12. Formal Logic I

But we still have not come to the concept. We get the idea by exposing ourselves to the impressions of the outside world. We then retain the idea as an image. Most people do not get beyond the idea in the course of their lives, they do not penetrate to the actual concept. What a concept is and how it relates to the idea is best shown by an example from mathematics. Take the circle. If we take a boat out to sea, until we finally see nothing but the sea and the sky, we can perceive the horizon as a circle when it is very calm. If we then close our eyes, we retain the idea of the circle from this perception as a memory image. To arrive at the concept of the circle, we have to take a different path. We must not seek an external cause for the idea, but we construct in our minds all the points of a surface that are equidistant from a certain fixed point; if we repeat this countless times and connect these points with a line in our minds, the image of a circle is built up in our minds. We can also illustrate this mental image with chalk on the blackboard. If we now visualize this image of the circle, which has been created not by external impressions but by internal construction, and compare it with the image of the sea surface and the horizon that presented itself to our external perception, we can find that the internally constructed circle corresponds exactly to the image of external perception.