The formal sciences are those where analytical propositions take the statements of mathematics and logic. In this way, his area of study is not the real world but rather the ideal world, empty forms of content that in many cases cannot be fully observable, but that are valid analytical instruments to understand reality. For instance: statistics, logic, mathematics.
The formal sciences are characterized by not coming into conflict with reality, since they do not have the responsibility of being verifiable. On the contrary, the formal sciences need to use propositions that they are demonstrable in a logical sense, and that they can happen: otherwise, these sciences make use of ‘axioms’ that are evident propositions that are accepted without requiring prior demonstration.
The use of axioms is related to the usual method of this type of science, which is the Deductive method: taking the axioms as a starting point and then proceeding in a derivative way, arriving at the propositions as necessary logical consequences of the previous propositions. It is said, then, that a formal system is composed of the following:
- A finite set of symbols that are used for the construction of formulas.
- A grammar formal, as a mechanism for the construction of well-formed formulas.
- A set of axioms
- A set of inference rules
- A set of theorems which includes everything that can be derived from the axioms.
They oppose the Factual Sciences
Usually the notion of formal sciences comes in contradistinction to the factual science, which are the ones who study the facts. Both one and the other are of great importance in today’s world, since they are a complement between the two: the contributions of some fundamental sciences in what is technological advance (such as chemistry or computer science) are supported by formal systems such as of mathematics.
Examples of Formal Sciences
- Theoretical Computer Science. Division within computer science, which focuses on the most abstract and mathematical aspects of the area. It includes the analysis of algorithms and especially the formal semantics of programming languages.
- Statistics. Science that is responsible for collecting, organizing, processing, analyzing and interpreting data in order to deduce the characteristics of a target population.
- Logic. Discipline that studies the formal procedures of reason, trying to know what type of procedures are used by the human brain through formal propositions.
- Math. Deductive science that is dedicated to the study of the properties of abstract entities and their relationships. Works with numbers, symbols, and geometric shapes.
- Systems theory. Interdisciplinary study of systems in general, in order to study the principles applicable to systems at any level in all fields of research.