Introduction to Logic for Inventors
The thinking process includes three main components: logical thinking, usage of intuition and serendipity. By definition, logic is the science of correct thinking; intuition is understood as subconscious processing of information; and serendipity is luck, or good fortune, in finding something good accidentally (by chance).
In this section we will discuss the main concepts of logical thinking. For those interested in a comprehensive overview of serendipity can visit "Chance Favors the Prepared Mind" section. If you are looking for a deep explanation of intuition processes, we advise you to examine psychological literature.
One of the famous examples of the use of logical thinking is Galileo's reasoning in his study of falling bodies. At that time, Aristotle's hypothesis that heavy bodies fall faster has been accepted. For example, by this hypothesis, a cannonball should fall faster than a small bullet.
1. The weight of two bodies together is larger than their separate weight.
2. The heavier body (the cannonball) will speed up the fall of the bullet while the bullet, being the lighter body and falling slower, will slow down the fall of the cannonball.
We see that these statements are contradictory. Galileo solved the contradiction with a paradoxical conclusion: all bodies, light or heavy, must fall with equal speed when they are unaffected by air resistance. Some time later, Galileo's student Tomasso Torrichelly, performed the following experiment: he pumped out the air from a pipe, and let objects as different weight-wise as a feather and a bullet fall in vacuum. The result of this experiment proved Galileo's conclusions.
Logic is one of the oldest sciences and we can understand why. Logic doesn't require any physical bodies or chemical solutions for its practice. The only required instruments are simple words. Logic provides "thinkers" with a word inventory and rules/directions for correct thinking.
From the early beginning logic helped people clarify their reasoning. But sometimes, when the rules of correct thinking are ignored, logic is forceless. For example, let's take the "Paradox of Liar", and the so-called "Protogora's Paradox".
"Paradox of Liar":
During a town meeting, one of the citizens of Crete exclaimed: "All citizens of Crete are liars." If we take the statement as truthful, then this citizen is also liar; therefore the above statement is lie. Hence, not all citizens of Crete are liars. These statements exclude each other, so we cannot rely on such statements in life.
The Problem: Protagoras, an ancient Greek philosopher, gave law lessons to a student who agreed to pay after he won his first case. But the student did not get clients, so Protagoras sued him.
Protagoras believes he will win because:
1. If the court sides with him, the student will have to pay.
2. If he loses, then his student would have won his first case and will therefore have to pay anyway.
Student believes the complete opposite:
1. If the court sides with him, then he will not have to pay.
2. If the court sides with Protagoras, then he would not have won his first case and therefore, will not pay.
Let's analyze the conclusions drawn by both sides and combine the conditions of their agreement with their reasoning. The student believes that if he wins, he will not pay by the verdict, but he ignored by the agreement, he has to pay because this would be his first victory. Again, we are faced with a paradox such as the "Liar's Paradox". So, it is a logical deadlock. By combining Protagoras' statements, another deadlock will be utilized.
Now, after seeing some logical mistakes, such as paradoxes, let's follow some examples of correct thinking.
The following example of logic has been used even in ancient Greece:
Any man = living organism
Socrates = man
Therefore, Socrates is a living organism.
The first 2 statements are called the premises and the last statement is called conclusion.
Now try to analyze the next example:
What you haven't lost, you have
You haven't lost a tail
Therefore, you have a tail.
Here we can see that from correct references taken separately, an incorrect conclusion is obtained. Such type of logical mistakes has a name - "sophism".
Sophism is a very common logical mistake. Be careful, or risk having a tail, as in the example above!
Now let's take a look at a second type of reasoning, the so-called "cause and effect consequence".
Examine the statements below:
If it rains, then the ground is wet.
If the ground is wet, then it rained.
In the first statement, rain is the cause and wet ground is the effect. It is true that every time it rains, the ground is wet. But in the second statement, rain, as the effect, does not follow. Ground can be wet for a variety of reasons, such as sprinklers.
Often in studies involving numerous variables and factors, distinguishing causes and effects can be exceptionally difficult. So keep in mind the example above, and be precise in selecting your causes and effects. Your choice can dramatically affect the duration of your work.
Notice that in correct reasoning, true premises always lead to a true conclusion. This explains why logic shows such a great interest to correct conclusions. Because existing conclusions can be used as premises towards new conclusions leading to a continuous array of conclusions that can be made without performing experiments and so on.
Conclusions are divided into two main types: deduction and induction.
The first signs of that correct reasoning can be done using deduction can be seen in Arthur Conan Doyle's stories of Sherlock Holmes. One of his stories "Sign of Four" actually started with the following: "The point of Holmes' Deductive Method".
Ex: Sherlock Holmes concludes that Dr. Watson visited the post office to send a telegram. Holmes noticed that Watson's shoes were covered in reddish clay, which could only be found at the post office. And Holmes was with Watson the whole morning; therefore Watson did not have time to write a letter.
In this example, we see that Holmes makes his conclusion on the basis of observation and legitimacy. For example, Watson's shoes were covered with reddish clay. This is an observation. A legitimacy in this case - shoes can be smudged with this type of clay only where it exists. This type of clay exists only around the post office; therefore, Watson visited the post office.
This type of conclusion is called a deduction, or a conclusion made from general to specific.
An induction, on the other hand, flows from a specific to general. Inductions can be complete and incomplete. Earlier, we discussed the idea of perpetual engine. The idea was drawn from an induction - night follows day, summer follows spring, this happens during one person's whole lifetime; therefore, there is eternal movement and must be an eternal engine. An induction is only true when EVERY instance is true. For example, every single day of billions of years would have to be the same for the idea of eternal movement to be true. So the eternal engine idea is an incomplete induction.
Now that you are familiar with logical paradoxes, induction and deduction, take a look at the following line, taken from George Orwell's Animal Farm:
"All animals are equal, but some are more equal than others."
We see that within this statement lay a logical contradiction. On one side, all animals are equal, on the other they are not. These sides cannot both exist at once. The same can be observed with Galileo's reasoning of why things of all weights must fall at the same speed.
Logical thinking can be further broken down into analysis and synthesis.
In the inventive field, analysis is defined as highlighting of all elements, conditions, component ties, etc. in a problem. During analysis, other similar problems' elements are also examined and evaluated. Analysis helps to clearly formulate the problem.
Synthesis is a logical operation that combines different elements (highlighted during analysis) in a new arrangement. Additional knowledge, such as solutions to similar problems, personal experience, etc. is the basis of transforming the elements of the problem into a solution.
Performance of synthesis can be successfully achieved (by a prepared mind) with the usage of and lateral thinking concept, introduced by Edward de Bono, and ideal result concept, which is examined in our "How to Solve Problems" section.
The purpose of this section is not to present comprehensive knowledge of logic. It is a very deep and paradoxical science, which plays an extremely vital role in correct thinking. Moreover, it is highly important in the inventing activity. With the examples above, we aimed at your understanding of the need for mastery of logic.
: A Guide to Critical Thinking
: Understanding and Shaping Arguments
Art of Reasoning
a Critical Thinker: A User-friendly Manual
Critical Thinking Puzzles
Lateral Thinking Puzzles
Thinking : Creativity Step-By-Step
Reasoning Matters! : A Constructive Approach to Critical Thinking
Introduction to Logic for High School Students (in Russian)
by John A. Oesterle
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