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A '''formal science''' is the academic study that is predominantly concerned with abstract [[formal systems]], for instance, [[logic]], [[mathematics]], and the theoretical branches of [[theoretical computer science|computer science]], [[information theory]], and [[statistics]].  

A '''formal science''' is the academic study that is predominantly concerned with abstract [[formal systems]], for instance, [[logic]], [[mathematics]], and the theoretical branches of [[computer science]], [[information theory]], and [[statistics]].

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". 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 changing definition of the word 'science' maybe primarily induces such a confusion. In the original Latin ''Regina Scientiarum'', as well as in [[German language|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 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 notion that formal science is also 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.

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 a posteriori (philosophy)|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.

==History==

==History==

The study of formal science began much earlier than natural science and the invention of [[scientific method]], with the most ancient mathematical texts available dates back to 1500BC-500 BC ([[ancient India]]), 1300-1200 BC ([[ancient Egypt]]), and 1800 BC ([[Mesopotamia]]). From then on different cultures such as the [[History of India|Indian]], [[Greeks|Greek]], [[Islamic]] made major contributions to mathematics.

The study of formal science began much earlier than natural science and the invention of [[scientific method]], with the most ancient mathematical texts available dates back to 1500BC-500 BC ([[ancient India]]), 1300-1200 BC ([[ancient Egypt]]), and 1800 BC ([[Mesopotamia]]). From then on different cultures such as the [[History of India|Indian]], [[Greeks|Greek]], [[Islamic]] made major contributions to mathematics.

Study on computer science and information theory did not begin until middle 20th century.

Study on computer science and information theory did not begin until middle 20th century.

==See also==

==See also==

* [[Abstraction]]

* [[Abstraction]]

* [[Formal]]  

* [[Formal]]  

==External links==

==External links==

 

* [https://www.math.uni-bonn.de/people/fotfs/ Interdisciplinary conferences — ''Foundations of the Formal Sciences''][https://en.wikipedia.org/w/index.php?title=Formal_science&action=edit]

* [http://www.math.uni-bonn.de/people/fotfs/ Interdisciplinary conferences — ''Foundations of the Formal Sciences''][http://en.wikipedia.org/w/index.php?title=Formal_science&action=edit]

[[Category: General Reference]]

[[Category: General Reference]]

[[Category: Formal Sciences]]

[[Category: Formal Sciences]]