A truly didactic education owes to include a heuristic approach. However, merely communicating with the research, is not sufficient, even if it is effective; because a researcher lacking a main philosophical axis to support the structure is nothing more than an amalgam of knowledge. Moreover, the basic characteristic of this knowledge is that they are local, in other words they are specific and very often their links alone are not capable but for very fragile dendrites, to bring any idea into their gulfs. The importance of such a situation originates from the fact that the individual who does not have a structured thought, seeks to confront this lack with verbal proficiency;
this way, one tends to act on improving eloquence, thus acquiring discernible results, instead of being devoted to form a thought of greater depth, an act of which impacts would certainly be more difficult to be perceived.
On the level of Lyceum “Aristotle's school and philosophy” there are only two kinds of respectable teaching for whom seeks the truth: Mathematics and Philosophy. One can rest great hopes on Science, its current condition however, is much so effete by diseases called empiricism and logical incoherence, those two areas of thought consist of the fertile ground on which the tree of Research will grow to elevate up to Knowledge. Thus, in education, these two branches should share some common time and be called “Elements of Epistemology ”. The course will be taught jointly by the professor of Mathematics with the one of Philosophy, will have a flexible selection structure, so as to permit the students a significant intervention. The course will include exclusively fundamental outcomes, that are demonstrated in an elemental way, such as the irrationality of square root or the sum of the prime numbers is finite. After these have been proven by the professor of Mathematics, they will be commented by the professor of Philosophy, who will explain, among others, their history, their consequences within the domain of knowledge and modifications they have provoked on the mentality of our civilization. Epistemology is necessary to scientific thought; having a fragile constitution, the assimilation of the conceptual changes in the beginning of the century, after the crisis of the foundations in Mathematics and the theories of Relativity and Quantum mechanics, is still incomplete; it is essential that the structure itself to be transformed, in order for the knowledge to be eventually perceivable in its entirety.
Epistemology: Critical study of sciences, towards the definition of their logical origin, their value and their reasoning.
References: Lygeros N: Proposition, in Hanneton n 5 , Dec 1989, p 8 Lygeros N: The notion of the black hole. Thessaly, 31st July 1998