HOW ARE THE AXIOMS FORMED?

When we speak of axioms refer to truths that are self-evident. This concept is repeated from ancient times up to now. Mathematicians and logicians work with them by their status as truths indisputable, becoming the base and foundation of the development of these sciences.

Always struck me as strict of the claim regarding the axioms. "The obvious truth that does not need demonstration". For me, used to seek the explanation of things, talk that exhaustively seemed a heresy. The benefits obtained from use can not be discussed. But we must find the justification that is back.

There remains therefore the question of its origin, where it comes from so much power and because it is up to us as an inexplicable mental inlay. When we find the source we will be enabled to specify its scope and its limitations.

Historically the axioms put in dire straits to the partisans of the experience as a source of knowledge. To be able to not explain them as originating from that source some empirical chose to treat them as exceptions.

If the mind of man is a "tabula rasa" at birth as modern neuroscience confirms it, we must accept all the consequences of this fact, we must therefore accept the empirical origin of the axioms.

We live in an era in which we have developed sciences which can help us in the search for the solution. In particular the genetic psychology and memory

Suppose the activity of a man in primitive times in their daily struggle. It is not a detailed narrative as the object is to highlight aspects of the elementary life that lead to an understanding of the proposed objective.

First day. A man wanders through the forest. Look an apple hanging from a tree, view the fruit, his hunger induces the secretion of a chemical related to anxiety and the desire, walking towards the tree, take fruit brings it to his mouth, eats it, after meal relief organic and psychological experiences.

All of this form in his memory a neuronal record. The registry in memory includes the participation of many neurons corresponding to different senses that have produced at the same time its own registry sharing data from the real fact. Thus participated cell vision, touch, hearing, taste, smell and possibly other complementary systems. The event was influenced by the chemical regulators of hunger, neurotransmitters, dopamine, endorphins etc which are poured into the blood stream and to the relevant brain systems.

In short, memory stored data of the senses and data of the chemicals that were in charge of the feelings of anxiety by hunger, expectation and fullness after ingesting it, so invaded the circulatory system with its enzymes.

Another day experience is repeated, man returns to see an apple and will do the same. This time each neuron visual recall your last action. The same will make neurons in other senses that recorded his participation in the first experiment. Of course chemicals will return both the remembered and few new ones corresponding to peculiarities of the new experience.

Two similar experiences with the particular details of each will be registered in your mind. Something similar will happen if the experiences are repeated several times

Times after it concludes

The experience of apple has become routine, the search is on a daily basis. Have you noticed that all them produce satiety, soothe the hunger, improve you the mood. The message of his reflection is constant: the fruits are similar, never the same. You know that by your memories, telling you also other details, over color, others about the odor, others on the texture to the touch.

There is no doubt, a single apple is equal to itself, there will never be another equally. A criterion of identity was born.  

It will be many years before this conclusion generalize and rise to the status of undisputed truth. It is the result of  the abstraction that is nothing more than a simplification of irrelevant data for the benefit of the important ideas, mechanism which is based on the comparison between neural memories present in mind that reflect the differences and the similarities. All of this based on experiences.

This way the man was building the identity axioms.