Information about Formal Science
A formal science is an 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.
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 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.
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 in 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 while the tradition from other cultures do not survive into the modern era.
As other disciplines of formal science rely heavily on mathematics, they did not exist until mathematics has 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.
Study on computer science and information theory did not begin until middle 20th century.
Overview
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".[1] 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 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.
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 Indian, Greek, Islamic made major contributions to mathematics.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 in 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 while the tradition from other cultures do not survive into the modern era.
As other disciplines of formal science rely heavily on mathematics, they did not exist until mathematics has 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.
Study on computer science and information theory did not begin until middle 20th century.
See also
- Abstraction
- Hypostatic abstraction
- Prescisive abstraction
- Abstract structure
- Abstraction in mathematics
- Abstraction in computer science
- Formal
- Formal language
- Formal method
- Formal system
References
Further reading
- Mario Bunge (1985), Philosophy of Science and Technology, Springer.
- Mario Augusto 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.
- Stephen Leacock (1906), Elements of Political Science, Houghton, Mifflin Co, 417 pp.
- Bernt P. Stigum (1990), Toward a Formal Science of Economics, MIT Press
- William L. Twining (1997), Law in Context: Enlarging a Discipline, 365 pp.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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Theoretical computer science is the collection of topics of computer science that focuses on the more abstract, logical and mathematical aspects of computing, such as the theory of computation, analysis of algorithms and semantics of programming languages.
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Information theory is a branch of applied mathematics and engineering involving the quantification of information to find fundamental limits on compressing and reliably communicating data.
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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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natural science refers to a rational approach to the study of the universe, which is understood as obeying rules or laws of natural origin. The term natural science
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The social sciences are a group of academic disciplines that study human aspects of the world. They diverge from the arts and humanities in that the social sciences tend to emphasize the use of the scientific method in the study of humanity, including quantitative and qualitative
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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Johann Carl Friedrich Gauss
Carl Friedrich Gauss, painted by Christian Albrecht Jensen
Born 30 March 1777
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Carl Friedrich Gauss, painted by Christian Albrecht Jensen
Born 30 March 1777
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Imperial College London (officially Imperial College of Science, Technology and Medicine) is a British university in London. Imperial's teaching and research have traditionally focused on science, engineering and medicine, although more recently its faculties in these areas
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University of Tokyo (東京大学 Tōkyō daigaku
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An academic department is a division of a university or school faculty devoted to a particular academic discipline. This article covers United States usage at the university level.
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The organization of faculties into departments is not standard, but most U.S.
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A faculty is a division within a university. The medieval University of Paris, which served as a model for most of the later medieval universities in Europe, had four faculties: the Faculties of Theology, Law, Medicine, and finally the Faculty of Arts, which every student had to
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German language (Deutsch, ] ) is a West Germanic language and one of the world's major languages.
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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history of mathematics is primarily an investigation into the origin of new discoveries in mathematics, to a lesser extent an investigation into the standard mathematical methods and notation of the past.
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mathematician is a person whose primary area of study and research is the field of mathematics.
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Problems in mathematics
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Pythagoras of Samos (Greek: Πυθαγόρας; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1]
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Sir Isaac Newton
Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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God
General approaches
Agnosticism Atheism
Deism Dystheism
Henotheism Ignosticism
Monism Monotheism
Natural theology Nontheism
Pandeism Panentheism
Pantheism Polytheism
Theism Theology
Transtheism
Specific conceptions
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General approaches
Agnosticism Atheism
Deism Dystheism
Henotheism Ignosticism
Monism Monotheism
Natural theology Nontheism
Pandeism Panentheism
Pantheism Polytheism
Theism Theology
Transtheism
Specific conceptions
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Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning,[1]
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A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. Empirical data is data that is produced by experiment or observation.
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Knowledge is defined (Oxford English Dictionary) variously as (i) expertise, and skills acquired by a person through experience or education; the theoretical or practical understanding of a subject, (ii) what is known in a particular field or in total; facts and information or
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a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori
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axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation.
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A definition is a statement of the meaning of a term, word or phrase. The term to be defined is known as the definiendum (Latin: that which is to be defined).
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Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning,[1]
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