we use everyday in every second. Logic is not about calculation, but it is about learning to organize our thoughts, and detecting the logic structure quickly. Giving examples in real life, this journal elaborates why logic is important in our life and how we can use it in everyday examples. Furthermore, it suggests the more complex application of logic in other fields. This journal accentuates the significance of logic and practical usage.

Introduction

In the status quo, people usually regard logic as a useless subject, since they don’t understand the practical use of it. This is what they say: logic is something that can be grasped inquisitively, and there’s no need to study it separately. However, logic helps us to think logically by minimizing the excessive generalization and decision making process. Let’s look at this example:

• p = It is raining. • q = The floor is wet.

Although rain makes the floor wet, the floor can be wet without rain. The accurate conclusion based on proper use of evidence is important.

Discussion

Let’s look at this logic statement: (p => q)

How can we ever use this sentence in real life? Or how can we ever interpret this sentence? Assuming that we already know that this statement is valid, we are going to analyze the sentence at an amateur level. The sentences p and q are propositional operators. Each sentence represents a different sentence. Let’s assume the sentences below:

• p = It will rain. • q = I will bring an umbrella.

As you can infer quickly, the arrow is the sign called implication, which means that if the left side is true, the right side is also true. However, it does not guarantee the truth value yet. As it will rain, I will bring an umbrella. Let’s see another example:

( p /\ q ) => ¬ r \/ ¬ q

Let’s assume that p and q retain the same value as before. If the sentence above is true and p /\ q is true, which should be the truth value of r? 

When we say that p /\ q is φ and ¬ r \/ ¬ q is ψ ( φ and ψ are placeholders, which represent statements in this case), ψ should be true because φ is already declared to be true (see the definition of an arrow above). The sign \/ forces either ¬ r or ¬ q to be true. However, as q is already set true (p /\ q is true, so p and q are all true), ¬ r is true. This logic seems intuitive, but in the computer program, this obvious reasoning doesn’t work. Below is how to prove that ¬ r should be true.

In line 1 and 2, the premises are set. If line 2 is true, ~r | ~q (or ¬ r \/ ¬ q) should be true, because if p & q is true, the statement on the right side should be true as well (line 3). 

From now on, we are going to use Or Elimination to derive ~r.

Or elimination tells us that if all the statements joined by | (or) imply the same conclusion, then the conclusion is true. If we think of this idea for a while, we can understand that easily. 

Since ~r or ~q is true, we are going to prove the sentences below (line 3-15):

• ~r => ~r • ~q => ~r

(~r => ~r) can be easily proven, because ~r equals to ~r. To prove (~q => ~r), we should use another technique. 

Because we already know that q is true, when we want to assume that ~q is true as well, we can easily derive ~r by the sentences below (line 9, 12, 13):

• r => q • r => ~q

Because we had already assumed that ~q is true, we can make a conclusion that (~q => ~r).

Therefore, we successfully fulfilled the criteria in the below.

• ~r | ~q • ~r => ~q • ~q => ~r

By the Or Elimination, we can prove ~r (line 15).

Why we should learn how to solve this question is in question. In fact, logic allows us to organize our thoughts into one and solve a single question. It corrects the blurred line between the truth and false, by preventing the wrong conclusions. Usually, the common misconception in real life is the sentence below:

(p => q) is logically equivalent to (q => p).

It seems intuitive to prove that statement false, but people make many mistakes around this. Let’s assume the statements below.

Conclusion

As you can realize from this problem solving, logic can be utilized to use numerous conclusions. How can we use logic in real life? Logic can be used in many academic settings, such as decoding, mathematics, programming, and other STEM related subjects. Meanwhile, logic is a good way to develop problem solving skills. Therefore, logic is an important component in life.