0. Introduction (concept)

0 – 3: After abstracting the images, brain groups them based on at least one similarity. Each group is called a concept. In other words, concept enables us to classify things around us.

For example: Tree is a plant with an elongated stem, or trunk, supporting leaves or branches (Wikipedia), so tree is a concept for a group of plants having characteristics above-mentioned. 

So dog is a concept, doctor is a concept; eating and liberty are concepts too.

Concept is totally subjective (exists in mind). Can you portray tree? You can portray one example of trees not the tree as a concept.

Besides, one thing can be categorized based on different concepts. A man can be a father, a doctor, a citizen, a costumer and so on.

Sometimes, we create a concept for other concepts. For example concept of motion for running, walking, falling, flying and so on. So the concepts are developed or built upon other concepts. Another example for hierarchy of concepts is classification of animals.

We are supposed to know the basic concepts to conceive higher ones. That’s what we do frequently in mathematics, for example the concept of exponent  had been developed to negative or fractional exponents. Nobody can understand the concept of negative exponent unless they have understood the concept of natural exponents. 

The more we abstract, the higher concept we create. To create a concept for Oedipus the King and Macbeth, one can classify them as drama related to kings, however if we abstract it more, we’ll see that the similarity is a failure regardless of being a king or an ordinary man, so the way they fail, makes a new concept called Tragedy.

Through the next posts it will be discussed how we create concepts in mathematics and how we create higher concepts out of basic concepts.

The last point about concept is that the basic concepts can't be defined, however our mind can conceive them. For example, nobody could define time. You can set a unit for time, but can you define the time itself? (If you use words such duration, to define duration you will need concept of time, so there's a loophole which doesn't lead us to any form of defining time)

We don’t need a definition for time. We just use its concept in our daily life. When you teach the concept of red to a kid, you might show them a red apple, a red rose, a red curtain and you repeat the words red apple, red rose and red curtain, WE HOPE THAT the kid’s mind would grasp the similarity which is RED. Then the kid tries to apply the concept to name the next red object such as red tomato, and you show that it’s correct or you give them a reward, so your approval consolidates the concept of red in their mind.

As long as we understand a concept and we know how to apply it, we don’t need a definition. A swimmer might not be able to define swimming, but they've understood it physically and mentally.

In mathematics you will see that the basic concepts such as number, point and line, can’t be defined. But we can understand them easily, so we build the higher concepts upon them.