Space Logic in Venn diagrams

If you read my topics on space extension, in this blog or my book, then you know what i mean when i say "N(X) grouping" and the "{N(K)} extraneous/overall part". And you know that Logic is not limited to analize language inferences and truths, because Logic compose and explain geometric space and material world too. Now, in the light of my new logical advances, we process to deduce and explain some parts. In this topic, we discuss the space logic in Venn diagrams, explain their extension, so that Logic can look herself in a mirror. Well, after reading this topic, you realize that Venn diagrams are wrong. That's right, good old John Venn didn't draw them well! Let's get to the details.

Let's study the simplest diagram, to not unnecessarily complicate this topic. The next diagram simply indicates that Socrates is a philosopher, placing Socrates circle inside the circle relating to the concept of philosopher. This is a half-syllogism. Socrates implies philosophy. In fact, if there is no philosopher, then can be no Socrates. Recall that in Venn diagrams, if concept A implies concept B, then circle A is inside circle B.

Let's try to describe the space logic of those two circles. To do this, we divide Socrates circle "S" into many points "sj". And the philosopher circle "F" will be composed of the smaller circle S plus the other points "fj".

Previous picture can be written as follows:

S = N(s) and {N(B)}

F = S and N(f) and {N(A)}

{N(A)} and {N(B)} are the extraneous/overall parts of the two geometric shapes. Specifically, {N(B)} means {group the sj points to compose the small circle S} and {N(A)} means {group the circle S and the fj points to compose the large circle F}.

We see that the logical implication is reversed: F implies S. In fact, if "S and N(f) and {N(A)}" is true, then S must be true, that is:

S and N(f) and {N(A)} --> S

In conclusion, looking at the picture, we deduce the opposite of what John Venn intended: philosophy implies Socrates!

How can we understand this contradiction? The answer is simple!

If a large circle contains a small circle, then the large circle implies the small circle and depends on it. In fact, if you remove the small circle, the large one inevitably becomes a donut with a hole. Conversely, if you remove the large circle, the small one contained within it is not deformed. This concept is expressed in the next picture. Recall that new logical tools i discovered describe the logic of the space, as well as that of propositions.

Now, the question is why John Venn chose to place logical implication toward the outside of the diagram, rather than the inside. In my opinion, John Venn's choice was psychological. Is based on how human beings perceive reality. The human approach to understanding the world is bottom-up. Since ancient times, humans looking particular objects around them, separate from each other, such as plants, animals, and people entering their vision. Later, turning their eyes to the sky, they think about abstract sense of things, looking for a general concept. Thus, instinctively, the most general concept "touches the sky" and contains the more specific ones, which appear separate from each other.

In despite of this, Logic would dictate the opposite. Logic dictate that the most general idea is a point at the center of the vision, so that all specific objects, intersecting it, would imply it. Obviously, this is impossible for human beings, because they don't see generic concepts at the center of their vision. The next picture draws the psychological approach of Venn diagrams. In Picture A, we see Venn diagrams as is. In Picture B, we see that these diagrams are similar to visual perception, whereby concrete things are located at the center. In Picture C, we see the correct Venn diagrams, where the philosopher and the sex are located at the center of the diagram, to graphically imply the external parts.

In conclusion we can say the following: 

really, John Venn didn't make a mistake. He chose a convention over another. Venn diagrams are valid, even if they are inverted with the space logic.

Two centuries ago occurs the same with Electronics. 

Initially, we thought that electric current moving from positive to negative, so all the formulas and diagrams were based on that convention. When we discovered electrons, we realize the opposite, but all these conventions remained valid, because they are not contradictory.