Characteristic formal sciences, object of study and examples

David Holt

The formal science they consist of a systematic body of coherent and rational knowledge. Its objective is not the physical-natural world, but fully abstract objects; However, the knowledge of the formal sciences can be applied in the physical-natural reality and are used by the factual or empirical sciences..

The method used by the formal sciences is deduction and, unlike the factual sciences, the formal sciences admit neither abduction nor induction. Therefore, a formal science works with forms; that is, with objects that only exist in the human mind and are obtained by abstraction.

Mathematics is considered a formal science. Source:

Likewise, the truth for the formal sciences is understood as a logical truth: it is a series of consequences that follow after considering all the possibilities or the ways in which the pre-established facts could have been combined. In this context, examples of formal science can be mathematics or logic.

A characteristic of the formal sciences is that they are branches of scientific knowledge that study formal systems. Consequently, a formal science validates its theory through a set of propositions, axioms, definitions, and inference rules..

The formal sciences are all analytical. This differentiates them from the natural and social sciences, which are empirically argued; that is, they require observation of the real world to find evidence in favor of a theory. Instead, formal science knowledge is called "theorems" and comes from mathematical proofs..

Furthermore, the rules or laws stipulated by the formal sciences are always followed, no matter what the case may be. Consequently, they are universal laws that do not study concrete phenomena, as occurs with factual sciences. The content of a formal science is empty, since it is maintained only in the form and in the causal relationships.

Regarding its origins, some point out that the formal sciences are as old as humanity, since from the beginning man has used mathematics and logic to organize his world. However, they began to be called this way from the Modern Age, when they were conceptualized and classified.

Article index

  • 1 Features
  • 2 Object of study
  • 3 Examples of formal science
    • 3.1 -Statistics
    • 3.2 -Geometry
    • 3.3 -Theoretical linguistics
    • 3.4 -Artificial intelligence
  • 4 References


The following are the most important characteristics of the formal sciences:

- The method used by the formal sciences is that of deduction.

- The criterion of a formal science to establish the truth is based on consistency or non-contradiction.

- The statements of a formal science are always analytical, which means that they are deduced through theorems or postulates.

- Formal science entities can only exist within the human mind.

- Mathematicians and logicians construct their own objects of study through empty symbols.

- The demonstration of a formal science is complete, total and final.

- The study of the formal sciences invigorates the habit of rigor.

Object of study

In general terms, it can be said that the object of study of the formal sciences is the forms; These can be presented as relationships, abstractions or ideal objects that have been constructed in the mind of man..

Some scientists claim that formal science is not so interested in the why of phenomena, but rather focuses on the how; that is, the inclination is towards the forms and not towards the content itself.

In conclusion, the formal sciences -also known as ideal sciences- are those that do not focus on the world or nature, nor on the chemical or physical laws that govern it..

His interest lies in the formal systems of relationships that do not have their own content, but that can be used during the analysis of any aspect of reality..

An example of the above can be evidenced with physics, which is a factual or empirical science that is responsible for the study of bodies, movement, space and matter. However, physics uses mathematics -which is a formal science- to carry out its analyzes and conclusions..

Examples of formal science


Statistics is a formal discipline in charge of organizing, interpreting and processing a series of data in order to establish certain characteristics of a certain population or social objective..

According to some authors, statistics can also be defined as the science that studies how information should be used in certain practical situations that generate uncertainties. On some occasions statistics has been defined as "data science", because it collects, classifies and interprets the latter..

Likewise, statistics allow researchers to take as a starting point a series of data to undertake their work, guaranteeing the analysis and objective obtaining of a set of results..

Statistics can be divided into two main groups:

Descriptive statistics

It consists of a method that numerically describes a set of data. Therefore, being a numerical method, descriptive statistics uses the number as a technique to describe.

The main characteristic of this type of statistic is that it does not allow to draw concrete conclusions; only gives numerical results.

Deductive, analytical or inferential statistics

It is responsible for studying the probabilities of success within the different possible solutions to a particular problem. In addition, inferential statistics creates a mathematical model that deduces the population behavior based on the conclusions obtained during the observation of the samples..

In contrast to descriptive statistics, deductive or inferential statistics do allow us to draw concrete conclusions.

-The geometry

Geometry is a formal science that starts from mathematics to study the measurements and properties of a figure located in a space or on a certain plane. In turn, geometry uses axiomatic or formal systems to represent different aspects of reality.

These axiomatic systems are constituted by symbols that, respecting certain rules, can join and form chains, which can also be linked to each other. For example, geometry is based on abstract notions such as curves, points and lines, among others..

It is important to note that geometry is one of the oldest disciplines that exist, since its origins date back to Ancient Egypt. In fact, important mathematicians and scholars relied on geometry to develop studies on the volumes, areas, and lengths of things; among these wise men Euclides and Herodotus stand out.

One of the most important figures in geometric studies was René Descartes, a French physicist and philosopher who proposed that the geometry of a shape could be expressed or represented by equations.

Geometry can be divided into two main branches:

Analytic geometry

It consists of a type of geometry that studies the figures through a coordinate system. This study does so by using methodologies from mathematical analysis.

Descriptive geometry

Descriptive geometry consists of a branch that is dedicated to solving spatial problems through operations that are expressed and developed on a plane; in this are represented certain figures from solid objects of reality.

-Theoretical linguistics

Theoretical linguistics is a formal science that comes from linguistics and is interested in the main aspects of natural languages, taking into account the structure of the language and the characteristics of the linguistic knowledge of the speakers.

Likewise, it can be established that theoretical linguistics is made up of other disciplines such as semantics, phonology, morphology and phonetics..

This science is based on the construction of universal schemes and theories, which can be valid for all the languages ​​spoken in the world. Consequently, theoretical linguistics does not aim to explain certain particular facts of a particular language, but rather points to the universality of linguistic structures.

For this reason, it can be said that theoretical linguistics is a formal science since, like statistics, this discipline is in charge of collecting data that allow the interpretation, analysis and cataloging of the grammatical and phonological structures of languages.

Furthermore, this branch of linguistics employs theoretical abstractions together with complex schemas that cannot be apprehended in reality, but exist only as ideal in the human mind..

-Artificial intelligence

Artificial intelligence (AI) is a branch of computer science that consists of the processing of a series of abstract data carried out by machines; this data allows electronic devices to perform a task or objective.

In other words, through a series of abstract and numerical data, artificial intelligence gives access to machines so that they can learn, perceive, reason or solve certain problems.

Some scientists define artificial intelligence as a computational branch that is responsible for studying computer models so that they can carry out activities that are typical of human beings through two main characteristics: behavior and reasoning.

The term "artificial intelligence" was coined by computer scientist John McCarthy in 1956, who established that AI is the science of ingenuity, because it allows building intelligent computer programs.


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