We explain what formal sciences are, what they are and how they differ from factual sciences.
What are formal sciences?
The formal sciences or ideal sciences are those whose object of study is the formsthat is, abstract objects and the relationships between them, such as numbers, proportions or representation systems.
In this way, formal sciences do not study the real world and nature, nor the physical and chemical laws that govern it, but rather the systems of relationships that arise from them in the human mind. These systems can, however, be applied to the analysis of any aspect of reality.
The best example of formal sciences is mathematics: it deals with the study of numbers, their sets and various relationships. Although numbers do not exist in reality, but are ideas and mental relationships, reality can be expressed and studied with them.
These sciences are analytical or non-empirical, which means that they do not validate their theories and knowledge through experimentation or observation of the real world, but rather through the study of the rules of thought that govern each systemsuch as propositions, axioms and definitions. Their method, therefore, is normally deductive, and they do not admit either induction or abduction.
For all these reasons, formal sciences are distinguished from factual sciences, whose objective is the study of the real world through the scientific method.
Characteristics of formal sciences
The main characteristics of formal sciences are:
- Its object of study is the formal systems and languages that human beings mentally design, that is, sets of abstractions.
- They do not deal with the real world, but their systems of relationships are useful for posing and studying real phenomena.
- Its essential purpose is to demonstrate the universal validity of certain possible reasonings within a formal system, known as axioms or theorems.
- His method of analysis is always deductive and, therefore, allows neither induction nor abduction. That is, its conclusions are always obtained from given premises.
- Their formal systems are expressed through symbols, formulas and variables that express relationships and not concrete references. For example, in an equation, x It is a variable that can represent any number.
See also: Deduction
Examples of formal sciences
Some examples of formal sciences are:
Math
Mathematics is the science that studies logical procedures of calculation and formal representation, such as numbers, equations and geometric objects.
Logic
Logic is the science that studies the methods of reasoning, that is, what are the mechanisms to obtain valid conclusions from certain propositions.
computer science
Computing, also known as computing or programming, is the science dedicated to studying computer systems that allow the automation (storage, retrieval, transmission) of information.
Arithmetic
Arithmetic is the science dedicated to studying operations between natural numbers and integers. It is considered a branch of mathematics and is also known as Number Theory.
Statistics
Statistics is the science that deals with the study of probabilities and proportions, as well as the laws that govern chance.
Geometry
Geometry is the science that studies geometric shapes in the plane, that is, the mental or graphic representations with which it is possible to express relationships and mental spaces.
See also: Sciences
Differences between formal and factual sciences
Formal sciences are distinguished from factual sciences, also called factual or empirical, in different aspects, such as:
| formal sciences | Factual sciences |
|---|---|
| Its object of study is the abstract systems with which human beings express certain logical aspects of thought. | Its object of study is the facts and phenomena that take place in reality. |
| Its purpose is to demonstrate the universal validity of certain formal reasoning. They have no contact with reality. | Its purpose is to create a mental representation as close as possible to reality in order to understand it. |
| His method of analysis is always deductive, never inductive or abductive. | Its method of analysis is empirical-analytical, which allows deduction, induction and abduction. |
| They seek the perfection of their deductive reasoning, that is, their theorems and axioms. | They seek to ensure that their mental models are as coherent as possible with the real phenomenon they describe. |
| They cannot be verified experimentally, but logically. | They can always be verified experimentally. |
| Their demonstrations are complete and final, that is, they do not depend on the moment and circumstances. | Their demonstrations are incomplete and partial, that is, they depend on the moment and the circumstances. |
| They do not present subclassifications. | They are divided into two categories: natural sciences (study nature) and social sciences (study society). |
| Examples of formal sciences are: mathematics, logic and statistics. | Examples of factual sciences are: biology, chemistry and physics. |
References
- Bunge, M. (2000). Scientific research: its strategy and philosophy. 21st century.
- Ortíz, F. (2003). Dictionary of scientific research methodology. Limousine Publishing.
- Tomalin, M. (2006). Linguistics and the Formal Sciences. Cambridge University Press.
