Formal science is a
branch of science studying disciplines concerned with abstract structures described by
formal system
A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms.
In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in ma ...
s, such as
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
,
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
,
theoretical computer science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation.
It is difficult to circumscribe the theoretical areas precisely. The Associati ...
,
artificial intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...
,
information theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
,
game theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...
,
systems theory
Systems theory is the Transdisciplinarity, transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, de ...
,
decision theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, ratio ...
and
theoretical linguistics
Theoretical linguistics is a term in linguistics that, like the related term general linguistics, can be understood in different ways. Both can be taken as a reference to the theory of language, or the branch of linguistics that inquires into the ...
. Whereas the
natural science
Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...
s and
social science
Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...
s seek to characterize
physical systems and
social system
In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. It is the formal Social structure, structure of role and status that can form in a smal ...
s, respectively, using
theoretical and
empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how t ...
methods, the formal sciences use language
tools
A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates ...
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.
Branches
#
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
(also a branch of
philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
)
#
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
#
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
#
Systems science
#
Data science
Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processing, scientific visualization, algorithms and systems to extract or extrapolate knowledge from potentially noisy, stru ...
#
Information theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
#
Computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
#
Cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...
Differences from other sciences
Because of their non-empirical nature, formal sciences are construed by outlining a set of
axioms and
definitions
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definit ...
from which other statements (
theorems
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
) are deduced. For this reason, in
Rudolf Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism.
...
'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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See also
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References
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.
*
* Bernt P. Stigum (1990). ''Toward a Formal Science of Economics''.
MIT Press
The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...
* 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
* {{Commonscat-inline, Formal sciences
Interdisciplinary conferences — ''Foundations of the Formal Sciences''
Branches of science