Formal science

Formal science

A formal science is a theoretical study that is concerned with theoretical formal systems, for instance, logic, mathematics, systems theory and the theoretical branches of computer science, information theory, economics, statistics, and linguistics.


The formal sciences are built up of theoretical symbols and rules.

The formal sciences can sometimes be applied to the reality, and, within certain limitations, they can be useful. People often make the mistake of confusing theoretical systems with reality, applying theoretical models as if they represent reality perfectly, or believing that the theoretical model is in fact the reality.

The difference between formal sciences and natural science is that formal sciences start from theoretical ideas and it leads to other theoretical ideas through thinking processes, while natural science starts from observation of the real world and leads to more or less useful models for a part of reality. You can never learn anything about reality from studying formal sciences alone. You can never prove anything about reality through the use of formal sciences.

Applied mathematics is to try to apply some theoretical mathematical model to reality. It is possible within certain limits and with certain restrictions and with a certain limit of precision.

If the map and the reality do not fit it is the map which is wrong, not the reality. A map is a theoretical representation (model) of reality.


The study of applied science began earlier than formal science and the formulation of scientific method, with the most ancient mathematical texts available dates back to 1800 BC (Babylonian mathematics), 1600 BC (Egyptian mathematics) and 1000 BC (Indian mathematics). From then on different cultures such as the Indian, Greek and Islamic mathematicians made major contributions to mathematics, while the Chinese and Japanese independently developed their own mathematical tradition.

Besides mathematics, logic is another oldest subject in formal science. Logic as an explicit analysis of the methods of reasoning received sustained development originally in three places: India from the 6th century BC, China in the 5th century BC, and Greece between the 4th century BC and the 1st century BC. The formally sophisticated treatment of modern logic descends from the Greek tradition, being informed from the transmission of Aristotelian 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 medieval China.

As 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 Pascal (1654), and Christiaan Huygens (1657) started the earliest study of probability theory (statistics) in the 17th century.

In the mid-twentieth century, mathematically-based studies such as operations research and systems engineering were developed. The rise of the computer gave a great impetus to these sciences and to theoretical computer science and information theory, allowing the study of complex systems beyond the range of traditional mathematical techniques. The rise of these disciplines made it clear that mathematics was only one of a range of formal or mathematical sciences, which differed from natural sciences in basing their knowledge on proof and computer simulation rather than real-life experiments.

Relation with science

It is arguable whether formal science is, besides natural science and social science, the third branch of science and some of the disciplines of formal science like mathematics and statistics are often even referred as natural science. For instance, Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". [Waltershausen] In some notable universities, e.g. Imperial College London and Tokyo University, their department of mathematics/statistics run under the faculty of natural science/science.

The changing definition of the word 'science' maybe primarily induces such a confusion. In the original Latin "Regina Scientiarum", as well as in German "Königin der Wissenschaften", the word corresponding to "science" means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to modern "scientific method" is of later date.

The notion that formal science is also natural science is also attributed to the close relation between formal science and disciplines such as physics or chemistry. Nowadays, mathematics and statistics are heavily applied in natural and social science and are deemed important and necessary by most of the scholars in those areas. Without adequate knowledge in mathematics, it is impossible to make sense of the subject matters. This close relation explains the notion and why formal science is often taught under the faculty of science in universities.

The original intention of scholars to study mathematics would be another reason for the notion. From the very early history of mathematics, until the recent centuries, mathematicians believed that the physical world is constructed according to mathematics. For example, Pythagoras believed that everything was related to mathematics and that numbers were the ultimate reality; he once said that "number is the ruler of forms and ideas and the cause of gods and demons." In later history, Isaac Newton also thought that God used mathematics to design the world. Therefore, the study of mathematics is identical to the study of nature. So it is not surprising that mathematics and other related formal science would be regarded as branches of natural science.

However, many scholars oppose including formal science as a branch of science. They admit that formal science is a very powerful tool to natural and social science, but it does not mean formal science is science. Most importantly, they define science as the discipline using scientific method which bases on observation and empirical study. As knowledge in formal science is a priori and always constructed by rules of deduction from axioms and definition without any empirical study, they refuse to classify formal science as a branch of science.

ee also

* Abstraction
** Hypostatic abstraction
** Prescisive abstraction
* Abstract structure
* Abstraction in mathematics
* Abstraction in computer science
* Formal
* Formal language
* Formal method
* Formal system
* Systems science


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
* 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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