Formal sciences are those that work with abstract or formal entities, such as numbers, symbols, and proportions. Their area of study is not the real world but rather the ideal world, where content-free forms are found that function as analytical tools for understanding reality. For example:mathematics, logic.
Formal sciences use the deductive method, in which the conclusion is derived from premises through logical reasoning. Since formal sciences require propositions that are logically demonstrable, they rely on axioms , which are self-evident statements that are accepted as universal truths without requiring prior proof.
Formal sciences are built on the basis of formal systems, which are composed of:
- A finite set of symbols used to construct formulas.
- A formal grammar, as a mechanism for the construction of well-formed formulas.
- A set of axioms.
- A set of inference rules.
- A set of theoremsthat includes everything that can be derived from the axioms.
See also:
- Hard and soft sciences
- Pure and applied sciences
Characteristics of formal sciences
Formal sciences have the following characteristics:
- Abstraction. They work with abstract concepts and formal structures, unrelated to the physical world.
- Deductive reasoning. They rely on deductive logic to derive theorems and results from axioms and definitions.
- Empirical independence. They do not depend on empirical observation or experimentation. Their results are true based on the internal consistency and logic of the system.
- Axiomatization. They are based on systems of axioms, which are initial propositions assumed without proof.
Examples of formal sciences
- Mathematics. It is the deductive science dedicated to the study of the properties of abstract entities and their relationships. It works with numbers , symbols, and geometric figures. Statistics, arithmetic, and geometry are branches of mathematics that are also considered formal sciences.
- Logic. It is the science that deals with how statements can be connected to generate valid conclusions. It provides a framework for evaluating the truth or falsity of statements systematically and objectively.
- Theoretical computer science. Within computer science, this focuses on the more abstract and mathematical aspects of the field. It includes the analysis of algorithms and, above all, the formal semantics of programming languages .
Difference between formal sciences and factual sciences
The notion of formal sciences is usually contrasted with factual sciences , which are those that study the facts and phenomena of reality. They are verifiable through observation and experimentation, and their methods allow for deduction, induction, and abduction. For example: natural sciences, social sciences.
The main differences between formal sciences and factual sciences are:
| Formal sciences | Factual sciences |
| They study abstract entities and their relationships. | They study observable natural and social phenomena. |
| They have as their object of study abstract concepts and logical structures. | They have as their object of study facts and phenomena of the real world. |
| They use the deductive method. | They use the inductive and experimental method. |
| They demonstrate theorems and propositions from axioms. | They discover and explain natural and social laws and principles. |
| They achieve logical results. | They achieve empirically verifiable results. |
| For example: mathematics, logic, theoretical computer science. | For example: physics, chemistry, biology, sociology, psychology. |
Both are fundamental in today’s world, as they complement each other: the contributions of some fundamental sciences to technological advancement (such as chemistry or computer science) are supported by formal systems such as mathematics.
