Formal Sciences


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A formal science is a branch of knowledge that is concerned with formal systems, for instance, logic, mathematics, systems theory and the theoretical aspects of computer science, information theory, microeconomics, decision theory, statistics, and linguistics.




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


The formal sciences can sometimes be applied to 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 science and natural science is that formal science starts from theoretical ideas and 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 an empirical part of reality. One can never learn anything empirical from studying formal sciences alone. One can never prove anything empirical 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.



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