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Formal sciences are disciplines concerned with

formal systems, such as logic, mathematics,

statistics,theoretical computer science, information

theory,game theory,systems theory, decision

theory, and portions oflinguistics.

Whereas natural sciences and other sciences likesocial sciences,behavioral sciences, and cognitive

scienceseek soundness ofscientific theory with

respect to observations in order to successfully

predict and perhaps accurately explain phenomena

in the external world, the formal sciences are

concerned with the internal properties offormal

systems, especially definitions of terms and rules

governing inferences.

Formal sciences sometimes aid constructing, assessing, and testing scientific theories and scientif

models, however, by revealing inconsistencies or invalid forms of inference.

Contents [hide]

1 History

2 Differences from other forms of science

3 See also

4 References

5 Further reading

6 External links

Formal sciences began before the formulation ofscientific method, with the most ancient

mathematicaltexts dating back to 1800 BC (Babylonian mathematics), 1600 BC (Egyptian

mathematics) and 1000 BC (Indian mathematics). From then on different cultures such as the Indi

Greek and Islamic mathematicians made major contributions to mathematics, while the Chinesea

J apanese, independently of more distant cultures, developed their own mathematical tradition.

Besides mathematics, which is not classified as a science[citation needed], logic is another example

one of oldest subjects in the field of the formal sciences. As an explicit analysis of the methods of

reasoning, logic received sustained development originally in three places : Indiafrom the 6th cent

BC, China in the 5th century BC, and Greece between the 4th century BC and the 1st century BC

History [edit source| edit beta ]

Formal sciences [sho

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Philosophy and history of science [sho

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//en.wikipedia.org/wiki/Formal_science[8/10/2013 1:41:09 AM]

Book: Formal science

The formally sophisticated treatment of modern logic descends from the Greek tradition, being

informed from the transmission ofAristotelian logic, which was then further developed by Islamic

logicians. The Indian tradition also continued into the early modern period. The native Chinese

tradition did not survive beyond antiquity, though Indian logic was later adopted in medievalChina

As a number of other disciplines of formal science rely heavily on mathematics, they did not exist

until mathematics had developed into a relatively advanced level. Pierre de Fermat and Blaise Pas

(1654), and Christiaan Huygens (1657) started the earliest study ofprobability theory. In the early

1800s, Gaussand Laplacedeveloped the mathematical theory ofstatistics, which also explained t

use of statistics in insurance and governmental accounting. Mathematical statistics was recognizeda mathematical discipline in the early 20th century.

In the mid-twentieth century, mathematics was broadened and enriched by the rise of new

mathematical sciences and engineering disciplines such as operations research and systems

engineering. These sciences benefited from basic research in electrical engineering and then by th

development ofelectrical computing, which also stimulated information theory,numerical analysis

(scientific computing), and theoretical computer science. Theoretical computer science also benefit

from the discipline ofmathematical logic, which included the theory of computation.

One reason why mathematics enjoys special esteem, above all other sciences, is thatits 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[1]

As opposed to empirical sciences (natural and social), the formal sciences do not involve empirica

procedures. They also do not presuppose knowledge of contingent fact, or describe the real world

this sense, formal sciences are both logically and methodologically a priori, for their content and

validity are independent of any empirical procedures.

Although formal sciences are conceptual systems, lacking empirical content, this does not mean th

they have no relation to the real world. But this relation is such that their formal statements hold inpossible conceivable worlds (see valid formula) whereas, statements based on empirical theorie

such as, say, General Relativity or Evolutionary Biology, do not hold in all possible worlds, and ma

even turn out not to hold in this world. That is why formal sciences are applicable in all domains a

useful in all empirical sciences.

Because of their non-empirical nature, formal sciences are construed by outlining a set ofaxioms

and definitions from which other statements (theorems) are deduced. In other words, theories in

formal sciences contain no synthetic statements; all their statements are analytic.[2][3]

RationalismAbstract structure

Abstraction in

mathematics

Abstraction in computer

science

Formal grammar

Formal language

Formal method

Formal system

Mathematical model

1. ^ Albert Einstein(1923). "Geometry and Experience". Sidelights on relativity . Courier DoverPublications. p. 27. Reprinted by Dover (2010), ISBN 978-0-486-24511-9.

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2. ^ Carnap, Rudolf(1938). "Logical Foundations of the Unity of Science". International Encyclopaedia

Unified ScienceI. Chicago: University of Chicago Press.

3. ^ Bill, Thompson (2007), "2.4 Formal Science and Applied Mathematics",The Nature of Statistical

Evidence, Lecture Notes in Statistics 189 (1st ed.), Springer, p. 15

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.

J ames Franklin(1994).The formal sciences discover the philosophers' stone . In: Studies in

History and Philosophy of Science. Vol. 25, No. 4, pp. 513533, 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

Marcus Tomalin (2006), Linguistics and the Formal Sciences. Cambridge University Press

William L. Twining (1997). Law in Context: Enlarging a Discipline. 365 pp.

Interdisciplinary conferences Foundations of the Formal Sciences

Categories: Formal sciences

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