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Formal science

Formal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems. The formal sciences aid the natural and social sciences by providing information about the structures used to describe the physical world, and what inferences may be made about them. Branches of formal science include: logic, mathematics, statistics, data science, information science, systems science, computer science. One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. Because of their non-empirical nature, formal sciences are construed by outlining a set of axioms and definitions from which other statements (theorems) are deduced. For this reason, in Rudolf Carnap's logical-positivist conception of the epistemology of science, theories belonging to formal sciences are understood to contain no synthetic statements, instead containing only analytic statements.

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Related concepts (16)
Philosophy
Philosophy (love of wisdom in ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, values, mind, and language. It is a rational and critical inquiry that reflects on its own methods and assumptions. Historically, many of the individual sciences, like physics and psychology, formed part of philosophy. But they are considered separate academic disciplines in the modern sense of the term.
Branches of science
The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups: Formal sciences: the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology. Natural sciences: the study of natural phenomena (including cosmological, geological, physical, chemical, and biological factors of the universe). Natural science can be divided into two main branches: physical science and life science (or biology).
Applied science
Applied science is the use of the scientific method and knowledge obtained via conclusions from the method to attain practical goals. It includes a broad range of disciplines such as engineering and medicine. Applied science is often contrasted with basic science, which is focused on advancing scientific theories and laws that explain and predict natural or other phenomena. Applied science can also apply formal science, such as statistics and probability theory, as in epidemiology.
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