THE ORIGIN OF LOGIC AND MATHEMATICS

THE ORIGIN OF LOGIC AND MATHEMATICS

The two sciences come from the desire to interpret the actions of the mother nature, moreover, they share their birth certificate. The two materials are based on the so-called axiom of identity or principle of identity, which was gradually formed in the brain of pious humans and then, with a maturity card, become a guiding principle of thought. So much so that some philosophers thought that this axiom, in conjunction with other derivatives of it, was embedded in the mind as evident truths that made a demonstration unnecessary.

The axiom, for philosophy and its universal character, which today interests us, says that a real thing is equal to itself in a given moment and nothing else. It is important to highlight the addition I make to the common way of saying it by including the phrase, "at a given moment", which excludes the passage of time and thus ignoring the changes that its evolution causes, as well as the psychological experience that is a product made on the basis of experiences from the past. Modernly it has to be completed saying that the principle or axiom of identity is "the equality of the real and physical thing with itself in a given moment of space time".

Mathematics is based on the axiom of identity when they establish the equality of the members in their expressions, which is nothing else than the identity compartment. Mathematics describes reality with truth only if its demonstrations and conclusions about phenomena remain true to the principle of identity. That is, the results obtained are correct in that they maintain the identification of a phenomenon faithfully through the process in which case Mathematics is true for that phenomenon according to the description that has been made of it at the beginning. This is when physics and mathematics come together. The first one must be a faithful description of the phenomenon under study, under penalty of inducing errors, the second must not exceed the physical description.

But, it has happened, that some scientists have been wrong in the description of a natural phenomenon to which they attributed conditions that did not represent their true identity, either by increasing, diminishing or altering their fundamental data. This is what happened to Newton in his conception of absolute space and time. It happens to Einstein when he proposes solutions for a static universe. In both cases the mathematics developed are useful and precise for the respective phenomena described, which does not guarantee that they are descriptions adjusted to the reality observed. The mathematics used has been irreproachable, the description of the phenomenon has failed, I say, because in the case of Newton the idea that space and time were absolute was not and is not satisfied with reality, something that was discovered after his death, and can be demonstrated experimentally. In the case of Einstein because the universe is not stationary but dynamic as is known from several experiments, which conclude that it is in permanent expansionary evolution. Einstein himself accepted the error that he could not repair, even though he tried. It is useful to remember that Gödel, the mathematician of indecibility, proves that truth is a category superior to demonstrability.

Logic, on the other hand, is a formal science whose main objective is to help the correction in thought, a purpose that is achieved with the help of means, modes and forms of precise reasoning adjusted to rules developed by it. But behind all the equipment that is served is the search for truth, full agreement between the object and the subject. That is, the object of Logic is to express in concepts the identity of things.

Recall that man begins the adventure of knowledge, first through the direct knowledge that provides the perception; then, exhausted this option, to continue developing this cognitive appetite, requires organizing the various ideas that shape and nuance the environment, is when logic is formed and justifies its deciphering function to help in the goal of getting to know higher. But throughout the mental journey must take care that the identity of the object is not altered. The errors of logic have proper names, here I separate them according to the intention: if they are unconsciously they will be paralogical, if they are deliberately incurred as sophisms. But there are many more.

The handling of the similarity between Logic and Mathematics has given rise to the emergence of a close collaboration between them that we now call Mathematical Logic or Symbolic Logic. With it we can solve complex problems.

What is truly key is, then, the demonstration of how the aforementioned mother axiom is formed in the human mind. To remove it from its enigmatic origin to one consistent with the human capacity to formulate it through its knowledge systems is the purpose of this s summary, for which I have to meet criteria according to evolution.

If the mind of man is a "clean slate” at birth as the philosopher says and confirmed by modern neurology, we must accept all the consequences of such a fact, therefore we must settle to be born without experience , with only certain genetic skills useful for survival, and that experiences, beginning with the maturity of the senses, are built over time, and that the origin of the axioms is not alien to this common brain process that we mentioned of edification of what will become human thought.

We will see the activity of a man in primitive times, in his day of struggle. It is not a detailed account because the object is to highlight the aspects of elementary life that lead to a mental construction, in this opportunity, of the axiom of identity.

One day.- A man wanders through the forest. He looks at an apple hanging from a tree, he sees the fruit, his hunger induces the secretion of some chemicals related to anxiety and desire, he walks towards the tree, take the fruit, he takes it to his mouth, eat it; after the ingestion he experiences organic and psychological relief.

From all this he forms a neural record in his memory. The memory register includes the participation of many neurons corresponding to different senses that have participated at the same time sharing the data of the real event. In this way, cells of vision, touch, hearing, taste, smell and possibly other neurons, as well as complementary systems such as the limbic, or areas capable of organizing memories such as the hippocampus, intervened.

In summary, the memory stored the data of the senses together with the data of the chemists who were in charge of the sensations of anxiety for hunger, of expectation and satiety after ingesting it, for this they invaded the circulatory system with their enzymes. .

Spend time

Another day he goes through the forest, it is routine to look for food, sometimes it repeats the paths, sometimes it looks for new places, today it thinks to remember the path, it has already walked there, but something suspended from a branch from the tree it catches his attention, he does not know what it is, but he receives the help of her own memory, it is that he awakens bringing back the memory of the apple, of the appetizing fruit that satiated her hunger on a previous occasion; but he is not sure, he approaches, the memory overlaps with the new observation, at moments the two ideas seem to guide his thoughts. The reactions are repeated, the man takes it, new images are crowded in his mind bringing him the forgotten data of his intake, which happened the first time: the texture of the skin, the softness of the pulp, etc. This time each visual neuron will remember its past action. The same will be done by the neurons of the other senses that recorded their participation in the first experience. Of course, the chemists will return, both the remembered ones and some new ones corresponding to personal singularities of the new experience.

The inexorable time passes. Because this scene is repeated often has recorded many similar experiences that have begun to compare automatically, without their express consent. You will remember in your mind, as a result of the comparisons that each recollection brings its particularities, its similarities and differences and is consciously questioned this time: will it be that I see the same as those I have liked before? Will there be two identical apples? His experience tells him no, he knows it, but he also knows that they all serve the same personal purpose. However, the question returns, subsists. Will there be two equal apples, he knows by data related to his memories that exactly not. Not exactly the same. Then another question arises: why not? If it is the same tree, the same general shape, the same color, the same smell. Something happens that he does not understand, something that exceeds the capacity of his senses. The idea of ​​total similarity, independent of details, has begun to mature. You are building the principle of identity.

Times later concludes

The message of his reflection is constant: fruits are similar, but never the same. He knows it, it is always the same, without exceptions. No doubt, an apple is just like itself, there will never be another like it. An identity criterion has been born. It will be many years before this conclusion becomes generalized and rises to the category of indisputable truth. Abstraction has intervened, which is nothing more than a simplification of irrelevant data for the benefit of important ones, a mechanism based on the comparison between neuronal memories already in the mind that reflect differences and similarities. All based on experiences.

Thus man has managed to build the identity axiom. Your applications will come many years later.