Formal science

Short description: Study of abstract structures described by formal systems

"Mathematics and Statistics" redirects here. It is not to be confused with Mathematical statistics, Mathematics, or Statistics.

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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 theoretical and empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems and the deductions that can be made from them.

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.[1]

## Contents

* 1 Branches
* 2 Differences from other sciences
* 3 See also
* 4 References
* 5 Further reading
* 6 External links

## Branches

1. Logic (also a branch of philosophy)
2. Mathematics
3. Statistics
4. Systems science
5. Data science
6. Information theory
7. Computer science
8. Cryptography

## Differences from other sciences

> 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.

> --Albert Einstein[2]

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.[3][4]

## See also

* Philosophy:Philosophy
* Philosophy:Abstract and concrete - Metaphysics concept covering the divide between two types of entities
* Philosophy:Analytic–synthetic distinction - Semantic distinction in philosophy
* Philosophy:Rationalism - Epistemological view centered on reason
* Science
* Cognitive science - Interdisciplinary scientific study of cognitive processes
* Mathematical sciences - Group of areas of study that are primarily mathematical
* Abstract structure
* Abstraction in mathematics
* Abstraction in computer science - Technique for arranging complexity of computer systems
* Philosophy:Formalism (philosophy of mathematics) - View that mathematics does not necessarily represent reality, but is more akin to a game
* Formal language - Sequence of words formed by specific rules
* Formal grammar - Structure of a formal language
* Formal methods - Mathematical program specifications
* Formal system - Mathematical model for deduction or proof systems
* Mathematical model - Description of a system using mathematical concepts and language
* Mathematics Subject Classification - Classification scheme for mathematics
* Philosophy:Semiotics
* Philosophy:Theory of forms - Philosophical theory attributed to Plato

## References

1. ↑ Ramoo, Dinesh (2024). Critical Thinking. Thompson Rivers University Open Press. https://criticalthinking.pressbooks.tru.ca/chapter/formal-vs-empirical-sciences/.
2. ↑ Albert Einstein (1923). "Geometry and Experience". Sidelights on relativity. Courier Dover Publications. p. 27. Reprinted by Dover (2010), ISBN 978-0-486-24511-9.
3. ↑ Carnap, Rudolf (1938). "Logical Foundations of the Unity of Science". International Encyclopaedia of Unified Science. I. Chicago: University of Chicago Press.
4. ↑ Thompson, Bill (2007), "2.4 Formal Science and Applied Mathematics", The Nature of Statistical Evidence, Lecture Notes in Statistics, 189 (1st ed.), Springer, p. 15

## Further reading

* Mario Bunge (1985). Philosophy of Science and Technology. Springer.
* Mario Bunge (1998). Philosophy of Science. Rev. ed. of: Scientific research. Berlin, New York: Springer-Verlag, 1967.
* C. West Churchman (1940). Elements of Logic and Formal Science, J.B. Lippincott Co., New York.
* James Franklin (1994). The formal sciences discover the philosophers' stone. In: Studies in History and Philosophy of Science. Vol. 25, No. 4, pp. 513–533, 1994
* Stephen Leacock (1906). Elements of Political Science. Houghton, Mifflin Co, 417 pp.
* {{Cite book
* Bernt P. Stigum (1990). Toward a Formal Science of Economics. MIT Press
* Marcus Tomalin (2006), Linguistics and the Formal Sciences. Cambridge University Press
* William L. Twining (1997). Law in Context: Enlarging a Discipline. 365 pp.

## External links

* Interdisciplinary conferences — Foundations of the Formal Sciences

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