The different disciplines that make up science can be ordered based on three parameters: by the object of study, by the method used and by its purpose. Another classification model consists of dividing the sciences into two large groups: the formal sciences and the factual or empirical sciences.
The formal ones
Logic and mathematics are two formal disciplines because they do not have a concrete empirical content, as in biology, meteorology or history.
Logic is a purely formal and abstract discipline. In a strict sense it does not have an observable, measurable and tangible content. It is actually a set of rules that are applicable to any type of knowledge, be it scientific or everyday life.
The rules of logic are those that allow you to think coherently and in a rational way. Thus, I cannot say that something is and is not both because I am violating the principle of non-contradiction and I cannot affirm that something is not identical to itself because I am going against the principle of identity.
Mathematics is purely abstract, since its content is mental and not material.
Remember that numbers do not exist anywhere in nature, since they are inventions of the human mind to count or calculate something about reality. In this sense, arithmetic, geometry or algebra are mathematical disciplines that are based on a series of principles that can be rationally demonstrated.
If we take any mathematical equation as a reference, its formulation is valid completely independent of reality.
In short, logic and mathematics make up formal systems that include a series of elements: axioms, symbols, inference rules, and theorems. These elements are expressed in the form of statements that are described through signs.
The factual ones have the formal sciences implicit
The set of disciplines that deal with studying facts need a formal structure so that their object of study makes sense. On the other hand, to show that a statement in biology or chemistry is formally true, there must be a correlation with the empirical data.
In short, the formal sciences are projected onto the world of observable facts. If we take the Pythagorean theorem as a reference, its formulation is valid for any reality in which there is a right angle forming a right triangle.
In short, the formal sciences and the factual sciences are complementary and should not be conceived as separate areas of knowledge.
Photos: Fotolia - Artisticco / Sergey Bogdanov
